Assignment

2.1 Demand  39

Normal and Inferior Goods and Services Returning to the jeans example, you have seen that an increase in income increases the demand for jeans and shifts the demand curve to the right. For some other goods and services, an increase in income decreases the demand and shifts the demand curve to the left. For example, an increase in income decreases the demand for intercity bus travel because people with more income can afford to rent or buy a car or even fly to their destinations.

These two different relationships between income and demand mean that goods and services fall into two categories: normal and inferior. When an increase in income increases the demand for a good or service and a decrease in income decreases that demand, the good or service is a normal good or service. As described earlier, a pair of jeans is an example of a normal good. So, too, is dining at Red Lobster. The majority of goods and services are normal. In contrast, when an increase in income decreases the demand for a good or service and a decrease in income increases that demand, the good or service is an inferior good or service. Used clothing and boxed mac and cheese are examples of inferior goods. It is important to note that the term inferior does not imply low quality. It refers only to the relation- ship between income and demand. In fact, depending on the income range, some goods can be both normal and inferior. For example, in lower income ranges, ground beef is a normal good—when the incomes of lower-income consumers rise, they demand more ground beef and fewer hot dogs or noodles. In higher income ranges, however, ground beef is an inferior good—when the incomes of middle-income con- sumers rise, they demand less ground beef and more roasts and steaks.

Price of Related Goods and Services: Substitutes and Complements Another factor that changes the demand and shifts the demand curve is the rela- tionship some goods and services have with other products. These relationships are of two types: substitutes and complements. Substitutes are alternative goods and services—a consumer buys one or the other. For example, if you are looking to buy a smartphone, you might choose an Apple iPhone or a Samsung Galaxy. Complements are separate goods and services that a consumer buys to use together—a consumer buys one and the other. For example, when purchased in a grocery store, hot dogs and hot dog buns are complements.

If the price of a substitute rises, the demand for the good in question increases, shifting its demand curve to the right. The reverse is also true: If the price of a substi- tute falls, the demand for the good in question decreases, and its demand curve shifts to the left. For example, chicken and beef are substitutes. You might have one or the other for dinner. Consider the demand for chicken. If the price of beef rises, consumers substitute chicken, increasing the demand for chicken and shifting the demand curve for chicken to the right. If the price of beef falls, consumers will buy more beef and less chicken, so the demand for chicken decreases, shifting its demand curve to the left. Keep in mind that in both cases the change in the price of beef creates a movement along the demand curve for beef but shifts the demand curve for the substitute, chicken.

If the price of a complement rises, the demand for the good in question decreases, and its demand curve shifts to the left. Of course, the reverse also is true: If the price of a complement falls, the demand for the good in question increases, and its demand curve shifts to the right. Think of the demand for bicycle helmets. Bicycles and bicycle helmets are complements. If the price of a bicycle rises, fewer people buy bicycles, decreasing the demand for bicycle helmets and shifting the demand curve for bicycle helmets to the left. Alternatively, if the price of a bicycle falls, then the demand for bicycle helmets increases, and the demand curve for bicycle helmets shifts to the right. Once again, remember that the change in the price of a bicycle creates a movement along the demand curve for bicycles but shifts the demand curve for the complement, bicycle helmets.

Normal good or service A good or service for which an increase in income increases demand and a decrease in income decreases demand.

Inferior good or service A good or service for which an increase in income decreases demand and a decrease in income increases demand.

Substitutes Alternative goods and services; a consumer buys one or the other.

Complements Separate goods and services purchased for use together; a consumer buys one and the other.

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40  CHAPTER 2 Demand and Supply

Consumers’ Preferences and Advertising Economists refer to people’s likes or dislikes for products as their preferences. Changes in preferences change demand. If preferences change and consumers like a good more than before, then demand increases, and the demand curve shifts to the right. Conversely, if preferences change and consumers like a good less, then demand decreases, and the demand curve shifts to the left.

What factors can lead to changes in preferences? The most relevant for managers is advertising. The goal of most advertising campaigns is to increase people’s prefer- ences for a product, thereby increasing demand. Watch an evening of network televi- sion or spend a few hours on the Internet and you will see almost too many advertisements to count. Not only individual firms but also some industries advertise. The National Milk Processor Education Program’s slogan “Got milk?” tried to change consumers’ preferences in favor of drinking milk to increase the demand for milk. (Chapter 13 examines such industry-wide promotions in more detail.) Of course, not all advertising tries to increase demand. For example, many states use funds from the 1998 Tobacco Master Settlement Agreement to run advertisements designed to dis- courage smoking and decrease the demand for cigarettes.4 Nonprofits also advertise, though often to promote donations rather than increase demand for a product.

New information can lead to changes in preferences. Sometimes this informa- tion might come from advertisements, as when Apple advertised its then-innovative new product, the iPad. Other times the information might come from news reports, as when they spread the information over the past couple of decades that salmon contains oils that are heart healthy. Regardless of the source, as the information becomes more widespread, consumers’ preferences may change, thereby changing the demand for the product and shifting its demand curve.

Financial Market Conditions The ability of individuals and firms to obtain loans in financial markets, such as the mar- ket for bank loans or the bond market, affects the demand for some goods. Most people need to obtain a loan to purchase big ticket items such as cars and homes. Similarly, most firms need to borrow to help finance their purchase of capital goods, as when Brinker International Restaurants purchased new kitchens for all of its Chili’s restau- rants. Financial market conditions affect the demand for these types of products. With good financial market conditions—when the interest rates on loans are low and finan- cial institutions’ lending standards are easy to meet—the demand for the goods pur- chased with the help of these loans is high. With bad financial market conditions—when it is difficult to obtain even a high-interest-rate loan—the demand for these goods is low.

Of course, financial market conditions have little to no effect on the demand for many goods. No one thinks about taking out a loan to buy a slice of pizza. But for the expensive goods that typically require a loan, financial market conditions can play a crucial role in demand. In the recession of 2007–2009, home mortgage loans became significantly more difficult to obtain. The demand for homes decreased so much that the number of homes purchased was about 25 percent lower in 2008 than in 2005.

Expected Future Price Changes in the expected future price of a good or service can change its current demand. For example, managers of refineries demand oil to refine into gasoline, fuel oil, and other products. If they think that turmoil in the Middle East will lead to higher crude oil

4 The Tobacco Master Settlement Agreement is a legal settlement agreement between the four major tobacco companies and 46 states that sued the companies to recover tobacco-related health-care costs.

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2.1 Demand  41

prices in the future, the current demand for crude oil increases as these demanders try to buy before the price rises. Conversely, if the refinery managers expect the future price of crude oil to fall, the current demand for crude oil decreases as these demanders delay buying crude oil until they can take advantage of the lower price. Of course, this factor does not affect the demand for all goods and services equally. It is stronger for durable goods, such as oil, than for nondurable goods, such as fresh fish, because demanders can more easily accelerate or delay their purchases of durable goods.

Number of Demanders A change in the number of demanders—the number of consumers or companies purchasing a good or service—changes demand and shifts the demand curve. An increase in the number of demanders increases demand and shifts the demand curve to the right. A decrease in the number of demanders decreases demand and shifts the demand curve to the left.

Demographic changes can lead to changes in the number of demanders. For example, older people use more pharmaceutical drugs than do younger people. As the average age in the population increases, the demand for pharmaceutical drugs increases, and the demand curve for pharmaceutical drugs shifts to the right.

Seasonal changes can also trigger changes in the number of demanders. The approach of fall and winter decreases the number of people who want to barbecue outdoors. So at the end of summer, the demand for barbecue grills decreases, and the demand curve for barbecue grills shifts to the left.

Changes in Demand: Demand Function The basic demand function you saw earlier in the chapter assumed that demand depends only on the price. Including the other factors just presented makes the demand function more complex and more realistic. For now, let’s focus on including just two additional factors, but know that you can incorporate other factors using a

Suppose that you are a manager at General Motors. The Cadillac Escalade is a full-size, luxury SUV produced by your firm that gets fewer miles per gallon of gasoline than other cars. During the recession of 2007–2009, people’s incomes plunged, it became very difficult to obtain loans, and the price of gasoline soared. What was the effect of these changes on the demand for the Escalade?

Answer Three factors changed: (1) Income fell, (2) loans became difficult to obtain, and (3) the price of gasoline soared. Start by looking at each effect separately. The Escalade is a normal good, so the fall in income decreased the demand for Escalades. The Escalade is also an expensive car, so the difficulty in obtaining loans decreased the demand. Finally, gasoline and automobiles are complements, so the higher price of gasoline decreased the demand for the Escalade. Individu- ally, each factor decreased the demand for Escalades, so combining them means that the demand for Escalades definitely decreased.

DECISION SNAPSHOT Demand for the Cadillac Escalade

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42  CHAPTER 2 Demand and Supply

similar process. Assume that the demand for jeans depends on their price, on the price of denim skirts (a substitute good), and on consumers’ average income. The equation for this more elaborate demand function is

Qd = f1P, PSKIRTS, INCOME2 2.2 where Qd is the quantity demanded, f is the demand function, P is the price of jeans, PSKIRTS is the price of the substitute good, and INCOME is consumers’ average income. The function in Equation 2.2 could literally be almost anything. However, if it is linear, it can be written as

Qd = a - 1b * P2 + 1c * PSKIRTS2 + 1d * INCOME2 2.3 In Equation 2.3, a, b, c, and d are coefficients. The meanings of the coefficients a and b are similar to before. For example, b is the change in the quantity of jeans demanded when the price changes by $1. The value of c is the change in the quantity of jeans demanded when the price of the substitute (denim skirts) changes by $1. Because skirts are a sub- stitute for jeans, there is a positive sign preceding the 1c * PSKIRTS2 term, showing that a $1 rise in the price of a denim skirt increases the demand for jeans. The value of d is the change in the quantity of jeans demanded when average income changes by $1. Because jeans are a normal good, an increase in average income increases the demand for jeans, so the sign preceding the 1d * INCOME2 term is positive.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$120

$140

$20

500 600 700300 400100 200

$40

$60

$80

$100

0

D1 D0

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$120

$140

$20

500 600 700300 400100 200

$40

$60

$80

$100

0

D0 D1

Figure 2.3 Changes in Demand

(a) An Increase in Demand (b) A Decrease in Demand

Demand increases and the demand curve shifts to the right when

• Income increases (for a normal good). • Income decreases (for an inferior good). • The price of a substitute rises. • The price of a complement falls. • Preferences change toward the good. • Financial market conditions are good. • The expected future price rises. • The number of demanders increases.

Demand decreases and the demand curve shifts to the left when

• Income decreases (for a normal good). • Income increases (for an inferior good). • The price of a substitute falls. • The price of a complement rises. • Preferences change away from the good. • Financial market conditions are bad. • The expected future price falls. • The number of demanders decreases.

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2.1 Demand  43

Demand for Lobster Dinners

You are a manager at Lobster Brisk, a seafood restaurant chain similar to Red Lobster. Your supervisor asks you to determine the quantity of lobster to buy for the chain’s Brisk Feast, an annual month-long promotion when Lobster Brisk features a variety of lobster dinners, including its signature lobster bisque soup. Your research department reports that the demand for lobster dinners is

Qd = 1,300,000 dinners - 1100,000 dinners * P2 + 132 dinners * INCOME2 where Qd is the quantity of lobster dinners demanded per week, P is the price of a lob- ster dinner, and INCOME is the average family income of Lobster Brisk customers.

a. If the average family income of Lobster Brisk customers is $40,000 and you set the price of a lobster dinner at $18 per dinner, what is the quantity of dinners demanded?

b. If you raise the price of a lobster dinner from $18 to $20 and the average family income remains equal to $40,000, what is the change in the quantity of dinners demanded? Is there a movement along the demand curve or a shift of the curve?

c. With the price of a lobster dinner set at $20, what is the change in the quantity of dinners demanded if your advertising brings in families with an average income of $42,000 rather than $40,000? Is there a movement along the demand curve, or does the curve shift?

Answer

a. The demand function shows that the quantity of lobster dinners demanded equals 1,300,000 dinners - 1100,000 dinners * $182 + 132 dinners * $40,0002 = 780,000 dinners.

b. The coefficient for the price variable, 100,000 dinners per dollar, shows that a $2 increase in the price of a lobster dinner decreases the quantity demanded by 100,000 dinners * 2, or 200,000 dinners per week. The increase in price leads to an upward movement along the demand curve.

c. The coefficient for the income variable, 32 dinners per dollar, shows that a $2,000 increase in the customers’ average income increases the quantity demanded by 32 dinners * $2,000, or 64,000 dinners per week. The increase in income leads to a rightward shift of the demand curve equal to 64,000 dinners.

SOLVED PROBLEM

The coefficients c and d affect the amount by which the demand curve shifts when the price of denim skirts and average income change, respectively. For example, if the coefficient d is equal to 200,000 pairs of jeans per dollar of income, then a $1,000 increase in average income shifts the demand curve to the right by 200,000 pairs * 1,000, or 200 million pairs, precisely the shift illustrated in Figure 2.2. Of course, in reality, no one simply hands you the values for the coefficients; analysts must estimate the values, often using regression analysis, which is explained in Chapter 3.

Figure 2.3 summarizes how the six factors discussed in this section—consumers’ income, the price of related goods and services, consumers’ preferences and adver- tising, financial market conditions, the expected future price of the product, and the number of demanders—change the demand and shift the demand curve. The fol- lowing section explores the other side of the market—supply.

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44  CHAPTER 2 Demand and Supply

2.2 Supply Learning Objective 2.2 Describe the factors that affect the supply of goods and services.

In markets for goods and services, firms are the suppliers. The primary factor influ- encing supply decisions is profit. Chapter 5 provides more detail about the effect of the pursuit of profit on firms’ behavior. In this chapter, assume that the larger the profit from producing a good or service, the more of the good or service the firms will produce. Conversely, the smaller the profit from producing a good or service, the less of the good or service the firms will produce.

Law of Supply The price of a good or service is a very important factor affecting firms’ profits. If the price rises and nothing else changes, the profit from producing the good or service will be larger, so firms will produce more in a given time period. Alternatively, the lower the price, the smaller the profit and the less firms will produce. The law of supply summarizes these insights: All other things remaining the same, the higher the price of the good or service, the larger the quantity supplied; the lower the price of the good or service, the smaller the quantity supplied.

5 These results are analogous to what you saw for the demand curve: A change in the price of the prod- uct creates a movement along the demand curve, called a change in the quantity demanded.

• All other things remaining the same, the higher the price of the good or service, the larger the quantity supplied; the lower the price of the good or service, the smaller the quantity supplied.

LAW OF SUPPLY

Supply Curve A supply curve illustrates the relationship between the price of a good or service and the quantity supplied.

Figure 2.4 illustrates a supply curve for jeans that shows the quantity of jeans suppliers will produce at different prices. At a price of $60 per pair, point A on the supply curve shows that the quantity of jeans produced is 300 million pairs per year. If the price rises to $80 per pair, point B on the supply curve shows that the quantity of jeans supplied increases to 400 million pairs per year. The supply curve in Figure 2.4 is linear, but like demand curves, supply curves are not necessarily straight lines. What is crucial is the positive slope of the supply curve, which reflects the law of supply: When the price rises, the quantity supplied increases, and when the price falls, the quantity supplied decreases.

A change in the price of the product causes a movement along the supply curve, which is called a change in the quantity supplied.5 If the price rises, the quantity supplied increases, leading to the movement upward along the supply curve illustrated by the arrow in Figure 2.4 between points A and B. If the price falls, the quantity supplied decreases, resulting in a movement downward along the supply curve.

Supply curve A curve illustrating the relationship between the price of a good or service and the quantity supplied.

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2.2 Supply  45

The Supply Function Supply can be represented using an algebraic function called the supply function just as demand was represented using the demand function. Suppose that the only factor affecting supply is the price of the product. In this case, the general supply function is

Qs = g1P2 2.4 where Qs is the quantity supplied, g is the supply function, and P is the price of the product. Equation 2.4 shows a general function. If the supply curve is linear, the sup- ply function is

Qs = r + 1s * P2 2.5 where Qs is the quantity supplied, P is the price of the product, and r and s are coef- ficients. The value of r is the quantity supplied if the price is $0, and the value of s is the change in the quantity supplied when the price changes by $1. The positive sign in the equation before the 1s * P2 term reflects the law of supply: An increase in the price increases the quantity supplied.

You can use Equation 2.5 to determine the coefficients of the supply function for the linear supply curve illustrated in Figure 2.4. As Figure 2.4 shows, when the price is $0, the quantity of jeans supplied is 0, so r equals 0. The value of s is the change in the quantity of jeans supplied when the price changes by $1, so s equals 5 million pairs of jeans per dollar.6 This value for s means that if the price of jeans rises by $1, the quan- tity supplied increases by 5 million pairs. Therefore, the supply function for the supply curve shown in Figure 2.4 is

Qs = 0 + 15 million * P2

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

B

A

Figure 2.4 A Supply Curve

The supply curve for jeans, S, shows the quantity supplied at all different prices. The slope of the supply curve reflects the law of supply: As the price of jeans rises, the quantity supplied increases. When the price rises from $60 to $80 per pair, the arrow shows there is a movement upward along the supply curve from point A to point B, and the quantity of jeans supplied increases from 300 million to 400 million pairs per year.

6 As with the value of the coefficient b on a linear demand curve, the value of s is the same at every point on a linear supply curve. Between points A and B on the supply curve in Figure 2.4, as the price of jeans rises by $20 (from $60 to $80), the quantity of jeans supplied increases by 100 million pairs (from 300 mil- lion to 400 million pairs). So between these two points, s equals (100 million pairs)/($20 per pair), or 5 million pairs per dollar.

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46  CHAPTER 2 Demand and Supply

As you may already have guessed, price is not the only thing that affects the supply of a product. The next section examines the other factors that affect supply and the supply curve.

Factors That Change Supply A change in price creates a movement along the supply curve, but other factors that affect supply shift the supply curve. These factors include cost, the price of related goods and services, technology, the state of nature, the expected future price of the product, and the number of suppliers. Of these six factors, the first five reflect firms’ profit-seeking behavior, while the last directly affects the amount of the product available at each price.

Cost One factor that affects the supply of all goods and services is the cost of producing them. Cost and price differ: Cost is what the producers pay to produce the product, and price is the amount the producers receive when they sell the product. When the cost of producing a good or service rises and nothing else changes, the profit from producing that good or service decreases. Firms respond to the fall in profit by decreasing their production. For example, suppose that the cost of producing jeans rises because of an increase in the price of the denim used in their manufacture. For any given price, this increase in cost decreases the profit from jeans, so firms respond by decreasing their production. In Figure 2.5, supply curve S0 is the initial supply curve before the change in cost, and supply curve S1 is the supply curve after the cost has increased. At the price of $80 per pair of jeans, before the rise in cost, firms supply 400 million pairs of jeans per year, point B on the initial supply curve, S0. After the rise in cost, the quantity supplied at the price of $80 decreases to 200 million pairs of jeans per year, point C on the new supply curve, S1. As Figure 2.5 shows, the quantity supplied decreases at not only the price of $80 per pair of jeans but also at all prices, so that the entire supply curve shifts to the left. The increase in cost leads to a decrease in supply.

Similarly, if the cost of production falls, the profit from producing the good or service rises. Firms respond to the higher profit by increasing their production of the good or service, so the supply increases and the supply curve shifts to the right.

Shift of the Supply Curve Versus a Movement Along the Supply Curve As was the case with the demand curve, the effect on the supply curve of a change in the price of the product is significantly different from the effect of a change in any other relevant factor, such as cost. Figure 2.4 illustrates that a change in price results in a movement along the supply curve, while Figure 2.5 shows that a change in cost results in a shift of the supply curve. The change in price illustrated in Figure 2.4 leads to a change in the quantity supplied, and the change in cost illustrated in Figure 2.5 leads to a change in supply. The only factor that creates a movement along the supply curve (and a change in the quantity supplied) is the product’s price. Changes in any of the other relevant factors shift the supply curve (and change the supply).

Price of Related Goods: Substitutes in Production and Complements in Production Changes in the prices of related goods in production change the supply of a product and shift its supply curve. There are two possible relationships between goods. Some

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2.2 Supply  47

products, called substitutes in production, are alternatives in production—a firm can produce one or the other. For example, bakeries such as the Great Harvest Bread Company can use their ovens to produce either white bread or wheat bread. For Great Harvest Bread, these two goods are substitutes in production. Other products, called complements in production, are produced simultaneously—a firm produces one and the other. For example, when refineries such as those operated by Shell Oil Company refine a barrel of oil, the refining process simultaneously produces gaso- line, kerosene, and diesel fuel. For Shell Oil, gasoline, kerosene, and diesel fuel are complements in production.7

For both substitutes in production and complements in production, the price of the second product affects the supply of the first.

• Substitutes in production. If the price of a substitute in production rises, firms switch production toward the substitute and away from the first product because the substitute has become more profitable. The supply of the first product decreases, and its supply curve shifts to the left. For example, if the price of wheat bread rises, how does this change affect the supply of white bread? Great Harvest Bread’s managers and managers of all bakeries use their ovens to pro- duce more wheat bread and less white bread, decreasing the supply of white bread and shifting the supply curve of white bread to the left. The reverse is also true: If the price of a substitute in production falls, the supply of the first good increases, and its supply curve shifts to the right.

• Complements in production. If the price of a complement in production rises, firms produce more of the complement because it has become more profitable.

Substitutes in production Products that are alternatives in production; a firm can produce one or the other.

Complements in production Products that are produced simultaneously; a firm produces one and the other.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S0

S1

BC

The increase in cost shifts the supply curve to the left.

Figure 2.5 A Shift in the Supply Curve

The figure shows a decrease in the supply of jeans. The supply curve shifts to the left, from S0 to S1. A leftward shift of the supply curve represents a decrease in supply because the quantity of jeans supplied decreases at all prices.

7 Traditionally, economists call products that are substitutes or complements for consumers simply substi- tutes or complements but refer to goods that are substitutes or complements for firms as substitutes in produc- tion or complements in production.

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48  CHAPTER 2 Demand and Supply

When firms produce more of the complement, they also automatically produce more of the first product. The supply of the first product increases, and its sup- ply curve shifts to the right. For example, if the price of gasoline rises, how does this change affect the supply of diesel fuel? The managers of Shell Oil’s refiner- ies and the managers of all refineries produce more gasoline by refining more oil. Because more oil is refined, the production of diesel fuel automatically increases. The supply of diesel fuel increases, and the supply curve of diesel fuel shifts to the right. Of course, if the price of a complement in production falls, the supply of the first product also decreases, and its supply curve shifts to the left.

Technology Changes in technology affect the supply in many markets. Economists take a broad view of technology by thinking of it as information that provides a recipe (or instruc- tions) describing how to combine various inputs in order to produce the output. It is common to view technology in terms of technological advances, the discovery of improved methods of production of existing goods or services or even methods of production of entirely new products or services. The automobile industry provides examples of both types of technological advances:

• The installation of industrial robots to produce cars illustrates a new and improved method of production.

• The introduction of hybrids or driverless automobiles illustrates the production of new products.

In both cases, a technological advance increases the supply of a good or service and shifts the supply curve to the right.

State of Nature Although you might first think that the state of nature affects only the supply of agricultural products, the concept is actually much broader. As a factor affecting supply, the state of nature includes both the wide-scale flooding in China’s Yang- tze River basin in the summer of 2016 that destroyed nearly 4 million acres of crops and caused a total of $28 billion in damages, and the earthquake and result- ing tsunami that devastated northern Japan in March 2011, severely damaging many of Japan’s automobile factories. Floods, tsunamis, earthquakes, hurricanes, and bad growing seasons are all examples of bad states of nature. Because these events either increase the cost of producing the affected goods and services or directly reduce the amount firms can produce, they decrease the supply of affected goods and services and shift their supply curves to the left. Conversely, a good state of nature—no flooding, an absence of tsunamis, fewer hurricanes than nor- mal, a good growing season—increases the supply of the affected products and shifts their supply curves to the right.

Expected Future Price Changes in a good’s expected future price can change its current supply. For exam- ple, Marathon Pipe Line owns six massive underground storage caverns for pro- pane. If the future price of propane is expected to rise, Marathon and other propane suppliers will delay selling propane today in order to take advantage of the higher price (and larger profit) expected in the future. Consequently, the current supply of

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propane decreases, and the supply curve shifts to the left. Conversely, if the future price of propane is expected to fall, the current supply of propane increases as Marathon and the other suppliers rush to sell now before the price and profit fall in the future. Of course, this factor does not affect the supply for all goods and ser- vices equally. Goods that can be stored or that have production processes that can easily be accelerated or delayed will have the strongest reaction to changes in the expected future price.

Number of Suppliers Of the factors that shift the supply curve, only a change in the number of suppli- ers is not motivated by profit. A change in the number of suppliers directly changes the amount of the product available at each price. When more firms enter a market, the number of suppliers increases, which increases the supply and shifts the supply curve to the right. When firms close or otherwise exit a market, the number of suppliers decreases, which decreases the supply and shifts the supply curve to the left.

Changes in Supply: Supply Function The supply function presented in Equation 2.4 assumes that supply relies only on the price of the product. Including other relevant factors from among the six just pre- sented makes the supply function more realistic. For now, this discussion focuses on just two additional factors, but as you will see shortly, you can add any of the others using a similar process. So assume that the supply of jeans depends on their price, the cost of producing each pair, and the number of firms producing jeans. In this case, a general equation for the supply function is

Qs = g1P, COST, NUMBER2 where Qs is quantity of jeans produced, g is the supply function, P is the price of jeans, COST is the cost of producing the jeans, and NUMBER is the number of sup- pliers. You can extend the linear supply function shown in Equation 2.5 to include the effects of the cost and number of firms:

Qs = r + 1s * P2 - 1t * COST2 + 1u * NUMBER2 The coefficients in the linear supply equation are r, s, t, and u. The meanings of the r and s coefficients are the analogous to those in Equation 2.5. For example, the value of s is the change in the quantity of jeans supplied when the price changes by $1. The new coefficients are t and u. The value of t is the Change in the quantity supplied when the cost of producing jeans changes by $1. The nega- tive sign in the equation for the 1t * COST2 term indicates that an increase in cost decreases the supply of jeans. The value of u is the change in the quantity of jeans supplied when the number of firms changes by one. The 1u * NUMBER2 term has a positive sign because an increase in the number of firms leads to an increase in the supply.

These new coefficients determine how much the supply changes and how much the supply curve shifts if there is a change in the cost or number of firms. For example, if the coefficient t is equal to 100 million pairs of jeans per dollar of cost, then a $2 increase in cost changes the supply by -100 million * 2, or -200 million pairs. In this case, the supply curve shifts to the left by 200 million pairs, precisely the shift illustrated in Figure 2.5.

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50  CHAPTER 2 Demand and Supply

Figure 2.6 summarizes the effects that the factors just discussed have on supply and the supply curve. Now that you have learned about the concepts of demand and supply separately, it’s time to discover how they interact to determine the quantity and price of a good or service.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$120

$140

$20

500 600 700300 400100 200

$40

$60

$80

$100

0

S0

S1

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$120

$140

$20

500 600 700300 400100 200

$40

$60

$80

$100

0

S0 S1

Figure 2.6 Changes in Supply

(a) An Increase in Supply (b) A Decrease in Supply Supply increases and the supply curve shifts to the right when

• Cost decreases. • The price of a substitute in production falls. • The price of a complement in production rises. • Technology advances. • The state of nature is good. • The expected future price falls. • The number of suppliers increases.

Supply decreases and the supply curve shifts to the left when:

• Cost increases. • The price of a substitute in production rises. • The price of a complement in production falls. • The state of nature is bad. • The expected future price rises. • The number of suppliers decreases.

The Supply of Gasoline-Powered Cars and the Price of Hybrid Cars

Suppose that the supply function for gasoline-powered cars is

Qs = 7,800,000 cars + 1300 cars * P2 − 1200 cars * P HYBRID2 where Qs is the quantity of gasoline cars supplied, P is the price of a gasoline-powered car, and PHYBRID is the price of a hybrid car. Suppose the price of a hybrid car is $39,000.

a. Are hybrids a complement in production or a substitute in production for gasoline- powered cars?

b. Suppose the price of a gasoline-powered car is $30,000 and the price of a hybrid car rises by $2,000. What is the effect on the supply curve of gasoline-powered cars? Draw a figure showing the initial supply curve and the new supply curve after the increase in the price of the hybrid.

SOLVED PROBLEM

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2.3 Market Equilibrium  51

2.3 Market Equilibrium Learning Objective 2.3 Determine the market equilibrium price and quantity using the demand and supply model.

In competitive markets, the actions of buyers and sellers jointly determine the price and quantity of a given good or service. As you have learned, the demand curve reflects the behavior of buyers, and the supply curve reflects the behavior of sellers. Combining the two curves allows managers to determine the price and quantity of the product.

Equilibrium Price and Equilibrium Quantity Figure 2.7 combines the demand curve, D, shown in Figure 2.1 and the supply curve, S, shown in Figure 2.4. The curves cross at a price of $60 per pair of jeans. This price, called the equilibrium price, is the only price at which the quantity demanded equals the quantity supplied.

If the price does not equal the equilibrium price, it will change so that it does. At any price higher than the equilibrium price, there is a surplus of jeans—sellers offer more jeans for sale than demanders want to buy. For example, at a price of $100 per pair, the supply curve shows that the quantity of jeans supplied is 500 million pairs, but the demand curve shows that the quantity of jeans demanded is only 100 million pairs. At this price, there is a surplus of 400 million pairs (500 million minus 100 mil- lion), resulting in undesired inventories of unsold jeans. The inventories, piling up

Equilibrium price The price at which the quantity demanded equals the quantity supplied.

Price (thousands of dollars per car)

Quantity (millions of gasoline-powered cars per year)

$33

$28

$29

9.69.49.29.08.88.68.4

$30

$31

$32

0

S1

S0

Answer

a. The term showing how the price of a hybrid car affects the supply of gasoline-powered cars, 1200 cars * PHYBRID2, is preceded by a negative sign, so an increase in the price of a hybrid decreases the supply of gasoline-powered cars. A hybrid is a substitute in production for gasoline-powered cars.

b. The $2,000 increase in the price of the hybrid car decreases the supply of gasoline-powered cars by 200 cars * $2,000 = 400,000 cars, so the supply curve of gasoline- powered cars shifts to the left by 400,000 cars. In the figure, the initial supply curve is S0. The increase in the price of a hybrid shifts the supply curve left to S1, a shift equal to 400,000 cars at every price.

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52  CHAPTER 2 Demand and Supply

ever higher, lead the firms’ managers to lower the price. As the price falls, suppliers cut their production plans, so the quantity supplied decreases and the quantity demanded increases. Both of these changes help decrease the surplus, but as long as there is a surplus, the unwanted inventories continue to accumulate, and the price continues to fall. Eventually, the price falls to the equilibrium price. At this price, there is no longer a surplus of jeans: The quantity of jeans supplied equals the quan- tity of jeans demanded: 300 million pairs. Because there is no surplus, the price stops falling once it equals the equilibrium price.

Similarly, at any price lower than the equilibrium price, there is a shortage of jeans—the quantity of jeans offered for sale is less than the quantity demanders want to buy. Suppose that the price is $20 per pair; at this price, the quantity of jeans demanded is 500 million pairs, but the quantity supplied is only 100 million pairs. The shortage is 500 million minus 100 million, or 400 million pairs of jeans. The shortage means that producers cannot keep jeans in inventory; every pair they place on the racks is gone almost immediately. So the managers raise the price of jeans. As the price rises, the quantity demanded decreases, and producers increase their production plans, so the quantity supplied increases. Although both changes reduce the shortage, the price rises as long as a shortage exists. Eventually, the price rises to $60 per pair. At this equilibrium price, there is no longer a shortage of jeans: The quantity of jeans demanded equals the quantity supplied: 300 million pairs. Once the price equals the equilibrium price, it stops rising because the shortage has been eliminated.

Because the only price that can persist and not change is the equilibrium price, it is reasonable to assume that the market price equals the equilibrium price. Now that you know the price, you need to determine the quantity. At the equilibrium price, the quantity demanded equals the quantity supplied. The equilibrium quantity is the quantity bought and sold at the equilibrium price, which equals both the quantity demanded and the quantity supplied. In Figure 2.7, the equilibrium quan- tity is 300 million pairs of jeans per year, the quantity bought and sold at the $60 equilibrium price.

Equilibrium quantity The quantity bought and sold at the equilibrium price.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

D

Equilibrium price: $60 Equilibrium quantity: 300 million

Figure 2.7 Equilibrium Price and Equilibrium Quantity

The intersection of the demand curve, D, and supply curve, S, determines the equilibrium price and equilibrium quantity. As shown, the equilibrium price is $60 per pair of jeans, and the equilibrium quantity is 300 million pairs. At any price higher than the equilibrium price, there is a surplus, which forces the price lower until it falls to the equilibrium price. At any price lower than the equilibrium price, there is a shortage, which forces the price higher until it rises to the equilibrium price. Only at the equilibrium price is there neither a surplus nor a shortage of jeans.

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2.3 Market Equilibrium  53

The equilibrium price and equilibrium quantity are examples of the general con- cept of equilibrium: a situation in which no automatic forces lead to change. Once at the equilibrium, the situation will persist until some factor changes. You will explore the idea of equilibrium further in future chapters, such as Chapters 5, 6, 7, and 8, when you learn how firms determine the price to charge and the quantity to produce.

Demand and Supply Functions: Equilibrium In Figure 2.7, the equilibrium price is $60 per pair of jeans, and the equilibrium quantity is 300 million pairs of jeans. You can use the demand function that corre- sponds to the demand curve in Figure 2.7, Qd = 600 million - 15 million * P2, and the supply function that corresponds to the supply curve, Qs = 5 million * P, to check that you get the same equilibrium price and quantity algebraically that you did graphically. At the equilibrium price, the quantity demanded, Qd, equals the quantity supplied, Qs, or Qd = Qs. Equating the demand function and the supply function gives

600 million - 15 million * P2 = 5 million * P To solve for the equilibrium price, first add 15 million * P2 to both sides:

600 million = 15 million * P2 + 15 million * P2 Next, add the terms on the right side of the equality:

600 million = 10 million * P

Finally, divide by 10 million to solve for the equilibrium price:

P = 600 million 10 million

= $60

precisely the same equilibrium price shown in Figure 2.7. Using the $60 equilibrium price in either the demand or the supply function yields the equilibrium quantity. For example, using the equilibrium price of $60 per pair of jeans in the supply function shows that Q = 5 million * 60, or 300 million pairs per year, which also corre- sponds to the equilibrium quantity shown in Figure 2.7.

More generally, if the demand function is linear and depends only on the price of the product, it can be written as Qd = a - 1b * P2. If the supply function is also linear and also depends only on the price, it can be written as Qs = r + 1s * P2. Then equating the demand function and the supply function gives

a - 1b * P2 = r + 1s * P2 This equation can be solved for the equilibrium price as

P = a - r s + b

Use this value for the price in either the demand or the supply function and some algebra to solve for the equilibrium quantity:

Q = 1a * s2 + 1b * r2

s + b

Equilibrium A situation in which no automatic forces lead to change; once at the equilibrium, the situation will persist until some factor changes.

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54  CHAPTER 2 Demand and Supply

Now that you have learned how to determine the equilibrium price and quan- tity in a competitive market, you are ready for a related topic: discovering why econ- omists have a strong preference for competitive markets and, as a result, use them as the standard of comparison for all other types of markets.

Equilibrium Price and Quantity of Plush Toys

You are a manager at Content Colleague, a company similar to Happy Worker, a Canadian company that manufactures vinyl, plush, and resin toys and collectibles. Your research specialist has given you demand and supply functions for one of your product lines, plush toys. The demand function for plush toys is Qd = 30 million - 12 million * P2. The supply function for plush toys is Qs = 3 million * P . Your supervisor asks you to determine the equilibrium price and equilibrium quantity of plush toys.

Answer To determine the equilibrium price and quantity, you need to set the demand function equal to the supply function:

30 million - 12 million * P2 = 3 million * P Now solve for the equilibrium price, P :

30 million = 13 million * P2 + 12 million * P2 30 million = 5 million * P

P = 130 million2 >15 million2 = $6 per stuffed toy animal

Use this equilibrium price in either the demand or the supply function to determine the equilibrium quantity. Using it in the supply function gives Q = 3 million * $6 = 18 million plush toys.

SOLVED PROBLEM

2.4 Competition and Society Learning Objective 2.4 Explain why perfectly competitive markets are socially optimal.

Society has a limited amount of resources, such as labor and capital. This limitation makes it impossible to produce unlimited amounts of a good or service, so it is important for society to obtain the greatest benefit from its resources. This section describes how competitive markets foster the optimal allocation of society’s scarce resources.

Total Surplus Figure 2.8 shows the demand and supply curves for jeans. You can use these to determine what quantity of jeans is the socially best quantity to produce.

As we described earlier, the market demand curve, D, shows the maximum price consumers are willing and able to pay for any particular pair of jeans. For example, point A shows that some consumer is willing to pay a maximum price of $100

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2.4 Competition and Society  55

for the 100 millionth pair. The maximum price the consumer will pay for a pair of jeans equals the consumer’s marginal benefit from that pair, so the consumer’s marginal benefit from this pair is $100. Why is the maximum price equal to the marginal benefit?

• If the marginal benefit exceeded $100, the consumer would be willing to pay more than $100. But the consumer is not willing to pay more than $100.

• If the marginal benefit was less than $100, the consumer would not be willing to pay $100. But the consumer is willing to pay $100.

Since the consumer’s marginal benefit from the pair of jeans cannot be greater than $100 nor can it be less than $100, the marginal benefit must be equal to $100. Because the consumer of this pair of jeans is the recipient of the benefit and is a member of society, the marginal benefit to society is equal to the consumer’s marginal benefit. So, society’s marginal benefit from the 100 millionth pair of jeans is $100.

The producer’s marginal cost of producing any particular pair of jeans can be determined from the supply curve. For example, in Figure 2.8, point B on the supply curve shows that the minimum price some firm is willing to accept to produce the 100 millionth pair of jeans is $20. The minimum price equals the producer’s mar- ginal cost of producing this pair. Why does the minimum price equal the marginal cost of producing the pair of jeans?

• If the marginal cost exceeded $20, the producer would not be willing to accept $20 for the jeans because that price would inflict a loss on the producer. But the producer is willing to accept $20.

• If the marginal cost was less than $20, then the producer would be willing (but not eager!) to accept a lower price because at a lower price the producer still would not incur a loss. But the producer is not willing to accept less than $20.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

A

B D

Figure 2.8 Marginal Benefit and Marginal Cost

The market demand curve, D, shows the highest price a consumer is willing to pay for any particular pair of jeans. This amount equals the marginal benefit to the consumer of that particular pair. Point A shows that the marginal benefit of the 100 millionth pair is $100. The supply curve, S, shows the lowest price a supplier is willing to accept for any pair of jeans. This amount equals the marginal cost of that particular pair of jeans. Point B shows that the marginal cost of the 100 millionth pair is $20. For this pair of jeans, society gains a surplus of marginal benefit over marginal cost of $80. For all of the jeans up to 300 million pairs, society enjoys a surplus of marginal benefit over marginal cost.

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56  CHAPTER 2 Demand and Supply

Since the producer’s marginal cost of producing the pair of jeans cannot be more than $20 nor can it be less than $20, the marginal cost must be equal to $20. Because the producer pays the marginal cost, the marginal cost to society is equal to the pro- ducer’s marginal cost. In other words, society’s marginal cost of the 100 millionth pair of jeans is $20.

The marginal benefit to society ($100) is greater than the marginal cost ($20). Therefore, producing and consuming this pair of jeans gives society a surplus of marginal benefit over marginal cost of $80. In Figure 2.8, the surplus is equal to the length of the double-headed arrow. The figure also shows that all jeans up to the 300 millionth pair (the equilibrium quantity) have a surplus of marginal benefit over marginal cost. If you apply the marginal analysis rule (produce each unit for which the marginal benefit exceeds the marginal cost), you will see that each of the 300 million pairs of jeans should be produced. The total surplus of benefit over cost to society from production of the 300 million pairs is the sum of the surpluses of all the pairs of jeans produced. When all 300 million surpluses are added, their sum is equal to the area of the green triangle in Figure 2.9.

The quantity of output that yields the largest total surplus for society is called the efficient quantity. In a competitive market, the equilibrium quantity equals the efficient quantity,8 so in Figure 2.9 the efficient quantity is 300 million pairs of jeans.

Efficient quantity The quantity of output that yields the largest total surplus of marginal benefit over marginal cost for society.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

D

Total surplus

Figure 2.9 Total Surplus

When the equilibrium quantity (300 million pairs of jeans) is produced, the total surplus of benefit over cost to society is equal to the area of the green triangle. The quantity that creates the largest total surplus is the efficient quantity.

8 There are exceptions to this rule. In particular, the rule fails if the producer does not pay some of the costs of production. For example, if the production creates pollution, then part of the cost of production is the cost of pollution, but the victims of the pollution rather than the producer pay this cost. The rule also fails if the consumer does not receive some of the benefits of consumption. For example, a person who has a flu shot benefits, but so, too, does everyone else who comes in contact with that person. In such cases, the equilibrium quantity does not have the largest total surplus. These topics are beyond the scope of this text, however, and are best left to courses covering microeconomic theory.

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2.4 Competition and Society  57

Underproduction and Overproduction What happens to society’s total surplus if the quantity produced is not the efficient quantity? Setting aside for a moment the question of why more or less might be produced, marginal analysis can help answer this question. Let’s begin by consider- ing the situation in which less than the efficient quantity of 300 million pairs of jeans is produced (underproduction) and then move to the situation in which more than efficient quantity of 300 million pairs is produced (overproduction).

• Underproduction. If production is less than 300 million pairs of jeans, some pairs that would have a surplus of marginal benefit over marginal cost are not produced. But according to marginal analysis, these units should be produced. Because these units have a surplus, failure to produce them lowers the total sur- plus, resulting in a smaller total surplus for society.

• Overproduction. If production is more than 300 million pairs of jeans, all of the pairs beyond 300 million have a marginal benefit that is less than their marginal cost. According to marginal analysis, from society’s perspective these units should not be produced. The production of any of these units subtracts from the total surplus, again resulting in a smaller total surplus for society.

Figure 2.10 shows the decrease in total surplus. The loss in total surplus from producing less or more than the efficient quantity is called the deadweight loss. A deadweight loss is a loss to society. No one gains from a deadweight loss.

At the most fundamental level, manufacturing jeans means that society is put- ting resources to use. When the quantity of jeans produced is the efficient quantity, resources are allocated optimally, with no deadweight loss and with the largest total surplus. In contrast, when less than the efficient quantity of jeans is pro- duced, a deadweight loss occurs because the marginal benefit of the last pair of jeans exceeds its marginal cost, which means resources are misallocated: More

Deadweight loss The loss in total surplus from producing less or more than the efficient quantity.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

D

Deadweight loss from underproduction

Deadweight loss from overproduction

Figure 2.10 Deadweight Loss

A deadweight loss is the loss in total surplus from producing less (underproduction) or more (overproduction) than the efficient quantity, 300 million pairs of jeans. Producing less (say, 200 million pairs) or more (say, 400 million pairs) results in a deadweight loss.

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58  CHAPTER 2 Demand and Supply

resources should be directed to producing jeans and fewer to producing other goods and services. When more than the efficient quantity of jeans is produced, a deadweight loss occurs because the marginal benefit of the last pair of jeans is less than its marginal cost, which again means resources are misallocated: Fewer resources should be directed to producing jeans and more to producing other goods and services.

Because the equilibrium quantity in a competitive market leads to the largest total surplus for society, economists use competitive markets as the standard of com- parison for other market structures. Although this conclusion has no direct implica- tion for you as a manager, it is the basis for the nation’s antitrust laws, which certainly do have important consequences for managerial decision making, as you will learn in Chapter 9.

Consumer Surplus Total surplus can be divided into consumer surplus and producer surplus. Keep in mind that the equilibrium price is the actual price that consumers pay (and suppliers receive). Some consumers are willing to pay more than this price, but the market does not require them to do so. For example, point A in Figure 2.11 shows what you saw in Figure 2.8—that some consumer is willing to pay $100 for the 100 millionth pair of jeans. But that consumer actually pays only $60 (the equilibrium price). The consumer surplus is the difference between the maximum price consumers are will- ing and able to pay for each unit of a product and the price actually paid, summed over the quantity of units purchased. For example, the consumer of the 100 millionth pair of jeans has a consumer surplus equal to $100 - $60 = $40 for that pair. The consumer surplus in the entire market is the total of all of these surpluses on all of the pairs of jeans purchased.

The demand curve in Figure 2.11 shows the maximum price consumers are will- ing to pay for each pair of jeans. The equilibrium price is the price consumers

Consumer surplus The difference between the maximum price consumers are willing and able to pay for each unit of a product and the price actually paid, summed over the quantity of units purchased.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

A

D

Consumer surplus

Figure 2.11 Consumer Surplus

The consumer surplus is the difference between the maximum price consumers are willing to pay for each pair of jeans and the price actually paid, summed over the total number of pairs of jeans purchased. The consumer surplus in the market is equal to the green triangular area under the demand curve (which shows the maximum price the consumer is willing to pay for any pair) and above the equilibrium price (which is the price actually paid).

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2.4 Competition and Society  59

actually pay, so the consumer surplus in the market equals the green triangular area under the demand curve and above the equilibrium price in Figure 2.11.

Consumer surplus presents an intriguing concept for managers. It reveals that consumers are willing to pay more than the amount they actually pay. Future chap- ters will explore pricing schemes that share the basic goal of transferring consumer surplus from consumers to suppliers as increased profit.

Producer Surplus The consumer surplus in Figure 2.11 is only part of the total surplus shown in Figure 2.9. The remaining piece goes to producers as producer surplus. The producer surplus is the difference between the actual price producers receive for each unit and the minimum price they are willing to accept to produce that unit, summed over the quantity of units produced. In Figure 2.12, as in Figure 2.8, point B shows that some producer is willing to produce and sell the 100 millionth pair of jeans for $20 (its marginal cost). But that producer actually receives $60 (the equilib- rium price). The producer surplus on this pair is $60 - $20 = $40.9 The producer surplus in the entire market is the total of the producer surpluses for all the units produced. In Figure 2.12, the producer surplus is the green triangular area under the equilibrium price and above the supply curve.

If you compare Figures 2.11 and 2.12, you will see that the consumer surplus is equal to the producer surplus. This result is a fluke; it occurs only by chance. However, if you compare Figures 2.9, 2.11, and 2.12, you will see that the total sur- plus shown in Figure 2.9 equals the sum of the consumer surplus in Figure 2.11

Producer surplus The difference between the actual price producers receive for each unit and the minimum price they are willing to accept to produce that unit, summed over the quantity of units produced.

9 Producer surplus and economic profit are related. In particular, the economic profit for all of the firms in the market equals the total producer surplus minus all of the firms’ fixed costs. But the details of this relationship are best covered in a microeconomic theory course.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

B D

Producer surplus

Figure 2.12 Producer Surplus

Producer surplus is the difference between the actual price suppliers receive for each unit and the minimum price they would be willing to accept to produce that unit (their marginal cost), summed over the quantity of units produced. The producer surplus in the market is equal to the green triangular area under the equilibrium price (which is the actual price the suppliers receive for each pair of jeans) and above the supply curve (which shows the minimum price the suppliers are willing to accept to produce any pair).

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60  CHAPTER 2 Demand and Supply

and the producer surplus in Figure 2.12. This result is not a fluke; it is always the case because the total surplus can always be divided into the part that goes to consumers (the consumer surplus) and the part that goes to producers (the pro- ducer surplus).

You have seen how to use the demand and supply model to determine the equi- librium price and quantity and why producing the equilibrium quantity is socially optimal because it maximizes the total surplus. The real power of the model, how- ever, comes from its ability to predict what happens to price and quantity if some- thing in the market changes, which is the topic of the next section.

Total Surplus, Consumer Surplus, and Producer Surplus in the Webcam Market

When a market is producing the efficient quantity, must the consumer surplus always equal the producer surplus? Use the market for webcams, and suppose that the equi- librium price is $30 and the equilibrium quantity is 3 million. Then draw two graphs to support your answer.

Answer Your graphs should look similar to those below. When the market produces the efficient quantity, 3 million webcams per year, the consumer surplus does not necessarily equal the producer surplus. In Figure a, the consumer surplus exceeds the producer surplus, while in Figure b, the producer surplus exceeds the consumer surplus. The amounts of the consumer surplus and producer surplus depend on the slopes and shapes of the demand and supply curves.

SOLVED PROBLEM

Price (dollars per webcam)

Quantity (millions of webcams per year)

$60

$10

5 63 41 2

$20

$30

$40

$50

0

S

D

Consumer surplus

Producer surplus

Price (dollars per webcam)

Quantity (millions of webcams per year)

$60

$10

5 63 41 2

$20

$30

$40

$50

0

S

D

Consumer surplus

Producer surplus

(a) (b)

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2.5 Changes in Market Equilibrium  61

2.5 Changes in Market Equilibrium Learning Objective 2.5 Use the demand and supply model to predict how changes in the market affect the price and quantity of a good or service.

The demand and supply model is a powerful tool that can predict what happens to price and quantity if something in the market changes. Making these predictions is an important managerial skill. Once you become familiar enough with figures using demand and supply curves, determining the impact of changes in demand or sup- ply will become second nature—you will know the answer immediately without needing a figure. Reaching that stage takes practice, however. This section begins by outlining a four-step procedure that shows how to use a demand and supply figure to predict the effect of a change. We then use this process to explore two scenarios: (1) changes in demand with no change in supply and (2) changes in supply with no change in demand. As a manager, however, you will often deal with situations in which more than one factor changes. The section concludes by presenting and then using a modified four-step procedure to deal with the more complex scenario of simultaneous changes in demand and supply.

Let’s start with the four-step procedure that you can use when one factor that affects the market changes:

1. Draw a demand and supply figure like the one shown in Figure 2.7, and label everything—the curves, the axes, and the initial equilibrium price and quantity.

2. Determine which curve, the demand curve or the supply curve, is affected by the factor that changes.

3. Determine whether the change shifts the curve to the right or to the left. 4. Add the new curve to your original diagram to determine the new equilibrium

price and quantity.

Now let’s apply this procedure, starting first with a change in demand.

Use of the Demand and Supply Model When One Curve Shifts: Demand What happens to the price and quantity of a good or service if demand increases or decreases? Let’s begin by examining the effect of an increase in demand. Recall that the factors that change demand and shift the demand curve include consumers’ income, the price of related goods and services, consumers’ preferences and adver- tising, financial market conditions, the expected future price of the product, and the number of demanders. The effect of the change in demand on the price and quantity of a good or service is the same regardless of the factor involved, so let’s return to our jeans example and presume that jeans are a normal good so that an increase in consumers’ income will increase the demand for jeans.

Increase in Demand Suppose that the economy enters a strong economic expansion, so people’s incomes increase. As a manager at a company that produces jeans, you are interested in how this change will affect the price in the market because that will affect the price you can charge for your jeans. Start with step 1 of the four-step procedure by drawing a demand and supply figure like that in Figure 2.13, with demand curve D0 and supply

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62  CHAPTER 2 Demand and Supply

curve S. The initial equilibrium price is $60 per pair, and the initial equilibrium quan- tity is 300 million pairs of jeans. From Section 2.1, you know that an increase in income for a normal good increases its demand (step 2) and shifts its demand curve to the right (step 3). Finally, draw the new demand curve, D1, in your figure (step 4). Figure 2.13 shows this as a shift of the demand curve to the right, from D0 to D1. The increase in demand raises the equilibrium price of a pair of jeans from $60 to $80 and increases the equilibrium quantity from 300 million to 400 million pairs per year.

Notice that the change in income shifts only the demand curve. There is a move- ment along the supply curve rather than a shift because a change in income is not one of the factors that shifts the supply curve. Regardless of the reason for an increase in demand, the demand curve shifts to the right, there is a movement along the supply curve, and the effects on the price and quantity are identical to what Figure 2.13 illustrates: The price rises and the quantity increases.

Decrease in Demand A decrease in demand has the opposite effect of the scenario illustrated in Figure 2.13. For example, suppose that people’s preferences change: They come to prefer yoga pants more and jeans less. Now start the four-step process once again by drawing your demand and supply diagram (step 1). From Section 2.1, you know that such a change in preferences decreases the demand for jeans (step 2) and shifts the demand curve for jeans to the left (step 3). Draw this new demand curve in your diagram, and determine the effect on the price and quantity (step 4).

Figure 2.14 illustrates this process. The initial demand curve is D0, and the initial supply curve is S. The change in preferences away from jeans decreases the demand for jeans and shifts the demand curve left to D1. After the change in preferences decreases the demand, the new equilibrium is where the new demand curve, D1, and the supply curve, S, intersect. The new equilibrium price is $40 per pair, and the new equilibrium quantity is 200 million pairs per year. As in the previous example,

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

D0

D1

New equilibrium

Initial equilibrium

Figure 2.13 An Increase in Demand for Jeans

When the demand for jeans increases, the demand curve shifts to the right, from D0 to D1. This shift increases the price of jeans, from $60 to $80 per pair, and increases the quantity, from 300 million to 400 million pairs per year.

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2.5 Changes in Market Equilibrium  63

only the demand curve shifts because a change in preferences is not among the fac- tors that shift the supply curve. Regardless of the reason for a decrease in demand, the effects on the price and quantity are identical to what Figure 2.14 illustrates: The price falls and the quantity decreases.

Use of the Demand and Supply Model When One Curve Shifts: Supply You have seen how to tackle changes that affect demand. Now you will learn how to handle changes that affect supply using the same four-step procedure. Recall that the factors that change supply and shift the supply curve include changes in cost, the price of related goods and services, technology, the state of nature, the expected future price of the product, and the number of suppliers. The effect on the price and quantity is the same regardless of the factor involved.

Increase in Supply Suppose that the producers of jeans develop new, more highly automated methods of manufacturing jeans. To determine the effect on the price and quantity of jeans, start by drawing a demand and supply diagram like that in Figure 2.15, with demand curve D and supply curve S0 (step 1). The intersection of supply curve S0 and demand curve D determines the initial equilibrium price ($60 per pair) and the ini- tial equilibrium quantity (300 million pairs). The new methods of automation are a technological advance, which affects the supply (step 2) by increasing it and causes a rightward shift in the supply curve (step 3). As shown in Figure 2.15, the supply curve shifts to the right, from S0 to S1 (step 4). The new equilibrium is where the new supply curve, S1, and the demand curve, D, intersect. The equilibrium price falls from $60 to $40 per pair, and the equilibrium quantity increases from 300 million to 400 million pairs per year.

Notice how the technological advance changes only the supply and shifts only the supply curve. The demand curve does not shift because technology is not one of

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S

D0D1

New equilibrium

Initial equilibrium

Figure 2.14 A Decrease in Demand for Jeans

When the demand for jeans decreases, the demand curve shifts to the left, from D0 to D1. This shift decreases the price of jeans, from $60 to $40 per pair, and decreases the quantity, from 300 million to 200 million pairs per year.

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64  CHAPTER 2 Demand and Supply

the factors that affect demand. Instead, there is a movement along the demand curve. Regardless of the reason for an increase in the supply, the effects on the price and quan- tity are identical to what Figure 2.15 illustrates: The price falls and the quantity increases.

Decrease in Supply Finally, suppose that the price of denim rises. This price hike increases the cost of producing jeans. How will the increase in cost affect the price and quantity of jeans? Again, use the four-step procedure to find the answer. Draw the initial supply curve, S0, and the demand curve, D, as shown in Figure 2.16 (step 1). The initial equilibrium is where the demand curve, D, intersects the original supply curve, S0. Now you must determine which curve is affected by the increase in cost. Only the supply curve shifts because a change in cost is not a factor that affects demand (step 2). The increase in cost decreases the supply and shifts the supply curve to the left, from S0 to S1 in Figure 2.16 (step 3). After the supply decreases, the new equilibrium is where the demand curve, D, intersects the new supply curve, S1 (step 4). Figure 2.16 shows that the increase in cost raises the price from $60 to $80 per pair of jeans and decreases the quantity from 300 million to 200 million pairs per year. The demand curve does not shift because cost is not one of the factors that affect demand. Instead, there is a movement along the demand curve. Regardless of the reason for a decrease in the supply of a good or service, the effects on the price and quantity are identical to what Figure 2.16 illustrates: The price rises and the quantity decreases.

Use of the Demand and Supply Model When Both Curves Shift So far you have learned about the effects of a shift in either the supply curve or the demand curve. In real-world markets, two or more factors can change at the same time, however, causing both curves to shift simultaneously. The ability to use the demand and supply model to determine the effect on the price and quantity when there is a change in both demand and supply is another important managerial skill. Although this situation is slightly more complicated than the one in which only the demand or only

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S0

S1

D

New equilibrium

Initial equilibrium

Figure 2.15 An Increase in Supply of Jeans

When the supply of jeans increases, the supply curve shifts to the right, from S0 to S1. This shift lowers the price of jeans, from $60 to $40 per pair, and increases the quantity, from 300 million to 400 million pairs of jeans per year.

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2.5 Changes in Market Equilibrium  65

the supply changes, if you practice solving problems when both change using the demand and supply model, once again eventually you’ll be able to quickly determine the answers without the model. Until that time, however, practice using figures and the following modified version of the four-step procedure described earlier:

1. Draw two demand and supply figures, and label everything—the curves, the axes, and the initial equilibrium price and quantity.

2. For the first factor that changes, determine (a) whether it is the demand curve or the supply curve that is affected and (b) the direction of the change.

3. Repeat step 2 for the second factor that changes. 4. In one of your demand and supply figures, draw the new demand curve with a

large shift and the new supply curve with a small shift. In the other figure, draw the new demand curve with a small shift and the new supply curve with a large shift. This step might appear odd, but it is necessary because the effect on the price or the quantity depends on which shift is larger. Then you must compare the answers to see if the effect on the price or quantity is certain or ambiguous.

To see how this modified procedure works, we will begin with situations in which demand and supply change in the same way: Both increase or both decrease. Then we will move to situations in which demand and supply change in opposite directions: One increases and the other decreases.

Similar Changes in Demand and Supply Suppose that both the demand and the supply of a particular product increase. Con- sider the following scenario: Jeans and denim skirts are substitutes for consumers and the price of denim skirts rises at the same time that more firms start to produce jeans. What will be the impact of these changes on the price and quantity of jeans?

Figure 2.17 demonstrates how to conduct the analysis of this scenario. Begin with step 1 by drawing two demand and supply figures (in parts a and b), with initial demand curve D0 and initial supply curve S0. The initial equilibrium price is $60 per pair

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$140

$20

$40

700600500400300200100

$60

$80

$100

$120

0

S0 S1

D

Initial equilibrium

New equilibrium

Figure 2.16 A Decrease in Supply of Jeans

When the supply of jeans decreases, the supply curve shifts to the left, from S0 to S1. This shift raises the price, from $60 to $80 per pair, and decreases the quantity, from 300 million to 200 million pairs of jeans per year.

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66  CHAPTER 2 Demand and Supply

of jeans, and the initial equilibrium quantity is 300 million pairs of jeans. Next, move to step 2: The increase in the price of denim skirts increases the demand for jeans and shifts the demand curve for jeans to the right. Follow with step 3: The increase in the number of firms increases the supply of jeans and shifts the supply curve to the right. Finally, step 4 is drawing the shifts with different sizes. In both parts of Figure 2.17, the demand curve shifts rightward from D0 to D1 and the supply curve shifts rightward from S0 to S1. In Figure 2.17(a), however, the demand curve has shifted by more than the supply curve. In this case, the price rises, from $60 to $80 per pair, and the quantity increases, from 300 million to 600 million pairs per year. Compare these results with those in Figure 2.17(b), in which the supply curve has shifted by more than the demand curve. In this case, the price falls, from $60 to $40 per pair, but the quantity still increases, from 300 million to 600 million pairs per year. (The result that the increase in quantity is the same in both situations is a coincidence.)

When both curves shift to the right, the quantity always increases. But unless you know which shift is larger, the impact on the price is ambiguous. If demand increases by more than supply, the price rises. If supply increases by more than demand, the price falls. In fact, in a third scenario, not illustrated in Figure 2.17, if demand increases by the same amount as supply, the price does not change. Know- ing the size of each effect—perhaps because your company’s research department has determined the relative sizes of the changes—will allow you to determine which result is appropriate so then you can predict the change in both price and quantity.

If both the demand and the supply decrease, the situation is the reverse of what you just learned: Both curves shift to the left. The effect on the quantity is certain: Quantity decreases. The effect on the price is uncertain. If demand decreases by more than supply, the price falls. If supply decreases by more than demand, the price

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$120

$140

$20

500 600 700300 400100 200

$40

$60

$80

$100

0

D1

S1

S0

D0

New equilibrium

Initial equilibrium

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$120

$140

$20

500 600 700300 400100 200

$40

$60

$80

$100

0

D1

S1

S0

D0

New equilibrium

Initial equilibrium

Figure 2.17 Increase in Demand for Jeans and Increase in Supply of Jeans

(a) Large Increase in Demand, Small Increase in Supply (b) Small Increase in Demand, Large Increase in Supply If the increase in demand exceeds the increase in supply, the price rises and the quantity increases.

If the increase in supply exceeds the increase in demand, the price falls and the quantity increases.

The quantity definitely increases. But without knowing which effect is larger, the price might rise (if the change in demand is larger, as in part a), fall (if the change in supply is larger, as in part b), or not change (not illustrated but occurs if the two changes are of the same magnitude).

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2.5 Changes in Market Equilibrium  67

rises. If demand and supply decrease by the same amount, the price does not change. In all cases, the quantity decreases, but until you know which effect is larger, the impact on the price is ambiguous.

Opposite Changes in Demand and Supply You have just learned what happens if both the demand and the supply change in the same direction. Let’s now examine what happens if one increases and the other decreases. Consider this scenario: Jeans are a normal good, and people’s incomes increase at the same time that significant flooding occurs in the regions where the jean factories are located, damaging many of the factories. What will be the impact of these two changes on the price and quantity of jeans?

Draw two demand and supply diagrams, such as those shown in parts a and b in Figure 2.18 (step 1). The increase in income increases the demand for jeans and shifts the demand curve to the right (step 2). The flooding, a bad state of nature, decreases the supply of jeans and shifts the supply curve to the left (step 2). As in the previous example, for step 4 you need to include the new demand and supply curves in your diagrams, but, following step 3, in one, you make the demand shift larger, and in the other, you make the supply shift larger. Figure 2.18 illustrates this. In both parts of the figure, the demand curve shifts rightward, from D0 to D1, and the supply curve shifts leftward, from S0 to S1. In Figure 2.18(a), the demand curve has shifted by more than the supply curve. In this case, the price of jeans rises, from $60 to $120 per pair, and the quantity increases, from 300 million to 400 million pairs per year. In Figure 2.18(b), however, the supply curve has shifted by more than the demand curve. The price of jeans still rises, coincidentally again from $60 to $120 per pair, but now the quantity decreases, from 300 million to 200 million pairs per year.

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$120

$140

$20

500 600 700300 400100 200

$40

$60

$80

$100

0

D1

S0S1

D0

New equilibrium

Initial equilibrium

Price (dollars per pair of jeans)

Quantity (millions of pairs of jeans per year)

$120

$140

$20

500 600 700300 400100 200

$40

$60

$80

$100

0

D1

S0S1

D0

New equilibrium

Initial equilibrium

Figure 2.18 Increase in Demand for Jeans and Decrease in Supply of Jeans

(a) Large Increase in Demand, Small Decrease in Supply (b) Small Increase in Demand, Large Decrease in Supply If the increase in demand exceeds the decrease in supply, the price rises and the quantity increases.

If the decrease in supply exceeds the increase in demand, the price rises and the quantity decreases.

The price definitely rises. But without knowing which effect is larger, the quantity might increase (if the change in demand is larger, as in part a), decrease (if the change in supply is larger, as in part b), or not change (not illustrated but occurs if the two changes are of the same magnitude).

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68  CHAPTER 2 Demand and Supply

When the demand increases and the supply decreases, the price always rises, but the impact on the quantity is ambiguous. If demand increases by more than supply decreases, the quantity increases. If, on the other hand, supply decreases by more than demand increases, the quantity decreases. In a third scenario, not illustrated in Figure 2.18, the quantity does not change if demand increases by the same amount that supply decreases. Until you know the relative magnitudes of the shifts, the effect on the quan- tity is uncertain. Of course, if you are working for a large company, your research department might be able to provide you with estimates of the sizes of the changes.

You have probably already guessed that the result of a decrease in demand and an increase in supply will be the opposite of what you just learned. With a decrease in demand and an increase in supply, the demand curve shifts to the left, and the supply curve shifts to the right. Regardless of the magnitude of the shifts, the effect on the price is certain: The price falls. The effect on the quantity is ambig- uous. If demand decreases by more than supply increases, the quantity decreases. If supply increases by more than demand decreases, the quantity increases. If the decrease in demand is the same size as the increase in supply, the quantity does not change. You must determine the relative sizes of the shifts in order to determine the impact on the quantity.

Demand and Supply Functions: Changes in Market Equilibrium As a manager, it is unlikely that you will use algebraic demand and supply functions to determine how the price and quantity of a good or service change when some relevant factor changes. But understanding how to solve for changes in price and quantity helps reinforce the graphical analysis just presented. To keep the algebra straightforward, let’s explore the effect of a single change—namely, how an increase in income affects the price and quantity of jeans.

The demand function that depends on the price and income is

Qd = a - 1b * P2 + 1d * INCOME2 and a simple supply function that depends only on the price is

Qs = r + 1s * P2 At the equilibrium price, the quantity demanded, Qd, equals the quantity sup-

plied, Qs. Equating the quantity demanded and the quantity supplied gives

a - 1b * P2 + 1d * INCOME2 = r + 1s * P2 2.6 Solving this equation for the equilibrium price10 gives

P = a + 1d * INCOME2 - r

s + b 2.7

Use this price in either the demand or the supply function to solve for the equilib- rium quantity. Using it in the supply function gives

Q = r + c s * a + 1d * INCOME2 - r1s + b2 d 2.8

10 To solve for the price, first add 1b * P2 to both sides of Equation 2.6 to get a + 1d * INCOME2 = r + 1s * P2 + 1b * P2. Then subtract r from both sides to get a + 1d * INCOME2 - r = 1s * P2 + 1b * P2. Next, collect the terms on the right side to give a + 1d * INCOME2 - r = 1s + b2 * P . Finally, divide both sides by 1s + b2 to get the expression for the price, P = 1a + 1d * INCOME2 - r21s + b2 .

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2.5 Changes in Market Equilibrium  69

After some algebra, Equation 2.8 can be written as

Q = 1r * b2 + 1s * a2 + 1s * d * INCOME2

s + b 2.9

The equilibrium price and quantity can now be determined using the values of the coefficients, a, b, d, r, and s, and the level of income. For example, suppose that a = 200 million pairs of jeans, b = 5 million pairs per dollar, d = 10,000 pairs per dollar of income, r = 0, s = 5 million pairs per dollar, and INCOME = $40,000. Using the values for the coefficients and income in the equations for the equilibrium price, Equation 2.7, and equilibrium quantity, Equation 2.9, gives P = $60 per pair and Q = 300 million pairs per year.

These equations for the equilibrium price and quantity show the effect of a change in income on the price and the quantity. If income falls to $20,000, you can plug this new value into the equations for the equilibrium price and quantity to show that the decrease in income changes the price, P, to $40 per pair and the quan- tity, Q, to 200 million pairs per year. Just as illustrated in Figure 2.14, a decrease in income decreases both the price and the quantity of a normal good.

Table 2.1 summarizes the results when both demand and supply change, so that both curves shift.

So now you know how the equilibrium price and quantity are determined in competitive markets and how they change with a change in a factor that influences those markets. In some markets, however, the government imposes price controls that place restrictions on the price so that it cannot reach its equilibrium. Price con- trols are covered in the next section.

Table 2.1 Summary of the Effects of Changes in Both Demand and Supply

DEMAND INCREASES, SUPPLY INCREASES

DEMAND DECREASES, SUPPLY DECREASES

Demand Increase

+ Supply

Increase

Demand Increase

= Supply

Increase

Demand Increase

* Supply

Increase

Unknown if Demand Increase

+ , = , or * Supply

Increase

Demand Decrease

+ Supply

Decrease

Demand Decrease

= Supply

Decrease

Demand Decrease

* Supply

Decrease

Unknown if Demand Decrease

+ , = , or * Supply

Decrease

Price c No change T Ambiguous T No

change c Ambiguous

Quantity c c c c T T T T DEMAND INCREASES, SUPPLY

DECREASES DEMAND DECREASES, SUPPLY

INCREASES

Demand Increase

+ Supply

Decrease

Demand Increase

= Supply

Decrease

Demand Increase

* Supply

Decrease

Unknown if Demand Increase

+ , = , or * Supply

Decrease

Demand Decrease

+ Supply

Increase

Demand Decrease

= Supply

Increase

Demand Decrease

* Supply

Increase

Unknown if Demand Decrease

+ , = , or * Supply

Increase

Price c c c c T T T T Quantity c No change T Ambiguous T

No change c Ambiguous

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70  CHAPTER 2 Demand and Supply

2.6 Price Controls Learning Objective 2.6 Explain the effects of price ceilings and price floors.

You have learned how to determine the equilibrium price and quantity using the demand and supply model. Sometimes, however, laws prevent the market price from reaching its equilibrium. For example, in Takoma Park, Maryland, the local government has passed an ordinance that limits the maximum rent landlords can charge. This is an example of a price ceiling, which is a government regulation that sets the maximum legal price. The federal government has also passed laws estab- lishing minimum prices. In 2017, the minimum price for runner peanuts is $354 per ton throughout the United States. Such laws are examples of a price floor, which is a government regulation that sets the minimum legal price. These types of govern- ment regulations can affect the market by making the equilibrium price illegal. As a manager, you need to know how they affect your firm. Let’s begin by examining the effects from a price ceiling and then move to those from a price floor.

Price Ceiling Figure 2.19 shows the market for apartments in a city like Takoma Park. The price measured along the vertical axis is the rent per month, and the quantity measured along the horizontal axis is the number of apartments rented per month. With no price ceiling, the equilibrium rent is $800 per month, and the equilibrium quantity is 1,200 apartments rented per month.

Suppose, however, that the city government sets a price ceiling of $600 per month. Because the price ceiling is below the equilibrium rent, the price ceiling

Price ceiling A government regulation that sets the maximum legal price.

Price floor A government regulation that sets the minimum legal price.

Demand and Supply for Tablets Both Change

The demand function for tablets is

Qd = 240 million - 10.5 million * P2 + 11,000 * INCOME2 where P is the price of a tablet and INCOME is average income. The supply function for tablets is

Qs = 1400,000 * P2 - 1200,000 * COST2 where COST is the cost of producing a tablet. Without calculating the values of the equilib- rium price and quantity, if the cost of producing a tablet rises by $1 and average income rises by $1, what is the effect on the equilibrium price and equilibrium quantity of tablets?

Answer

The increase in cost decreases the supply, which raises the price and decreases the quantity; the increase in income increases the demand, which also raises the price but increases the quantity. Clearly, the price rises. The effect on the quantity depends on which change is larger. The $1 increase in cost decreases the supply by -200,000 * $1, or -200,000 tablets, so the supply curve shifts to the left by 200,000 tablets. The $1 increase in income increases the demand by 1,000 * $1, or 1,000 tablets, so the demand curve shifts to the right by 1,000 tablets. The decrease in supply is larger than the increase in demand, so the quantity of tablets decreases.

SOLVED PROBLEM

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2.6 Price Controls  71

makes the equilibrium rent illegal.11 The law forces the rent down, from $800 to $600. As the rent falls, there is a movement along the demand curve from point A to point C, so that the quantity demanded increases from 1,200 to 1,500 apartments. Simulta- neously, there is a movement along the supply curve from point A to point B, repre- senting a decrease in the quantity supplied to 900 apartments. With the lower rent, some landlords will convert their buildings from apartments to condominiums; oth- ers may elect to stop renting their basements as apartments because they decide that with the lower rent, it is simply not worth the hassle. With the rent control, although tenants want to rent 1,500 apartments, only 900 are rented because that is the quan- tity supplied. There is a shortage of 600 apartments, or 1,500 demanded minus 900 supplied. If there is no price control, a shortage pushes the price higher. With a price ceiling, the price cannot rise, however, so the shortage persists indefinitely.

A shortage has two effects:

• Search. Because many buyers are frustrated in their attempt to buy the product, they search to find it. Search, the activity of finding a seller who has the good or service available for sale, is costly in terms of both the time and effort spent and the direct costs, including gasoline and other transportation costs.

• Black markets. As a result of a persistent shortage and the frustration of buyers who cannot find the product to buy, black markets—markets in which buyers and sellers illegally purchase and sell goods or services at unlawful prices— frequently arise.

Price ceilings harm the affected suppliers because they receive a lower price for their product. Demanders who buy the product at the lower ceiling price and do not have to undertake much search benefit from a price ceiling. Demanders who either can- not find the product at all or wind up paying substantial search costs before buying it are harmed. As you learned in Section 2.4, society is worse off because the rent control forces the quantity away from the efficient amount, thereby creating a deadweight loss.

Search The activity of finding a seller who has the product available for sale.

Black market A market in which buyers and sellers illegally purchase and sell goods or services at unlawful prices.

Price (rent per month)

Quantity (apartments per month)

$200

$400

$600

$800

$1,000

$1,200

300 600 900 1,200 1,500 1,800 2,1000

Shortage

S

A

B C

D

Price ceiling

Figure 2.19 A Price Ceiling

Without a price ceiling, the equilibrium rent is $800 per month, and the equilibrium quantity is 1,200 apartments rented per month. If the government imposes a price ceiling of $600 per month, the quantity of apartments demanded is 1,500 (point C), and the quantity supplied is only 900 (point B). There is a shortage equal to the length of the light red double-headed arrow, which is 1,500 apartments minus 900 apartments, or 600 apartments per month.

11 If the price ceiling is set above the equilibrium price, it has no effect: Because the equilibrium price remains legal, the price remains at its equilibrium.

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72  CHAPTER 2 Demand and Supply

Price Floor The government has imposed price floors in the markets for some agricultural prod- ucts. The minimum wage in the labor market is another example of a price floor. In this section, we examine the effects of both of these price floors.

Price Floor in an Agricultural Market Figure 2.20 shows the market for peanuts. Suppose that in the absence of government intervention, the equilibrium price is $520 per ton of peanuts, and the equilibrium quantity is 1.6 million tons per year. Further suppose that the government imposes a price floor of $535 per ton. This price floor is above the equilibrium price of $520 and makes the equilibrium price illegal.12 The price must rise from the equilibrium price to the floor price of $535. As Figure 2.20 shows, the price rise creates a movement along the supply curve from point A to point C and increases the quantity supplied to 2.2 million tons per year. The price rise also creates a movement along the demand curve from point A to point B and decreases the quantity demanded to 1.0 million tons per year. With the price floor, peanut consumers buy only 1.0 million tons of pea- nuts. There is a surplus of peanuts equal to 2.2 million tons supplied minus 1.0 mil- lion tons demanded, or 1.2 million tons. If there was no price floor, a surplus would push the price lower. With a price floor, the price cannot fall, so the surplus persists indefinitely.

To maintain the price floor in agricultural markets, the government must some- how take the surplus off the market. At times, it has done so by paying farmers not to grow the crop, which decreases the supply and eliminates the surplus before it occurs. At other times, it has purchased the surplus and either stored it or used it as food aid abroad. Because the government removes the surplus, all producers gain from a price floor because they receive a higher price. All demanders lose from a price floor because they pay a higher price.

12 If the price floor is set below the equilibrium price, it has no effect: Because the equilibrium price remains legal, the price remains at its equilibrium.

Price (dollars per ton of peanuts)

Quantity (millions of tons of peanuts per year)

$510

$520

$530

$540

$550

$560

0.4 0.8 1.2 1.6 2.0 2.4 2.80

Surplus

S

B C

A

D

Price floor

Figure 2.20 A Price Floor

Without a price floor, the equilibrium price is $520 per ton of peanuts, and the equilibrium quantity is 1.6 million tons of peanuts per year. If the government imposes a price floor of $535 per ton, the quantity of peanuts supplied is 2.2 million tons (point C), and the quantity demanded is only 1.0 million tons (point B). There is a persistent surplus of peanuts equal to the length of the green doubled-headed arrow, 1.2 million tons of peanuts per year.

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2.6 Price Controls  73

Minimum Wage in the Labor Market To this point, the discussion has dealt exclusively with markets for the products firms produce. But there also are markets for the inputs firms use, such as labor. These markets are often highly competitive, especially for low-skilled labor. There is a significant difference between product markets and input markets: In a product market, households demand the product, and firms supply it. In an input market, such as the labor market, households supply labor, and firms demand it. Even with this difference, the law of demand and the law of supply still apply in labor markets:

• The law of demand in the labor market. When the wage rate rises and nothing else changes, workers become more expensive to employ. Managers respond to the increased cost by decreasing the quantity of labor they demand. Similarly, when the wage rate falls and nothing else changes, managers increase the quan- tity of labor they demand. The downward slope of the labor demand curve, LD, in Figure 2.21 shows this inverse relationship between wage rate and quantity of labor demanded.

• The law of supply in the labor market. When the wage rate rises and nothing else changes, some people respond by increasing the hours they will work. In addi- tion, people who were not working at the lower wage rate decide that the higher wage rate will make it worthwhile to take a job. As a result, workers increase the quantity of labor supplied when the wage rate rises. Conversely, when the wage rate falls and nothing else changes, workers decrease the quantity of labor they sup- ply. This direct relationship between wage rate and quantity of labor supplied is illustrated by the upward slope of the labor supply curve, LS, in Figure 2.21.

The minimum wage can have an effect in the market for low-skilled labor. In the absence of government intervention, in Figure 2.21 the equilibrium wage rate and employment are determined at point A, where the labor demand and labor supply curves intersect. In this case, the equilibrium wage rate is $10 an hour, and the equi- librium quantity is 40 million hours of labor per year.

Wage rate (dollars per hour)

Quantity (millions of hours of labor per year)

$5

$10

$15

$20

$25

$30

10 20 30 40 50 60 700

Unemployment

LS

B C

A

LD

Minimum wage

Figure 2.21 A Minimum Wage

Without a minimum wage, the equilibrium wage rate is $10 per hour, and the equilibrium quantity is 40 million hours of labor per year. If the government sets a minimum wage of $20 per hour, the quantity of labor supplied is 50 million hours (point C), and the quantity demanded is only 20 million hours (point B)— that is, 20 million hours of labor are employed. There is a surplus, or unemployment, of 30 million hours per year, equal to the length of the light red double- headed arrow.

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74  CHAPTER 2 Demand and Supply

The federal government and many state and local governments have estab- lished minimum wage laws for the labor market. A minimum wage is the lowest legal wage rate an employer can pay a worker. It is effectively a price floor in the labor market. Proponents of minimum wages sometimes call them “living wages.”

Suppose that the government imposes a minimum wage of $20 per hour in the labor market, as illustrated in Figure 2.21. Because the minimum wage is set above the equilibrium wage rate, it makes the equilibrium wage rate illegal and therefore changes the outcome in the labor market.13 The lowest wage rate that can be paid (or received) is $20 per hour, so the wage rate must rise from its equilibrium value of $10 per hour. The rise in the wage rate creates a movement along the labor supply curve from point A to point C and increases the quantity of labor supplied to 50 million hours per year. The rise in the wage rate also creates a movement along the labor demand curve from point A to point B and decreases the quantity of labor demanded to 20 million hours per year. The quantity of labor employed with the $20 minimum wage is 20 million hours per year, the quantity that firms demand. At the minimum wage, there is a surplus of 30 million hours of labor, equal to 50 million hours of labor supplied minus 20 million hours of labor employed. This surplus of hours rep- resents unemployment: Workers are searching for work but are unable to find it because of the lower demand.

Unlike the situation in agricultural markets, the government does not employ the surplus of labor. The workers remain unemployed. Consequently, not all low- skilled workers gain from the minimum wage. Workers who retain their jobs receive a higher wage rate, so they gain. Workers who lose their job and cannot find another or find one only after a long and costly search lose. Of course, all employers who hire low-skilled workers lose because they must pay a higher wage rate.

Minimum wage The lowest legal wage rate an employer can pay a worker.

13 Similar to the situation with a price floor, if the minimum wage is set below the equilibrium wage rate, the minimum wage has no effect: Because the equilibrium wage rate remains legal, the wage rate remains at its equilibrium.

The Effectiveness of a Minimum Wage

In Figure 2.21, the initial equilibrium wage is $10 per hour, and employment is 40 mil- lion hours per year.

a. Suppose that the government sets a minimum wage of $5 per hour. What effect does this minimum wage have on the wage rate and quantity of employment? Draw a graph to support your answer.

b. Suppose that the government sets a minimum wage at $15 per hour. What effect does this minimum wage have on the wage rate and quantity of employment? Draw a graph to support your answer.

Answer

a. The minimum wage has been set below the equilibrium wage so it will have no effect. In particular, your figure should look similar to Figure a. It shows that at the minimum wage of $5 per hour, the quantity of labor demanded, 50 million hours, exceeds the quantity supplied, 35 million. At this wage rate, there is a shortage. Nothing prevents the wage rate from rising, so the shortage pushes the wage rate

SOLVED PROBLEM

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Wage rate (dollars per hour)

Quantity (millions of hours of labor per year)

$5

$10

$15

$20

$25

$30

10 20 30 40 50 60 700

LS

LD

Minimum wage

back to its initial equilibrium level, $10 per hour. Once at the equilibrium wage, employment remains equal to 40 million hours per year.

b. The minimum wage has been set above the equilibrium wage, so it will have an effect. Your figure should look similar to Figure b. The wage becomes $15 per hour, the minimum wage. At this wage rate, the quantity of labor supplied, 45 million hours, exceeds the quantity demanded, 30 million. So employment is 30 million hours per year, the quantity of labor firms will hire, and unemployment (a surplus) is 15 million hours per year, shown in Figure b by the double-headed arrow. Unemployment persists because the wage rate cannot fall, since $15 per hour is the minimum legal wage.

(a) (b)

Wage rate (dollars per hour)

Quantity (millions of hours of labor per year)

$5

$10

$15

$20

$25

$30

10 20 30 40 50 60 700

LS

LD

Minimum wage

2.7 Managerial Application: Using the Demand and Supply Model  75

2.7 Using the Demand and Supply Model Learning Objective 2.7 Apply the demand and supply model to make better managerial decisions.

As a manager, you can use the demand and supply model to predict how the costs or the price of your product might change. Let’s begin by exploring how the model can help you predict your costs and thereby increase your profit.

Predicting Your Costs Kellogg Company, a major cereal and cookie manufacturer based in Battle Creek, Michigan, buys tons of corn annually. Because corn is a significant expense for the firm, its purchasing managers carefully monitor corn prices. Although Kellogg is a major corn buyer, the market for corn is so huge that the firm has no influence on its price. Suppose that a similar company employs you in its purchasing department. Your company also has no influence on the price of corn, but just like Kellogg’s pur- chasing managers, you, too, will carefully monitor the market for corn.

MANAGERIAL APPLICATION

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76  CHAPTER 2 Demand and Supply

Between 2004 and 2008, oil prices rose from $40 per barrel to near $90. In response, the U.S. Congress passed the Energy Policy Act of 2005 and the much more ambitious Energy Independence and Security Act of 2007. These laws required refineries to add renewable fuels, largely ethanol, to the gasoline they refined. Within four years, this legal requirement nearly tripled the amount of ethanol produced, from 3.5 billion gal- lons in 2004 to 9.3 billion gallons in 2008. In the United States, corn is the primary input used to produce ethanol. The demand and supply model provides a straightforward way to determine how passage of these laws affected the price (and quantity) of corn.

As ethanol producers stepped up their purchases of corn to make more ethanol, there was a vast increase in the number of buyers of corn. You have learned that an increase in the number of buyers increases the demand and shifts the demand curve to the right. As illustrated in Figure 2.22, from 2006 to 2007 the increase in demand raised the price of corn from an average of about $3.50 per bushel to $5.00 per bushel. This change also increased the quantity, but the key for you as a purchaser is the higher price you will be forced to pay. Knowing that the price of corn will rise in response to the passage of these laws gives you a potential edge: If you can buy corn using a long-term contract before the price rises, you can save your company a sub- stantial sum of money. Of course, people in the purchasing departments of other companies and major growers of corn will also be alert to the possibility of a higher price, so you will need to act quickly to scoop up any savings. But it’s clear how using the demand and supply model gives you an opportunity to reduce your costs.

Predicting Your Price In addition to providing information about the inputs you buy, the demand and sup- ply model can give you key insights into changes in the price of the products and services you sell. Suppose that you are an executive working for a company like Toy- ota. You are overseeing the pricing and production of hybrid cars like Toyota’s Prius. Your firm, of course, is one of many automakers producing and selling hybrids. A crucial selling point of hybrids is their notable fuel economy. For example, many

Price (dollars per bushel of corn)

Quantity (billions of bushels of corn per year)

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

2.5 5.0 7.5 10.0 12.5 15.0 17.50

S

D1

New equilibrium

Initial equilibrium

D0

Figure 2.22 The Market for Corn

When the government passed laws requiring that refineries add ethanol to gasoline, the demand for corn increased, and the demand curve for corn shifted to the right, from D0 to D1. This shift raised the price of corn, which has the potential to raise your company’s costs dramatically.

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hybrid models have EPA fuel economy ratings over 50 mpg. Consumers view hybrids as substitutes for gasoline-powered cars—they buy hybrids to avoid buying as much gasoline as they would if they purchased a gasoline-powered car. So the demand for hybrids depends on the price of gasoline. Since it reached its peak of near $4.00 per gallon in 2012, the price of gasoline has fallen substantially. This remarkable decrease in price has reduced the cost of operating a gasoline-powered car. Suppose that gov- ernment analysts forecast that gasoline prices will remain low for the next several years and your research department agrees with this prediction. How can you use the demand and supply model to increase your profit?

Because hybrids are a substitute for gasoline-powered cars, the lower price of gasoline decreases the demand for hybrids. In Figure 2.23, the demand curve for hybrids shifts left, from D0 to D1. The decrease in demand lowers the price and quantity of hybrid cars. Knowing that the price and quantity will decrease in the future allows you to make better, more informed decisions. You can take several approaches in order to produce fewer hybrids:

• You might begin planning to run one shift a day on the assembly lines produc- ing hybrids rather than two.

• You could explore converting assembly lines away from producing hybrids and toward producing more popular vehicles.

• You might try to make deals with your suppliers to decrease purchases of hybrid components, such as batteries, so they will not pile up in inventory, where they could depreciate due to technological obsolescence or simply aging.

• The federal government has imposed Corporate Average Fuel Economy regula- tions that automakers must meet. These standards set average-miles-per-gallon requirements for the automakers’ fleets of small cars, small trucks, large cars, and large trucks. Knowing that the demand for high-mpg hybrid cars will decrease means you must take other actions to meet these targets.

Using the demand and supply model can allow you to make decisions such as these that can help increase your firm’s profit.

Price (thousands of dollars per hybrid car)

Quantity (thousands of hybrid cars per year)

$15

$20

$25

$30

$35

$40

50 100 150 200 250 300 3500

S

D0

Initial equilibrium

New equilibrium

D1

Figure 2.23 The Market for Hybrid Cars

When the price of gasoline falls, the demand for hybrid cars decreases, so the demand curve shifts to the left, from D0 to D1. This shift lowers both the price and the quantity of hybrid cars.

2.7 Managerial Application: Using the Demand and Supply Model  77

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78  CHAPTER 2 Demand and Supply

Revisiting How Managers at Red Lobster Coped with Early Mortality Syndrome

At the start of the chapter, you learned that early mor-tality syndrome (EMS) in Asia affected the supply of shrimp. Using what you have learned in this chapter, you can classify EMS as a bad state of nature. A bad state of nature decreases supply, so you know that the supply curve for shrimp shifts to the left. Thailand is the world’s largest shrimp exporter. EMS caused the price of Thai shrimp to rise about 40 percent, from $4,500 to $6,000 per ton of shrimp, as shown in Figure 2.24. It also decreased the quantity of shrimp from 600 thousand tons to 300 thousand tons per year.

Using this sort of analysis, Red Lobster’s managers realized that EMS was a potentially severe problem even

before it spread from its initial location in China. Using demand and supply analysis, the managers knew that the price of shrimp might soar. They quickly arranged to buy shrimp under long-term contracts at a fixed price, lock- ing in the price before other buyers and sellers of shrimp realized that the price was soon to skyrocket. Once other buyers and sellers learned that the price of shrimp was heading up, its price under new long-term contracts also rose. As EMS spread, the price of shrimp rose, as analyzed above. But the long-term contracts temporarily insulated Red Lobster from the higher price. The managers’ use of the demand and supply model significantly increased profit for Red Lobster.

Price (dollars per ton of shrimp)

Quantity (thousands of tons of shrimp per year)

$1,500

$3,000

$4,500

$6,000

$7,500

$9,000

150 300 450 600 750 900 1,0500

S0

Initial equilibrium

New equilibrium

D

S1

Figure 2.24 A Decrease in the Supply of Shrimp

When the supply of shrimp decreases, the supply curve shifts to the left, from S0 to S1. This shift raises the price of shrimp, from $4,500 per ton to $6,000 per ton, and decreases the quantity of shrimp, from 600 thousand tons to 300 thousand tons per year.

Summary: The Bottom Line

2.1 Demand • The law of demand states that, everything else remain-

ing the same, a higher price decreases the quantity demanded and a lower price increases the quantity demanded. This law explains the downward slope of the demand curve.

• A change in the price of a product results in a change in the quantity demanded and a movement along the

demand curve. Changes in other relevant factors— including consumers’ income, the price of related goods and services, consumers’ preferences and advertising, financial market conditions, the expected future price of the product, and the number of demanders—change the demand and shift the demand curve. If demand increases, the demand curve shifts to the right. If demand decreases, the demand curve shifts to the left.

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Key Terms and Concepts  79

2.2 Supply • The law of supply states that, every else remaining the

same, a higher price increases the quantity supplied and a lower price decreases the quantity supplied. This law explains the upward slope of the supply curve.

• A change in the price of a product results in a change in the quantity supplied and a movement along the sup- ply curve. Changes in other relevant factors—including cost, the price of related goods or services, technology, the state of nature, the expected future price of the product, and the number of suppliers—change the supply and shift the supply curve. If supply increases, the supply curve shifts to the right. If supply decreases, the supply curve shifts to the left.

2.3 Market Equilibrium • In the demand and supply model, the intersection of

the demand and supply curves determines the equilib- rium price and quantity. The equilibrium price sets the quantity demanded equal to the quantity supplied. The equilibrium quantity is the quantity bought and sold at the equilibrium price.

• The market price is the equilibrium price, and the mar- ket quantity transacted is the equilibrium quantity.

2.4 Competition and Society • Perfectly competitive markets are socially optimal

because the equilibrium quantity maximizes society’s total surplus of benefit over cost from the product. Pro- ducing more or less than the equilibrium quantity decreases the total surplus by creating a deadweight loss.

• Consumer surplus is the difference between the maxi- mum price consumers are willing to pay and the price they actually pay, summed over the quantity con- sumed. Producer surplus is the difference between the price the firm actually receives and the lowest price it would be willing to accept to produce the product, summed over the quantity produced. The total surplus is the sum of the consumer surplus and the producer surplus.

2.5 Changes in Market Equilibrium • To use the demand and supply model to predict how

changes in relevant factors affect the price and quantity of a product, determine whether the factor changes demand and/or supply and whether it causes an increase or a decrease.

• If only demand or only supply changes, the demand and supply model shows how both the price and the quantity change. If both the demand and the supply change, the demand and supply model unambiguously predicts changes in either price or quantity. Without information about the relative size of the changes, the change in the other variable is ambiguous.

2.6 Price Controls • Price ceilings set the maximum legal price. If a price

ceiling is set below the equilibrium price, the new price in the market becomes the ceiling price, and a shortage results. The shortage leads to increased search and the creation of black markets.

• Price floors set the minimum legal price. Price floors are often set in agricultural markets and in the labor mar- ket. If a price floor is set above the equilibrium price, the new price in the market becomes the floor price, and a surplus of the product results. In agricultural markets, the government buys the surplus to maintain the price floor. In the labor market, the labor surplus is unemployment.

2.7 Managerial Application: Using the Demand and Supply Model

• The demand and supply model can help guide pur- chasing and production decisions.

• The demand and supply model can help you predict when the price of inputs will rise or fall, thereby leading you toward profitable decisions about when to buy them. The model can also help you predict the future price of a product, enabling you to make profitable decisions about whether to expand or contract your business or when to increase or decrease your production.

Key Terms and Concepts Black market

Complements

Complements in production

Consumer surplus

Deadweight loss

Demand curve

Demand function

Efficient quantity

Equilibrium

Equilibrium price

Equilibrium quantity

Income effect

Inferior good or service

Market

Minimum wage

Normal good or service

Price ceiling

Price floor

Producer surplus

Search

Substitutes

Substitutes in production

Substitution effect

Supply curve

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80  CHAPTER 2 Demand and Supply

Questions and Problems All exercises are available on MyEconLab; solutions to even-numbered Questions and Problems appear in the back of

this book.

2.1 Demand Learning Objective 2.1 Describe the factors that affect the demand for goods and services.

1.1 Which represents the law of demand: a shift of the demand curve or a movement along the demand curve? Explain your answer.

1.2 “Romaine lettuce is far more nutritious than ice- berg lettuce. Therefore, iceberg lettuce is an infe- rior good.” Is this description of iceberg lettuce as an inferior good correct in economic terms? Explain your answer.

1.3 Suppose that banks increase the amount of infor- mation they require from potential borrowers before approving car loans. How would this change affect the demand curve for automobiles?

1.4 What effect does each of the following have on the demand curve for jeans? a. A decrease in income if jeans are a normal good b. A fall in the price of jeans c. A rise in the price of cargo pants, a substitute

for jeans d. A widespread perception that wearing jeans

is not as fashionable as it once was

1.5 Your firm, Content Colleague, is similar to Happy Worker, a Canadian company that designs and manufactures toys and collectibles. Your research analyst has estimated the demand function for your stuffed toy animals is

Qd = 30 million - 12 million * P2 a. If you set the price of a plush toy at $5, how

many will consumers buy? b. If you increase the price of a plush toy by $1,

how will this change the quantity that your customers buy?

2.2 Supply Learning Objective 2.2 Describe the factors that affect the supply of goods and services.

2.1 What is the difference between cost and price? If the cost of producing a good or service rises, what is the effect on the supply curve? What is the effect on the supply curve of an increase in the price of the good or service?

2.2 How does an increase in the price of the cheese used to produce pizza affect the supply curve of pizza?

2.3 Toyota’s factory in Georgetown, Kentucky, can use its assembly lines to produce either the Toy- ota Camry or the Camry Hybrid. a. For this Toyota factory, are the Camry and

Camry Hybrid substitutes in production or complements in production?

b. How will the supply of the Camry respond to an increase in the price of the Camry Hybrid?

2.4 What effect does each of the following have on the supply curve of jeans? a. A rise in the price of transporting the jeans

from Thailand, where they are made, to the United States, where they are sold

b. A fall in the wages paid the workers who sew jeans

c. A rise in the price of jeans d. An increase in the number of companies

manufacturing jeans

2.3 Market Equilibrium Learning Objective 2.3 Determine the market equilibrium price and quantity using the demand and supply model.

3.1 Among all possible prices, what makes the equi- librium price unique?

3.2 If the price in a market is less than the equilibrium price, what happens to restore the equilibrium price?

3.3 The figure shows a hypothetical market for NFL-caliber punters. a. How many punters will the NFL hire?

Explain your answer. b. What salary will these punters receive?

Explain your answer.

Salary (millions of dollars per year)

Quantity (punters per year)

$1

$2

$3

$5

$6

$4

$7

10 20 30 40 50 60 700

S

D

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Questions and Problems  81

3.4 The demand function for a product is Qd = 1,000 - 10P, and its supply function is Qs = 100 + 2P. Calculate the equilibrium price and equilibrium quantity of the good. Check your answer by drawing the demand and supply curves in a figure.

2.4 Competition and Society Learning Objective 2.4 Explain why perfectly competitive markets are socially optimal.

4.1 Carefully explain how economists a. Use the demand curve to measure the mar-

ginal social benefit of a good or service. b. Use the supply curve to measure the mar-

ginal social cost of a good or service. c. Measure the total surplus of a unit of a good

or service.

4.2 Describe the social gains from competitive markets.

4.3 Explain how producing less than the equilibrium quantity decreases society’s total surplus and how producing more than the equilibrium quan- tity also decreases society’s total surplus.

2.5 Changes in Market Equilibrium Learning Objective 2.5 Use the demand and supply model to predict how changes in the market affect the price and quantity of a good or service.

5.1 Does an increase in the price of jet fuel shift the demand curve for airline travel, the supply curve of airline travel, or both? Explain your answer.

5.2 How does a change in people’s preferences in favor of wearing jeans shift the demand curve for jeans? The supply curve? How does a decrease in the number of producers of jeans shift the demand curve for jeans? The supply curve?

5.3 High-quality pasta products are made from 100 percent semolina, which is made from durum wheat. Suppose that a drought decreases the quantity of durum wheat. Answer each of the following questions. Draw demand and supply diagrams to illustrate each answer. a. How will the drought affect the equilibrium

price and quantity of high-quality spaghetti? b. How will the drought affect the equilibrium

price and quantity of spaghetti sauces? c. For consumers, pasta and rice are substitutes.

How will the drought affect the equilibrium price and quantity of rice?

Price (dollars per television)

Quantity (millions of televisions per year)

$250

$500

$750

$1,000

$1,250

$1,500

20 40 60 80 100 120 1400

S1

D

S0

5.4 Peanut butter and jelly are complements for consumers. What happens to the equilibrium price and quantity of jelly if the peanut har- vest is especially bountiful? Explain your answer, and illustrate it with a demand and supply figure.

5.5 The figure shows the market for televisions. The initial supply curve is S0. After a change occurs, the supply curve becomes S1.

a. Before the change occurs, what were the ini- tial equilibrium price and quantity? After the change occurs, what are the new equilib- rium price and quantity?

b. Give an example of a change that could lead to the shift illustrated in the figure.

c. Based on your answer to part b, if you are an executive at a firm like LG Corporation, a Korean manufacturer of televisions, what managerial decisions will you make?

5.6 Baseball gloves are made from cowhide. Sup- pose that reports of bovine spongiform encepha- lopathy (mad cow disease) have decreased the demand for beef. Using a demand and supply diagram, explain the impact of mad cow disease on the equilibrium price and quantity of base- ball gloves.

5.7 Suppose that you own Lauderdale Aerial Spray- ing, a large Texas crop-dusting company. Drones are able to spray crops at lower cost than manned planes. Currently, Federal Avia- tion Administration (FAA) regulations prohibit

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82  CHAPTER 2 Demand and Supply

the use of drones for crop dusting or other preci- sion agricultural use. a. If the FAA eliminates these regulations, what

will happen to the price and quantity of crop spraying? Explain your answer using a demand and supply figure.

b. If the FAA eliminates these regulations, what will happen to the price and quantity of soy- beans, which require regular spraying? Explain your answer using a demand and supply figure.

5.8 As an executive with KB Home, a large home builder, you know that new homes are a normal good and that incomes are growing. Builders use plywood in the construction of new homes, and the price of plywood has soared because of environmental restrictions on logging. What do you expect will happen to the equilibrium price and quantity of new homes? Use demand and supply figures to help explain your answer.

5.9 The demand function for pork is Qd = 300 - 100P + 0.01INCOME, where Qd is the tons of pork demanded in your city per week, P is the price of a pound of pork, and INCOME is the average household income in the city. The supply function for pork is Qs = 200 + 150P - 30COST, where Qs is the tons of pork supplied in your city per week, P is the price of a pound of pork, and COST is the cost of pig food. a. If INCOME is $50,000 and COST is $5, what

are the equilibrium price and quantity of pork?

b. If INCOME falls to $40,000 and COST does not change, what are the new equilibrium price and quantity of pork?

c. If INCOME is $50,000 and COST rises to $10, what are the new equilibrium price and quantity of pork?

d. If INCOME is $40,000 and COST is $10, what are the new equilibrium price and quantity of pork?

5.10 Suppose that a competitive market is in equilib- rium and the firms in this industry employ many workers who are paid the minimum wage. a. If Congress raises the minimum wage that

the firms must pay their workers, what hap- pens to the equilibrium price and output?

b. What happens to the consumer surplus?

2.6 Price Controls Learning Objective 2.6 Explain the effects of price ceilings and price floors.

6.1 Why does a price ceiling set above the equilib- rium price have no effect on the market?

6.2 Why is an increase in the minimum wage apt to affect teenagers more than other age groups?

6.3 Suppose that you are a manager working for Yum in the Taco Bell division. Taco Bell employs many employees at the minimum wage. If the mini- mum wage is already set above the equilibrium wage rate and then the government raises it still higher, what are the effects in the labor market? How do the changes in the labor market affect Taco Bell?

2.7 Managerial Application: Using The Demand and Supply Model Learning Objective 2.7 Apply the demand and supply model to make better manage- rial decisions.

7.1 You are a manager at a firm like Whirlpool in a market with other manufacturers of refrigerators. The figure shows the initial market demand and supply curves for refrigerators. You know that refrigerators are a normal good and income is increasing, so the demand for refrigerators will change by 100,000 at every price.

Price (dollars per refrigerator)

Quantity (thousands of refrigerators per year)

$250

$500

$750

$1,000

$1,250

$1,500

50 100 150 200 250 300 3500

S

D

a. What are the initial equilibrium price and quantity of refrigerators? After the change in income, what are the new equilibrium price and quantity?

b. Based on your answer to part a, what mana- gerial decisions might you make?

7.2 In Section 2.7, you learned how to analyze the effect on cereal producers of laws that required

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MyLab Economics Auto-Graded Excel Projects  83

the addition of significant amounts of ethanol to gasoline. Suppose that at the same time these laws were passed, consumers’ incomes increased. If name-brand cereal, such as that produced by Kellogg, is a normal good, what will be the impact on the price and quantity? Use a demand and supply figure as part of your answer.

7.3 Ethanol producers persistently lobby the govern- ment to issue regulations increasing the amount of ethanol that oil refiners must add to gasoline. Using the demand and supply model, explain why ethanol producers lobby the government for these regulations.

7.4 Young adult males drink more beer than other age and gender groups. Why do executives at breweries track the demographics of the various nations in which they operate?

7.5 Say that you are a manager working for a casual dining chain similar to Brinker International Restaurants’ chain of Chili’s restaurants. Just like Chili’s, baby back ribs are one of your major sale items. Baby back ribs come from pigs. Answer each of the following questions inde- pendently; that is, when answering part b, assume that the situation in part a is not occur- ring. Use demand and supply figures to explain your answers. a. You read that droughts are raising the price

of corn and soy, both major foodstuffs for pigs. What action(s) should your firm take?

b. Dining out at casual restaurants such as Chili’s or your restaurant is a normal good. You read predictions that the economy will soon sink into a recession, with people’s incomes falling. What do you expect will hap- pen to the price and quantity of dining at casual restaurants?

c. Upper management has asked you to pre- pare recommendations for the next one to two years. You read that droughts are raising the price of corn and soy and that the econ- omy will soon enter a recession. Based on what you have discovered, what will happen to the price and quantity of casual dining? What managerial recommendation(s) will you make to your superiors?

7.6 Increased consumption of natural foods by pet owners has led to increased demand for natural foods for their pets. The Colgate-Palmolive Company produces and sells Hill’s Science Diet cat food. Suppose that you work for a similar company, also producing “scientific” cat food. Your marketing team presents research showing that consumers do not consider so-called scien- tific cat food natural. Based on the trend toward natural cat foods, what do you expect will hap- pen to the equilibrium price and quantity of sci- entific cat food? Based on this result, what recommendation(s) would you make to top management?

MyLab Economics Auto-Graded Excel Projects 2.1 Saxum Vineyard, in Paso Robles, CA, is one of

the more than 8,000 wineries in the United States. While Saxum produces a number of different kinds of wine, it focuses its production on Syrah (also known as Shiraz). Saxum sells its wines all over the United States. Suppose the market demand function for Syrah is as follows.

Qd = 200 - 38.18P + 8.35PS - 2PC + 10INC + 0.8TS + 0.5M21

where Qd is the monthly demand for bottles of Syrah (in millions), P is the price of Syrah, PS is the average price of substitute bottles of wine (other varieties), PC is the average price of a pound of cheese and is used to gauge the price of complementary goods, INC is average U.S. income (in thousands of dollars), TS is the num- ber of wine trade shows and competitions each year that firms can attend to market their wines, and M21 is the number (in millions) of millenni-

als over the age of 21. This last variable captures a change in consumer preferences; millennials are drinking wine at a much higher rate than previ- ous generations. The market for Syrah also has supply, pro- duced by Saxum Vineyard and other wineries, which can be stated as follows:

Qs = -100 + 22.93P - 5PPI - 10PS + 8TEMP + 1SUP

where Qs is the monthly supply of bottles of Syrah (in millions), P is the price of Syrah, PPI is the Producer Price Index (an index used to gauge changes in the costs of production in the United States), PS is the price of substitute wines that could easily be produced instead of Syrah, TEMP is the expected temperature during the harvest season for grapes, and SUP is the number of wineries that supply Syrah in the market (in thousands).

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84  CHAPTER 2 Demand and Supply

Using the market supply and demand func- tions for Syrah, fill in the template provided with the coefficient for each function. Using the infor- mation below, fill in the value for each of the vari- ables except Price of Syrah. Then set up your Qd and Qs to automatically calculate as you adjust the values for each variable.

Demand:

• Price of substitutes: $18 • Price of cheese: $15 • Income: $53,000 • Trade shows: $3 • Millennials = 43 million

Supply:

• PPI: 111 • Price of substitutes: $18 • Temperature: 60 • Number of suppliers: 8,000

Now that you have set up your demand and supply functions, answer the following questions: 1. When the price of Syrah increases by $1, what

is the effect on quantity demanded and quan- tity supplied?

2. How much does a $1 decrease in the price of substitute bottles of wine shift the demand and supply curves?

3. Suppose that the price of Syrah is currently $22 per bottle. How many bottles will be demanded and supplied monthly? Is there a shortage or surplus and of how much?

4. If the market price of Syrah falls to $16 per bottle, how many bottles will be demanded and supplied monthly? Is there a shortage or surplus and of how much?

5. Trying prices in $1 increments between $16 and $22, at what price and quantity does the market equilibrium occur?

6. Suppose that the PPI increases to 123.222. If the price of wine stays at $20 per bottle, what quantity will be supplied in the mar- ket, and will the increase in the PPI create a shortage?

7. With the increase in PPI to 123.222, at what price will the market be in equilibrium? What quantity will be demanded and supplied at this price?

2.2 We are going to use Excel to examine changes in the consumer and producer surpluses in a competitive market when the market is not in equilibrium. Consider the market for corn in the United States. Suppose the demand and supply functions for corn are as follows:

Qd = 100 - 14.5P Qs = 0 + 5.5P

where Q is bushels of corn (in billions) and P is the market price per bushel. Using the template provided, enter the coef- ficients for demand and supply, and set up your Qd and Qs to automatically calculate as you adjust the value for price. When the mar- ket is not at its equilibrium, the amount sold in the market will be the minimum of the quan- tity demanded and the quantity supplied. So to determine the quantity sold, use Excel’s MIN function, and set the cell reference to Qd and Qs. Set up Excel to calculate consumer surplus (CS), producer surplus (PS), and total surplus (TS) for you using the following formulas:

CS = .5*(Demand Intercept - Price)*Total Sold in Market PS = .5*Price*Total Sold in Market TS = CS + PS

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Once you have this set up, answer the following questions: 1. Start at a price of $3 per bushel, and increase

the price in $0.50 increments until you reach market equilibrium. What are the equilib- rium price and quantity?

2. What happens to the consumer, producer, and total surpluses as you increase the price from $3 to the equilibrium?

3. Now increase the price from the equilibrium by $0.25 two times. What happens to the market quantity and the consumer, producer, and total surpluses as you increase the price to a level higher than the equilibrium?

4. Do these results support the discussion in the text about overproduction, underpro- duction, and the efficient market quantity? Explain why or why not.

MyLab Economics Auto-Graded Excel Projects  85

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C H

A P

T E

R

3 Measuring and Using Demand Learning Objectives After studying this chapter, you will be able to

3.1 Explain the basics of regression analysis. 3.2 Interpret the results from a regression. 3.3 Describe the limitations of regression analysis and how they affect its use by managers. 3.4 Discuss different elasticity measures and their use. 3.5 Use regression analysis and the different elasticity measures to make better managerial

decisions.

Managers at the Gates Foundation Decide to Subsidize Antimalarial Drugs

The Bill and Melinda Gates Foundation (Gates Foundation) is the world’s largest philanthropic organization, with a trust endowment of nearly $40 billion. The foundation provides grants for education, medical research, and vac- cinations around the world. As of 2015, the foundation had made total grants of $37 billion. The goal of the Gates Foundation is not maximizing profit. Instead, its goal is to save lives and improve health in developing countries.

In 2010, the Global Fund to Fight AIDS, Tuberculosis and Malaria presented proposals to the Gates Foundation to subsidize antimalarial drugs in Kenya and other nations of sub-Saharan Africa. Although the Gates Foundation pro- vides nearly $4 billion in grants per year, there are more than $4 billion worth of competing uses for its resources. Consequently, before the managers accepted these proposals, they needed to determine their expected impact: How many people would these projects save compared to alternative uses of the funds? The managers

realized that lives hinged on their decision, so they wanted to be certain that they were getting the most value for their money.

The proposed subsidy programs would lower the price patients pay for the drugs. As you learned in Chapter 2, according to the law of demand, a decrease in the price of a product increases the quantity demanded. Antimalarial drugs are no exception; if their price falls, more patients will buy them. To make the proper decision about the proposals, however, the foundation’s manag- ers needed a more quantitative estimate: Precisely how many additional patients would buy the drugs when their prices were lower?

This chapter explains how to answer this and other questions that require quantitative answers. At the end of the chapter, you will learn how the Gates Foundation’s managers could forecast the number of patients they would help by subsidizing the drugs.

Sources: Karl Mathiesen, “What Is the Bill and Melinda Gates Foundation?” The Guardian. March 16, 2015; Gavin Yamey, Marco Schaferhoff, and Dominic Montagu, “Piloting the Affordable Medicines Facility-Malaria: What Will Success Look Like?” Bulletin of the World Health Organization, February 3, 2012, http://www.who .int/bulletin/volumes/90/6/11-091199/en; Erinstar, “Availability of Subsidized Malaria Drugs in Kenya,” Social and Behavioral Foundations of Primary Health Care Policy Advocacy, March 11, 2012, https://sbfphc.wordpress .com/2012/03/11/availability-of-subsidized-malaria-drugs-in-kenya-18-2.

86  

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3.1 Regression: Estimating Demand  87

Introduction According to the law of demand, when you raise the price of your product, the quantity your customers buy decreases. In some cases, this qualitative information is all you need to know, but in other cases, you need a more precise estimate. Your de- cision to raise the price of your product by 10 percent might depend on its impact on the quantity demanded: Will it decrease by 5 percent or by 20 percent? To make the best decision, you need more precise information about the demand for your prod- uct. Understanding how to obtain this information and what it means is important, but as a manager, knowing how to use it is even more important.

Chapter 3 features two important quantitative concepts: regression analysis and elasticity. Regression analysis (or, more simply, regression) is a statistical method used to estimate the relationship between two or more variables. Regression analysis can be used to estimate the coefficients of the demand func- tion, the a and b in the equation Qd = a - 1b * P2, or the coefficients of any other relationship. As a manager, you will probably not conduct the actual regression analysis, but you will quite likely rely on demand estimates from your marketing research department. This chapter will help you understand how to interpret those estimates and use the results of the regression to make predictions and forecasts that can be important for your business.

Sometimes you will not have the data necessary to use regression analysis. In those cases, you may be able to use elasticity to help predict consumer response to a change in your price. For instance, the price elasticity of demand will help you deter- mine whether your 10 percent price hike will decrease your sales by 5 percent or by 20 percent.

Regression and elasticity build on the concepts presented in Chapter 2 by allow- ing you as a manager to gain a more quantitative understanding of demand as well as other important relationships between key variables, such as cost and total pro- duction. To achieve these important goals, Chapter 3 includes five sections:

• Section 3.1 explains regression analysis, the most common technique for estimating rela- tionships such as those represented by a demand curve.

• Section 3.2 demonstrates how to interpret regression results, including how to calculate the range of values within which a regression coefficient is likely to fall, test the hypothesis that the value of a coefficient equals zero, and measure the fit of the regression.

• Section 3.3 describes weaknesses of regression analysis and how they affect its use. • Section 3.4 introduces the price elasticity of demand, income elasticity of demand, and

cross-price elasticity of demand, which deal with how strongly consumers respond to changes in the price of the product, income, and the price of a related good, respectively.

• Section 3.5 demonstrates how you can use regression analysis, price elasticity of de- mand, income elasticity of demand, and cross-price elasticity of demand to make better managerial decisions.

3.1 Regression: Estimating Demand Learning Objective 3.1 Explain the basics of regression analysis.

Chapter 2 illustrated a demand curve for jeans, described algebraically as

Qd = a - 1b * P2

Regression analysis A statistical method used to estimate the relationship between two or more variables.

Elasticity A measure of the responsiveness of the demand for a product to a change in a factor affecting the demand.

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88  CHAPTER 3 Measuring and Using Demand

In Figure 2.1 in Chapter 2, the linear demand curve was used to calculate that the coefficient a was equal to 600 million pairs of jeans and that the coefficient b was equal to 5 million pairs of jeans per dollar. The negative sign in the equation reflects the law of demand: A higher price reduces the quantity demanded. As a manager, however, you will never be given a figure with a linear demand curve for use to compute these values. Instead, you must use data on the quantity sold and the price charged to calculate the best estimates for the coefficients. The method used to make these estimates is regression analysis. Regression is used to estimate the coefficients of a demand function as well as many important eco- nomic relationships, such as the relationship between a firm’s quantity and its cost. Studying the details of regression will help you understand the strengths and weaknesses of reports submitted to you and thereby help you make better decisions.

The Basics of Regression Analysis The Capital Grille is a chain of upscale steak restaurants. Suppose that you are an upper-level executive working for a similar chain. To make better decisions, you want to know the demand for your company’s dinners. Assume that the demand function for steak dinners at your restaurants can be written as

Qd = a - 1b * P2 where Qd is the dependent variable we are predicting and P is the independent variable, also called the explanatory variable. This is a univariate equation because there is only one independent variable. Adding other independent variables that affect customer demand, such as income or the price of a related good, transforms a univariate equation into a multivariate equation because it includes more than one independent variable. We use the simpler univariate case to explain regression analysis because the more complicated—and probably more realistic—multivariate case is similar. The goal of regression analysis is to estimate the coefficients of the demand function, a and b in the equation we are using, so that we can find how the dependent variable, Qd, changes when the independent variable(s) change(s).

The demand equation in this example has only one independent variable, the price of a dinner (P). Even if you included many other independent variables, however, you would not be able to precisely replicate the quantities demanded. There always will be some error because there are inevitably random elements in demand that you cannot capture. For example, a particularly severe snowstorm might lead some consumers to eat at home rather than drive to the restaurant. Alternatively, the popularity of dining at this restaurant chain might skyrocket af- ter a popular rap artist mentions it in an interview. Because these factors occur randomly, you will never be able to accurately capture their impact on the demand for dinners. So you add a random error term to the demand equation to account for the randomness and get

Qd = a - 1b * P2 + h where h is the random error term. You will never know for sure what h equals. But assume that h is random, has a mean (average) of zero, and is normally distributed, which means it has the usual bell-shaped distribution that you have undoubtedly seen for variables such as weight or height.

Your goal of obtaining the best estimates for the coefficients a and b now must take into account the random error term. If you knew that the error term was always zero, so that a - 1b * P2 always equaled Qd, the restaurant chain’s managers could set different prices at a few of its locations and collect data on the quantity of dinners

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3.1 Regression: Estimating Demand  89

sold. They could then plot quantities and prices in a standard demand and supply graph and determine the a and b coefficients from the straight line plotted—a would equal the horizontal intercept, and b would equal the inverse of the slope, as shown in Figure 2.1 in Chapter 2.

The presence of the random error term complicates your task. For example, Figure 3.1 shows 21 hypothetical data points for the price and quantity of steak din- ners demanded at your restaurants. You can obtain these types of data by setting different prices at different locations and then collecting data over several months on the average quantity of dinners sold each day.

The random element of demand makes it impossible to draw a straight line connecting the scattered points. Even so, Figure 3.1 shows that the points lie around a negatively sloped straight line, which would be the demand curve. However, it is possible to draw many lines through this cluster of points. Each line would give slightly different estimates of the a and b coefficients and there- fore different estimates of the demand function, Qd = a - 1b * P2. Using only Figure 3.1, we cannot determine which of these lines best approximates the actual demand curve.

Regression Analysis Regression analysis gives estimates for the a and b coefficients—say, an and bn —thereby choosing one of the many lines through the data points. But which line should it select? Intuitively, the line that is closest to the data points seems desirable—that is, the line that makes the difference between the actual quantities, Qd, and the predicted quantities—say, Qd—as small as possible. Using the actual prices and the estimated an and bn coefficients in the demand function will give the predicted quantities, Qd = an - 1bn * P2. The differences between the actual quantities and the predicted quantities, Qd - Qd, are called the residuals. The goal of regression is to make the resid- uals as small as possible.

8

8

8

Figure 3.1 Price and Quantity Data for Dinners

The figure plots the price of dinners and the quantity demanded per day at different restaurants in the chain. Because there is a random element to demand, the points on this scatter diagram do not fall precisely on a straight line; however, the data do cluster around a negatively sloped straight-line demand curve.

Price (dollars per dinner)

Quantity (dinners per day)

$75

$45

$50

1,1001,000900800700600500

$55

$60

$65

$70

0

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90  CHAPTER 3 Measuring and Using Demand

There are various ways of minimizing the residuals. The most common regres- sion technique is ordinary least squares (OLS) regression. OLS regression locates the line through the scatter of data points that minimizes the sum of the squared resid- uals between the actual quantities and the predicted quantities. We called the ac- tual random term h, so let’s call the estimated residual for the first quantity hn1, for the second quantity hn2, and so forth. OLS regression minimizes the sum of the squared residuals. Figure 3.1 includes 21 data points, so the sum of the squared residuals OLS minimizes is

hn21 + hn22 + hn23 + Á + hn221 You can use one of many statistical programs to calculate the regression coeffi-

cients, an and bn . Microsoft Excel can perform OLS regressions. Other statistical soft- ware programs go further, allowing calculation of even more sophisticated regressions. We’ll restrict ourselves to OLS regression because that is by far the most commonly used technique in business. Let’s use Microsoft Excel 2013 to demonstrate how to calculate the OLS regression line for the 21 data points in Figure 3.1, so that you can see and interpret the reported results.

The first step in using Microsoft Excel is to click the “Data” tab. Then make sure the “Data Analysis” icon is present (see the arrow in Figure 3.2). If the icon is not present, follow the instructions in Figure 3.2 to install it.

To conduct the regression, start by entering the data. Use two columns in your spreadsheet. Label the first “Quantity” and the second “Price.” Next, enter the data. First, enter the dependent variable, quantity. Then enter the independent variable, price. Figure 3.3 illustrates this process for the data in Figure 3.1 about the price and quantity of steak dinners at your restaurant chain. Once you have entered all the data,

1. Click the “Data” tab and then the “Data Analysis” icon. 2. When the “Data Analysis” box pops up, highlight the “Regression” entry, and

click “OK.”

Figure 3.2 Microsoft Excel: The Data Analysis Icon

The “Data Analysis” icon (see the arrow) is necessary to conduct regression analysis using Microsoft Excel. If the icon is missing, you must install the Analysis ToolPak, an add-in included in Excel. To install the Analysis ToolPak:

• Click on the “File” tab. • Click on “Options.” • When the “Excel Options” window opens, click on “Add-ins.” • At the bottom of the “Add-ins” screen, click “Go.” • Find the “Analysis ToolPak” box, check it, and click “OK.”

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3.1 Regression: Estimating Demand  91

Figure 3.3 Microsoft Excel: Entering Data

The dependent variable is entered in column A under the heading “Quantity.” The independent variable is entered in column B under the heading “Price.”

3. The “Regression” box, which enables you to specify the range of data you want to use and where you want to display the results, will pop up. For the data you are using, complete the “Regression” box as illustrated and ex- plained in Figure 3.4.

4. In the “Regression” box, click “OK,” and Excel will estimate the regression.

The procedure just outlined estimates a univariate regression. Frequently, however, you will want to estimate a multivariate regression. For example, in- stead of price alone, you might want to explore whether the demand for dinners at your chain also depends on the price charged by Sea’s Harvest, a competitive upscale fish restaurant. So suppose that you also have data on the prices for a dinner at Sea’s Harvest for each of the 21 quantity/price observations given in Figure 3.3. In this case, you would enter the heading “Competitor Price” in cell C1 and the data on these prices directly below it. You now have two independent,

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92  CHAPTER 3 Measuring and Using Demand

or X, variables. Consequently, in the “Regression” box, you would specify the “Input X Range” as $B$1:$C$22, which is the new range for the independent vari- ables. Click “OK,” and Excel now estimates your multivariate regression.

Regression Results: Estimated Coefficients and Estimated Demand Curve Figure 3.5 shows the results from the univariate regression analysis of the data on price and quantity of steak dinners. Excel also includes a section of results enti- tled “Analysis of Variance (ANOVA).” Because we do not need this section for our regression analysis, it is not displayed in Figure 3.5. The results shown have been limited to two decimal places. Often analysts report the results with many more decimal places, but that is false precision.

Figure 3.4 Microsoft Excel: The “Regression” Box

The “Input Y Range” refers to the dependent variable, the quantity. The “Input X Range” refers to the independent variable, the price. For this example and these data, use the ranges shown. Be certain to include the cell with the title of the variable as part of the range. Also, check the “Labels” box as shown.

Figure 3.5 Microsoft Excel: Results of Regression

These are the results of the Excel regression using the data in Figure 3.1.

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3.1 Regression: Estimating Demand  93

The first result to note is the “Coefficients” column. The coefficient labeled “Intercept” is our an (recall that an is the horizontal intercept of the demand equation). The estimate from the regression is that an equals 1,999.82. This value for an means that the estimated demand curve crosses the horizontal axis at a quantity of 1,999.82 din- ners per day. The coefficient labeled “Price” is our bn (recall that bn is the coefficient that multiplies the price variable). Excel estimates that bn equals −20.04, which means that for every dollar increase in the price, consumers decrease the quantity of steak dinners they demand at your restaurant chain by 20.04 dinners per day. So, using these estimated coefficients, we find that the estimated demand curve is

Qd = 1,999.82 - 120.04 * P2 Figure 3.6 uses these coefficients to plot the estimated demand curve, labeled D,

and shows its relationship to the actual data points. Although the estimated de- mand curve is closer to some data points than to others, this demand curve mini- mizes the sum of the squared residuals between the actual quantities and the pre- dicted quantities.

As a manager, you can use the estimated demand curve for dinners at your restaurant chain to forecast the quantity of steak dinners demanded at different prices. For example, if you set a price of $62 per dinner, the estimated demand curve predicts that the quantity of dinners demanded is 1,999.82 - 120.04 * $622, or 757.3 dinners per day. This prediction represents a point on the estimated demand curve—specifically, the white point in Figure 3.6. The actual quantity for the price of $62 (from the data in Figure 3.3) is 793.4 dinners per day. The difference between the actual quantity and the predicted quantity, 793.4 dinners – 757.3 dinners = 36.1 dinners, is the estimated residual. This difference results from the effect of the random factors on the actual quantity.

Figure 3.6 An Estimated Demand Curve for Steak Dinners

The demand curve estimated using ordinary least squares regression is labeled D. The white dot shows that at the price of $62 per dinner, the predicted quantity of dinners demanded is 757.3.

Price (dollars per dinner)

Quantity (dinners per day)

$75

$45

$50

1,100

D

1,000900800700600500

$55

$60

$65

$70

0

Estimated demand curve

Predicted quantity for P 5 $62 is 757.3 dinners per day.

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94  CHAPTER 3 Measuring and Using Demand

As a manager, you need to know how to interpret the results from a regression. For example, you need to know how close the estimated coefficients are to the true coefficients. This topic is covered in the next section.

Regression Analysis at Your Steak Chain

You are an upper-level executive at an upscale steak restaurant chain. Suppose that you have the same data shown in Figure 3.3 but only for prices from $70 to $55 per dinner. Using those 17 data points of price/quantity, estimate a univariate regression, and use it to answer the following questions:

a. What are the estimated coefficients? What is the new estimated demand function?

b. Did the omission of the data points with prices from $54 to $50 per dinner make a large change in the estimated demand function?

Answer

a. The estimate from the regression is that an equals 1,990.48 and bn equals −19.90. The new estimated demand function is Qd = 1990.48 - 119.90 * P2.

b. Omitting the five data points did not lead to a large change in the estimated coeffi- cients. The estimated an changes from 1,999.82 to 1,990.48, a change of 0.5 percent, and the estimated bn changes from −20.04 to −19.90, a change of 0.7 percent. These changes are very small.

SOLVED PROBLEM

3.2 Interpreting the Results of Regression Analysis

Learning Objective 3.2 Interpret the results from a regression.

The estimated demand curve shown in Figure 3.6 might not be the same as the actual demand curve. In other words, the estimated coefficients from the univariate regression, an = 1,999.82 and bn = −20.04, might not be identical to the actual coeffi- cients. Of course, the same is true when your analysts estimate a multivariate regression. Consequently, before you use the estimated demand curve, you need to know how confident you are that the estimated coefficients are close to the true coefficients. Measuring that confidence is the first step in interpreting the results from a regression. Fortunately, the procedure used is the same for the coefficients from both multi variate and univariate regressions.

Estimated Coefficients The estimated coefficients from any regression depend on the data, which in turn depend in part on the random element of the demand. Consequently, reestimating the regression with new data means the estimated coefficients will change randomly because the new data will contain new values of the random element. For example,

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3.2 Interpreting the Results of Regression Analysis  95

if your analysts ran the same pricing experiment reported in Figure 3.3 a second time, setting the same 21 different prices at the same locations they used before, they would gather 21 new quantity data points which would differ from the original quantities due to the random fluctuations in demand. Your analysts could use these new data points to estimate a new regression. This new regression would have new estimates for an and bn that would differ from the initial estimates because of the ran- dom element. Indeed, if your chain ran this experiment a large number of times, you would wind up with a large number of estimates for an and bn . The large number of estimates would create a distribution that would allow you to use statistics to make inferences about the true values of a and b. But as a manager, you know it is simply not feasible to run this pricing experiment more than once, much less a “large number” of times!

Fortunately, such replication is unnecessary. If you look again at the regression results in Figure 3.5, you will see that next to the column for “Coefficients” is a col- umn labeled “Standard Error.” The standard error reflects the fact that the estimated coefficients have a random element. The standard error of a coefficient is a measure of how much the estimated coefficient is likely to change if another set of data is col- lected and another regression estimated. For example, the estimated coefficient for price, bn, is −20.04, with a standard error of 1.37. Compared to the coefficient esti- mate, this standard error is relatively small. A small standard error means that the change from reestimation of the regression probably will be small, which, in turn, means that the estimated coefficient is likely close to the true value. A large standard error, however, means that the change may be large, which suggests that the esti- mated coefficient might not be particularly close to the true value. You can go beyond this qualitative description of the effect of the size of the standard error to construct a range that for repeated samples has a pre-selected probability of con- taining the true value of the coefficient. For example, you can construct a range that will contain the true value of the coefficient 95 percent of the time. Such a range is called a confidence interval.

Confidence Intervals In randomized pricing experiments like the one we suppose that your restaurant chain conducted, OLS regression has a very nice statistical property: The esti- mated coefficients are unbiased, meaning that they are systematically neither greater than nor less than the actual true values. Moreover, the statistical proper- ties of OLS regression mean that if you gather many data samples and reestimate the regression many times, all the new estimated coefficients you obtain will cre- ate a range that is centered around the true value of the coefficients. These facts provide a starting point for the confidence interval. Because the estimated coeffi- cients from your regression are unbiased, they are your best estimate of the true value of the coefficients. Consequently, the range of the confidence interval will be centered around the estimated coefficients. For instance, if you are calculating a confidence interval for the b coefficient, the range of the confidence interval will be centered around −20.04, the estimated value bn from the regression.

The range for a confidence interval depends on two factors:

1. The size of the standard error. Because the standard error measures how much the estimated coefficient is likely to change with reestimation of the regression using a new data sample, the larger the standard error, the larger the possible change of the coefficient. It follows that the larger the standard error, the larger the confidence interval.

Confidence interval A range that for repeated samples has a pre-selected probability of containing the true value of the coefficient.

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96  CHAPTER 3 Measuring and Using Demand

2. How confident the manager wants to be that the range contains the true value of the coefficient. The more confident the manager wants to be, the larger the confidence interval. Conventionally, 95 percent or 99 percent is used as the desired level of confidence, though nothing prevents managers from using other levels. A 95 percent confidence level means that if the pricing experiment is run over and over, each time estimating the demand function regression, 95 percent of the time the confidence in- terval from any regression will contain the true value of the coefficient.

Analysts can use a statistical formula to calculate a confidence interval. Happily, however, most statistical software automatically calculates and reports the endpoints of the confidence interval. Excel automatically reports the two ends of the 95 percent confidence interval for the estimated coefficients, called “Lower 95%” and “Upper 95%.” For example, in Figure 3.5, the 95 percent confi- dence interval for bn runs from −22.92 to −17.17. This result means that you can be 95 percent confident that this range contains the true value of b. This range has an important managerial implication: You are 95 percent confident that in response to a dollar increase in price, your customers will decrease the quantity of dinners they demand by an amount that lies between 22.92 and 17.17 dinners per day.

Figure 3.5 also reports the two ends of the 95 percent confidence interval for the estimated intercept, an. In a multivariate regression with more than one independent variable, the statistical software will usually present the lower and upper ends of a confidence interval for each coefficient separately. Calculating a confidence region for two or more coefficients jointly requires a more sophisticated test, which is best covered in a class devoted to business statistics.

Hypothesis Testing Often you will be interested in the impact of a particular variable on your predic- tion. For example, we mentioned earlier that as a manager of a steak restaurant chain, you might be interested in determining whether the demand for steak dinners depends not only on the price you set but also on the price charged by Sea’s Harvest, the competing fish restaurant. Let’s suppose that a multivariate regression results in the estimated coefficient for the price of meals at Sea’s Harvest presented in Table 3.1.

The estimated coefficient, 8.04, is positive and indicates that a $1 increase in the price of a dinner at Sea’s Harvest increases the demand at your restaurant chain by 8.04 dinners per day. But the standard error of this coefficient is large compared to the coefficient, so the 95 percent confidence interval ranges all the way from −4.83 dinners per day up to 20.91 dinners per day. Given this broad range, you might wonder if the price charged at Sea’s Harvest actu- ally affects the demand for your steak dinners. In particular, if the true

Table 3.1 Results for an Estimated Coefficient for Meals at Sea’s Harvest

Coefficient Standard Error t Stat P-value Lower 95% Upper 95%

Competitor Price 8.04 6.12 1.31 0.21 −4.83 20.91

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3.2 Interpreting the Results of Regression Analysis  97

coefficient turns out to be zero (which is among the values included in the confi- dence interval), then the price charged at Sea’s Harvest has no effect on the de- mand for your steak dinners. In this case, as a manager you can ignore the price charged at Sea’s Harvest. So you want to know if the estimated coefficient— which is your best estimate of the true coefficient—is different from zero. Fortunately, there is a statistical test to determine whether an estimated coeffi- cient is significantly different from zero. This test, like all statistical tests, begins with two fundamental steps:

1. The test starts by posing the null hypothesis, which in this case is that “the true coefficient equals zero.” For example, as a manager at the steak chain, your null hypothesis is that in the demand for your meals, the true coefficient for Sea’s Harvest’s price is zero, in which case the price of fish dinners does not affect the demand for your steak dinners. If you reject (or “nullify”) the hy- pothesis that the true coefficient equals zero, then you have rejected the null hypothesis in favor of the alternative hypothesis, that the true coefficient is not equal to zero, so that the price of fish dinners affects the demand for your steak dinners.

2. You can never know for sure what the true coefficient equals, so there is some probability that you might draw the wrong conclusion. Accordingly, you must select how confident you want to be that rejecting (nullifying) the null hypothesis is the correct decision. The most common confidence levels are the same as those you saw before for confidence intervals, 95 percent and 99 percent. When you reject the null hypothesis at a confidence level of, say, 95 percent, you know that 95 percent of the time rejecting the null hy- pothesis is the correct decision. Of course, that means that 5 percent of the time you are making the incorrect decision—5 percent of the time the null hypothesis is correct, but you are rejecting it. The significance level of a test is the probability that you are making the wrong decision. For example, the 95 percent confidence level has a significance level of 1 – 0.95 = 0.05, or 5 percent.

In our restaurant example, you want to test the null hypothesis that the true value of the coefficient for the price of meals at Sea’s Harvest is zero. To do this, you use what is called a t test by calculating a measure called a t-statistic. The t-statistic equals the estimated coefficient divided by its estimated standard error.

Regression software, such as Excel, reports the t-statistic for each coeffi- cient. In Table 3.1, the competitive price coefficient for meals at Sea’s Harvest has a t-statistic of 1.31, calculated from 8.04/6.12. The t-statistic is positive if the estimated coefficient is positive, and it is negative if the estimated coeffi- cient is negative. The sign of the t-statistic is unimportant; what is important is its magnitude (absolute value). If the magnitude of the t-statistic is large, then the definition of the t-statistic shows that the estimated coefficient is large com- pared to its estimated standard error. In this case, the confidence interval is unlikely to include zero, so it is unlikely that the true coefficient equals zero.1

Significance level The probability of making the wrong decision, which is equal to 1 minus the confidence level.

t-statistic The estimated coefficient divided by its estimated standard error.

1 The t test is closely related to the confidence interval. If the 95 (99) percent confidence interval includes zero, the t test will not reject the null hypothesis that the true coefficient equals zero at the 95 (99) percent confidence level.

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98  CHAPTER 3 Measuring and Using Demand

So a large t-statistic leads you to reject the null hypothesis (that the true coeffi- cient equals zero) in favor of the alternative hypothesis (that the true coefficient is not zero).

How large must the t-statistic be to reject the null hypothesis? Statisticians have calculated the probability of each value of the t-statistic when the null hypothesis is true. This distribution provides the critical value of the t-statistic—that is, the value of the t-statistic above which the null hypothesis is rejected.

The critical value depends on the confidence level, with a higher confidence level (a lower significance level—that is, a lower probability of error) leading to a larger critical value. The critical value also depends on the number of obser- vations, but it does not change much once there are more than 40 or 50 observa- tions. For a large number of observations, the 95 percent confidence level (the 5 percent significance level) has a critical value of 1.96. (For the 99 percent con- fidence level, the critical value is 2.58.) If the computed value of the t-statistic exceeds 1.96, you can reject the null hypothesis, knowing that you are making the correct decision at least 95 percent of the time.

In Table 3.1, the computed value of the t-statistic is 1.31, which is below the 95 percent confidence level critical value, so you cannot reject the null hypothesis. Instead, you retain the null hypothesis that the true coefficient is zero, which means that the price of meals at Sea’s Harvest has no effect on the demand for steak dinners at your restaurant chain. Contrast this result with the t-statistic for the price coeffi- cient (the bn ), reported in Figure 3.5 as −14.59. The absolute value of the t-statistic, 14.59, is well above the 95 percent confidence level critical value of 1.96, so you can easily reject the null hypothesis in favor of the alternative hypothesis that the true coefficient is not zero.

Table 3.1 (along with Figure 3.5) reports one other result: the P-value. Assuming that the null hypothesis is correct (the true coefficient equals zero), the P-value is the probability in repeated samples of obtaining a value of the t-statistic equal to or larger than the computed t-statistic reported in the results. Table 3.1 shows that when the t-statistic is 1.31, the P-value is 0.21, or 21 percent. So even when the true coefficient equals zero, if you repeatedly re-estimated the regression each time using new data you gather, 21 percent of the time the computed t-statistic would be 1.31 or larger. If you rejected the null hypothesis that the true coefficient is zero based on a t-statistic equal to 1.31 or larger, you would be making an error 21 percent of the time. So, the P-value is equal to the significance level of testing the null hypothesis; that is, it is equal to the probability of erroneously rejecting the null hypothesis. Conventionally, users reject a null hypothesis when the significance level is 0.05 (5 percent) or less, which makes the confidence level 0.95 (95 percent) or more. Only when the P-value is 0.05 or less should you reject the null hypothesis in favor of the alternative hypothesis that the coefficient is not zero.

The P-value is useful because it gives you finer detail than the t-statistic about how strongly you reject (or do not reject) a hypothesis. The results of a t-statistic are usually reported simply as “reject” or “do not reject” and that is it. Returning to Figure 3.5 dealing with the univariate demand function for steak dinners, you see that the estimated coefficient for the price of a steak dinner has a P-value so small that it is rounded to 0.00 (0 percent). In other words, there is virtually a 0 percent chance you are making a mistake by rejecting the null hypothesis that the true coefficient is zero. In this case, you can very confidently reject the null hypothesis, which means you can be very confident that the price of a steak dinner affects the quantity of steak dinners demanded.

Critical value The value of the t-statistic above which the null hypothesis is rejected.

P-value Assuming the null hypothesis is true, the probability in repeated samples of obtaining a value of the t-statistic equal to or larger than the computed t-statistic.

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3.2 Interpreting the Results of Regression Analysis  99

The following box summarizes guidelines for interpreting regression coefficients.

t test If the magnitude of the t-statistic is larger than the critical value:

• Reject the null hypothesis that the true value of the coefficient equals zero.

• Accept the alternative hypothesis that the true value of the coefficient is nonzero.

If the magnitude of the t-statistic is less than the critical value:

• Fail to reject (accept) the null hypothesis that the true value of the coefficient equals zero.

P-value If the P-value is less than the significance level (typically 0.05 or 0.01):

• Reject the null hypothesis that the true value of the coefficient equals zero.

• Accept the alternative hypothesis that the true value of the coefficient is nonzero.

If the P-value is larger than the significance level (typically 0.05 or 0.01):

• Fail to reject (accept) the null hypothesis that the true value of the coefficient equals zero.

TESTING REGRESSION COEFFICIENTS

Fit of the Regression In addition to establishing your confidence in the values of the regression coefficient, you may want to know how accurate the regression is overall—that is, how close the predicted values are to the actual data points. For the estimated demand curve shown in Figure 3.7(a), you can see that the predicted values (the points on the esti- mated demand curve) are close to the actual data points. The estimated demand curve shown in Figure 3.7(b) is not particularly close to the data points, so the pre- dicted values are not close to the actual values. Is it possible to measure how well the regression fits the data? The answer is yes: One of the results reported by Excel in Figure 3.5 provides a measure of the fit between the regression and the data. The R2 statistic (R-squared statistic), more commonly called simply R2 (R squared), is a measure of how much of the variation in the observed values of the dependent variable is captured by the predicted values of the regression. Specifically, R2 is the fraction of the data points’ variation accounted for by the regression’s predicted val- ues. It ranges from 1.00 (100 percent) to 0.00 (0 percent). The closer R2 is to 100 per- cent, the more closely the predicted values fit the actual data.

The R2 statistic for the demand curve in Figure 3.7(a) is 0.92. The predicted val- ues from the regression account for 92 percent of the variation in the observed values of the dependent variable, which indicates a very good fit. The R2 statistic for the demand curve in Figure 3.7(b) is 0.52. The predicted values from this regression ac- count for only 52 percent of the variation in the observed values of the dependent variable, which indicates a poorer fit.

R2 statistic A measure of how much of the variation in the observed values of the dependent variable is captured by the predicted values of the regression.

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100  CHAPTER 3 Measuring and Using Demand

Confidence Intervals and Predictions for the Demand for Doors

You are a manager of a company similar to Pella Corporation, a producer of high-quality doors and windows. The members of your marketing group give you the results of their research into the demand for your company’s doors. They report that the estimated coefficient for the effect of price on the demand for doors is -700 doors per dollar, with a standard error of 200 doors per dollar and a 95 percent confidence range of -1,092 doors per dollar to -308 doors per dollar. a. Is the estimated coefficient significantly different from zero at the 95 percent confi-

dence level? Explain your answer.

b. If you raise the price of a door by $10, what decrease in quantity do you expect? Using the 95 percent confidence interval, what would be the largest decrease in quantity? The smallest?

SOLVED PROBLEM

Figure 3.7 Fit of Estimated Demand Curves

(a) Demand Curve with a High R 2

The estimated demand curve, D, is close to the data points, so it has a higher R2 statistic.

(b) Demand Curve with a Low R 2

The estimated demand curve, D, is not close to the data points, so it has a lower R2 statistic.

Price (dollars per dinner)

Quantity (dinners per day)

$75

$45

$50

1,100

D

900700500 1,000800600

$55

$60

$65

$70

0

Estimated demand curve

Price (dollars per dinner)

Quantity (dinners per day)

$75

$45

$50

1,100

D

900700500 1,000800600

$55

$60

$65

$70

0

Estimated demand curve

When you receive a report based on regression analysis, you must be con- cerned with R2. If it is small—say, 0.12 (12 percent)—you need to be aware that the predicted values do not capture much of the variation in the actual values of the dependent variable. In other words, the predicted values are not particularly close to the observed, actual values. If R2 is large—say, 0.88 (88 percent)—you can be more confident in the results because the predicted values are close to the observed, actual values.

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3.3 Limitations of Regression Analysis  101

3.3 Limitations of Regression Analysis Learning Objective 3.3 Describe the limitations of regression analysis and how they affect its use by managers.

When you receive a report including analysis based on a regression equation, you need to know the potential limitations of the regression. We will discuss two possi- ble weaknesses: (1) the specification of the regression—that is, which variables are included; and (2) its functional form—that is, how the variables are entered in the function the analyst estimated.

Specification of the Regression Equation Whenever you examine regressions you must always consider whether they include all of the relevant factors. If not, you should view the results and analysis with at least a touch of skepticism. For example, as a manager at your high-end steak restaurant chain, you might receive a regression analysis from your market research team, using data accumulated over 21 years, that shows how the price of a steak dinner affects the quantity of steak dinners demanded. Price is the only independent variable, so the regression equation is similar to what you have already seen, Qd = a - 1b * P2. In the last section, the research department collected the data at several locations at a single point in time. In the current case, the data have been accumulated over more than two decades. Because the data cover 21 years, a long period of time, another relevant variable that affects consumer demand is surely missing: their incomes. As you learned in Chapter 2, income is a factor that affects demand, and income has definitely changed over the last 21 years. Omitting this important variable could result in a low R2, which means predictions using the equation might not be very accurate. Its omission might also bias the estimated price coefficient because, if both price and income have been trending higher over the past 21 years, then the price coefficient could be capturing both the effect of changes in price and also the effect of changes in income. Because analysts may be able to obtain income data, you should probably return the report to the market research team with a request to include income as an additional independent variable in the regression.

Unlike income, some potentially relevant variables are simply not measurable. For example, there may have been a couple of years during the 21-year period when there was a substantial scare about mad cow disease, an untreatable and fatal disease that attacks the brain. If enough consumers believed that they might catch mad cow disease by eating steaks, their preferences would have changed, decreasing the demand for steak dinners. Perfectly measuring this type of change in preferences is

Answer

a. The estimated coefficient is significantly different from zero because the magnitude of its t-statistic, which equals 700>200 = 3.5, easily exceeds the critical value of 1.96.

b. Using the estimated coefficient, you expect the increase in price to change the quantity demanded by -700 doors * $10 = -7,000 doors. Using the range of the 95 percent confidence interval, the largest decrease would occur if the coefficient equaled -1,092 doors, in which case the decrease in quantity demanded would be 1,092 doors * $10 = 10,920 doors. The smallest decrease in the quantity demanded would occur if the coefficient equaled −308 doors, in which case the decrease in quantity demanded would be 308 doors * $10 = 3,080 doors.

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102  CHAPTER 3 Measuring and Using Demand

impossible. In the short run, the only course of action is to omit this variable and hope that its omission does not have a large effect on the results. In the long run, it might be possible to accumulate more data for years not affected by this factor and ultimately omit from the regression analysis those years that could be anomalous.

Functional Form of the Regression Equation So far, all of the figures showing price and quantity data points for steak dinners have strongly suggested a straight-line demand curve. But what if the price and quantity data points looked like those in Figure 3.8? In this case, you might suspect that the true demand curve is not a straight line because the data points seem to lie around a con- vex (bowed inward) curve. Analysts can use various transformations of the data to account for the nonlinearity of a demand curve. One of the most common is to take the natural logarithms of both the price and the quantity data and then assume that the true demand curve is linear in the natural logarithms, a specification called log-linear:

ln Qd = a - 1b * ln P2 + h where ln Qd is the natural logarithm of the quantity, ln P is the natural logarithm of the price, a and b are coefficients, and h is the random error term. This functional form results in a demand curve with an inward bow, as illustrated in Figure 3.8. For a log-linear demand curve, the regression is estimated using the transformed data series ln Qd for the dependent variable and the transformed data series ln P for the independent variable. Figure 3.9 illustrates the estimated demand curve that results from this regression.

Figure 3.9 shows that a log-linear specification yields a demand curve that can fit the convex shape of the data points. The log-linear specification has an additional advantage: When the data are in logarithms, the estimated bn coefficient is equal to the price elasticity of demand, a concept you will learn about in the next section. For now, you just need to know that this result can be useful.

The predictions from the log-linear regression are for ln Qd. However, the result usually desired is Qd; that is, you want to know the predicted quantity, not

8

8

Figure 3.8 Alternative Data for Steak Dinners

The data points in this scatter diagram of an alternative data set for the price of dinners and the quantity demanded per day do not seem to cluster around a negatively sloped straight-line demand curve.

Price (dollars per dinner)

Quantity (dinners per day)

$75

$45

$50

1,1001,000900800700600500

$55

$60

$65

$70

0

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3.3 Limitations of Regression Analysis  103

its logarithm. Mathematically, you can change the logarithm of a number to the number itself by raising e to the logarithm of the number. So to obtain Qd itself, it is common to use elnQd. For reasons dealing with the statistics of the error term, this procedure is an approximation, but any error is usually small and therefore is typi- cally ignored.

The examples of regression we have used all focus on estimating the demand function. But regression is used for much more than simply estimating demand functions. For example:

• Every 5 to 10 minutes, at the front of each popular attraction, The Walt Disney Company posts estimated wait times for the attraction. Regression is used to help forecast these wait times.

• The Portland Trailblazers have used a sophisticated type of regression to help forecast the probability that college basketball players will have successful NBA careers.

• Schneider Logistics, a part of the large transportation company Schneider National, uses regression models to help predict the profitability of different freight flows.

Clearly, regression analysis plays an important role in many aspects of many dif- ferent businesses.

Using regression to estimate the coefficients of the demand for your product results in precise estimates of how much consumers respond to changes, enabling you to make better decisions about pricing and production. There will be times, however, when you do not have enough data to use regression analysis to estimate the demand for your product. In other situations, you might want precise estimates of, say, the effect of a change in supply on the price you must pay for an input, and again you may not have enough data to estimate a regression. In these and other cases, another tool, called elasticity, sometimes can provide the valuable informa- tion you need.

8

8

Figure 3.9 Estimated Nonlinear Demand Curve

A nonlinear (log-linear) demand curve best fits the data points in Figure 3.8.

Price (dollars per dinner)

Quantity (dinners per day)

$75

$45

$50

1,100

D

1,000900800700600500

$55

$60

$65

$70

0

Estimated demand curve

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104  CHAPTER 3 Measuring and Using Demand

SOLVED PROBLEM Which Regression to Use?

Your research department gives you the following two estimated demand curves. The estimated demand curve to the left is log-linear, and the estimated demand curve to the right is linear.

Price (dollars per dinner)

Quantity (dinners per day)

$75

$45

$50

1,100

D

1,000900800700600500

$55

$60

$65

$70

0

Price (dollars per dinner)

Quantity (dinners per day)

$75

$45

$50

1,1001,000900800700600500

$55

$60

$65

$70

0

D

a. Which regression do you think has the highest R2—the one with the log-linear speci- fication or the one with the linear specification? Explain your answer.

b. Are the predicted quantities from one demand curve always closer to the actual quantities than the predicted quantities from the other demand curve?

c. Which estimated demand curve would you use to make your decisions? Why?

Answer

a. The log-linear specification is closer to more of the data points than the linear speci- fication. So the R2 of the log-linear specification exceeds that of the linear specification.

b. Even though the predicted quantities from the log-linear specification are closer to most of the actual quantities, there are a few predicted quantities that are closer when using the linear specification. In particular, for prices of $67 and $64, the pre- dicted quantities from the linear specification are closer to the actual quantities than the predictions from the log-linear specification.

c. As a manager, you want to base your decisions on the most accurate information possible. The log-linear specification has the higher R2, which means that it does a better job of capturing the variation in the actual quantities than does the linear specification. Consequently, you should use the log-linear specification as the basis for your decisions.

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3.4 Elasticity  105

3.4 Elasticity Learning Objective 3.4 Discuss different elasticity measures and their use.

At its most basic level, elasticity measures responsiveness: How strongly does the quantity demanded of a product respond to a change in one of the factors affecting demand? This section describes elasticity for three of these factors: the price of the product, income, and the price of a related good. Elasticity gives a quantitative mea- sure of the strength of the demand response to all three factors.

The Price Elasticity of Demand The most fundamental elasticity is the price elasticity of demand. The price elasticity of demand measures how strongly the quantity demanded changes when the price of the product changes—it measures the movement along a demand curve resulting from a change in the price. More specifically, the price elasticity of demand (e) is the absolute value of the percentage change in the quantity demanded divided by the percentage change in the price:

e = ` Percentage change in quantity demanded Percentage change in price

` 3.1

Recall that, according to the law of demand, whenever the price of a product rises, the quantity demanded falls, and whenever the price falls, the quantity demanded rises. So in the formula the sign of one of the changes is always positive and that of the other is always negative. Because the resulting elasticity would always be nega- tive, it is common to take the absolute value to eliminate the negative sign.2

The percentage change in the quantity demanded is (∆Qd>Qd2 * 100, where the ∆ means “change in.” The percentage change in price is 1∆P>P2 * 100. Combining these shows that the price elasticity of demand equals

e = ` 1∆Q d>Qd2 * 100

1∆P>P2 * 100 ` = ` 1∆Qd>Qd2 1∆P>P2 ` 3.2

Why does the price elasticity of demand use percentages? For a linear demand curve, such as Qd = a - 1b * P2, it might seem more logical to use the estimated value of b as the measure of elasticity because, as you learned in Chapter 2, b tells you how much the quantity demanded changes in response to a $1 change in the price. For example, the estimated demand function for steak dinners at your restaurant chain had an estimated value for bn of −20.04, which meant that a $1 increase in the price of a steak dinner decreased the quantity demanded by approximately 20 dinners per night. But suppose that you were interested in the decrease per week rather than the decrease per day. In that case, you would estimate the demand function using quantity data accumulated for seven days rather than for a single day. With this change, a $1 increase in the price decreases the quantity of steak dinners demanded (for the week) by approximately 140 dinners per week. The estimated value of bn would increase sevenfold, to 7 * −20.04, or −140.28. If you used bn as your measure of elasticity, you would see that it changed by merely switching the quantity from daily demand to weekly demand. Indeed, any change in the units of quantity or price af- fects the estimated value of bn. If your chain of steak restaurants had locations in

Price elasticity of demand A measure of how strongly the quantity demanded changes when the price changes, equal to the absolute value of the percentage change in the quantity demanded divided by the percentage change in the price.

2 Some sources, however, retain the negative sign. In those cases, you can convert the elasticities you find there to the elasticity we discuss by dropping the negative sign.

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106  CHAPTER 3 Measuring and Using Demand

England, the estimated value of bn for the U.K. demand function would be different from that of the U.S. demand function simply because the price in the United Kingdom is measured in pounds and the price in the United States is measured in dollars even if the response to a $1 change in the price is identical for the two demand functions.

To avoid the problems of using a measure of elasticity that changes with the units, economists have defined the price elasticity of demand using percentages because percentages do not change when the units change.

Using the Price Elasticity of Demand Equation 3.1 enables you to calculate the price elasticity of demand using information on the percentage change in the quantity demanded and the percentage change in the price. For instance, if a 10 percent increase in the price of a good leads to a 5 percent decrease in the quantity demanded, the price elasticity of demand for the good equals

` -5 percent 10 percent

` = 0.5

Equation 3.1 can also be rearranged to calculate (or predict) the percentage change in the quantity demanded that results from a percentage change in the price or the percentage change in the price that results from a percentage change in the quantity. For example, suppose that at your steak restaurants you determine the price elasticity of demand for steak dinners is 1.3 and the price of a dinner rises by 6 percent. What does the decrease in the quantity of dinners demanded equal? To answer this question, rearrange the formula for price elasticity of demand to isolate the percentage change in the quantity demanded:

e * 1Percentage change in price2 = 1Percentage change in quantity demanded2 3.3 Using the value for the price elasticity of demand and the percentage change in the price in Equation 3.3, the percentage change in the quantity demanded will be 1.3 * 6 percent = 7.8 percent. With the knowledge that you will sell 7.8 percent fewer dinners, you can now make better managerial decisions.

In addition to your steak dinners, suppose that your restaurants also serve chicken. Because of lower food costs for chicken, suppose that analysts predict the quantity of chicken will increase by 10 percent. The price elasticity of demand for chicken is approximately 0.4. Managers at your restaurant chain will be interested in how much the price of chicken will fall with the increase in quantity. Once again, you can use the equation for price elasticity of demand to forecast the fall in the price. This time you rearrange the equation to isolate the percentage change in price:

1Percentage change in price2 = 1Percentage change in quantity2 e

In the rearranged equation, two changes have been made:

• The calculation uses the percentage change in the quantity rather than the per- centage change in the quantity demanded. This change reflects the fact that at equilibrium the percentage change in the quantity demanded must equal the percentage change in the quantity.

• Because you already know that an increase in the quantity lowers the price, there is no negative sign in the percentage change in price term.

You can combine the rearranged equation with the elasticity and the predicted change in quantity to predict that the percentage fall in the price will be 10 percent/0.4 = 25 percent. This information is valuable to managers of the chain

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3.4 Elasticity  107

because it helps them make better decisions about potential menu specials—featuring more dishes with chicken might increase profit!

Elasticity Along a Linear Demand Curve Rearranging the formula for the price elasticity of demand from Equation 3.2, e = |1∆Qd>Qd2 >1∆P>P2|, helps demonstrate a possibly unforeseen result in the behavior of the price elasticity of demand at different points along a linear, down- ward-sloping demand curve:

e = 4 ∆QdQd ∆P P

4 = ` ∆Qd Qd

* P ∆P

` = ` ∆Q d * P

Qd * ∆P ` = ` ∆Q

d * P ∆P * Qd

` = ` ∆Q d

∆P *

P Qd

`

In this string of equalities, the second equality reflects the division of ∆Qd>Qd by ∆P>P; the third equality is the result of multiplying the two fractions; the fourth equality switched the terms in the denominator; and the last equality breaks the fraction into two components. In the last expression, |1∆Qd>∆P2 * 1P>Qd2|, the term 1∆Qd>∆P2 is the change in the quantity demanded brought about by a $1 change in the price. Sound familiar? In the algebraic equation for the linear demand function you have been using, Qd = a - 1b * P2, the coefficient b is the change in the quantity demanded brought about by a $1 change in the price. So in the last expression, substi- tute the coefficient b for the 1∆Qd>∆P2 term to show that for a linear demand curve3

e = |b * 1P>Qd2| 3.4 You can use Equation 3.4 to calculate the price elasticity of demand at any one point

on a linear, downward-sloping demand curve, so Equation 3.4 is called the point elasticity formula. In Figure 3.10, a linear demand curve showing the price and quantity of

3 Section 3.A of the Appendix at the end of this chapter uses calculus to derive a general version of Equation 3.4 for any demand function.

Figure 3.10 Price Elasticity of Demand Along a Linear Demand Curve

The point elasticity formula, e = |b * 1P>Qd2|, can be used to calculate the price elasticity of demand at each of the points on a linear demand curve. On a linear, downward-sloping demand curve, the price elasticity of demand falls in value moving down the curve.

Price (dollars per baseball cap)

Quantity (baseball caps per day)

$35

$5

$10

70 D

605040302010

$15

$20

$25

$30

0

B

A

e 5 5.0

e 5 2.0

e 5 1.0

e 5 0.5

e 5 0.2 e . 1

e 5 1

e , 1

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108  CHAPTER 3 Measuring and Using Demand

baseball caps, the price elasticity of demand can be calculated at any of the points on the demand curve. The value of b for the demand curve illustrated in the figure is −2 base- ball caps per dollar. Using the point elasticity formula, you find that at point A on the demand curve, the elasticity equals � -2 * 1$20>202 � = 2.0. And at point B, the elastic- ity is � -2 * 1$10>402 � = 0.5. Equation 3.4 and Figure 3.10 show a remarkable result: The price elasticity of demand changes with movements along the linear demand curve. In particular, moving downward along the demand curve, the price elasticity of demand falls in value. At the midpoint of the demand curve, the price elasticity of demand equals 1.0. At points above the midpoint, it exceeds 1.0, and at points below the midpoint, it is less than 1.0. As a manager, keep in mind that the price elasticity of demand will be different at each point on a linear demand curve. If your decision revolves around a certain price, you must be certain that you use the elasticity at that price.

You can also use Equation 3.4 to calculate the elasticity at points on an estimated demand curve. Assuming that the demand curve is linear, the regression analysis gives Qd = an - 1bn * P2, where bn is the estimated value of the b coefficient and Qd is the predicted quantity demanded. Then for any price (P), you can use the estimated value of bn and the predicted quantity demanded, Qd, in Equation 3.4 to calculate the estimated value of the price elasticity of demand at that point on the demand curve:

en = � bn * 1P>Qd2 � 3.5

Elasticity Along a Log-Linear Demand Curve Calculating the price elasticity of demand for a log-linear demand curve, ln Qd = a - (b * ln P), is immediate: The elasticity equals the value of the b coeffi- cient. Refer to the Appendix at the end of this chapter to see a proof of this result using calculus. In Figure 3.11, the b coefficient for the illustrated demand curve for baseball caps is −1.00, so the price elasticity of demand equals 1.00 at points A and B. In fact, at all points on this demand curve, the price elasticity of demand is equal to 1.00. Demand curves for which the price elasticity of demand is the same at all points are called constant elasticity of demand curves.

88

8

8

Figure 3.11 Price Elasticity of Demand Along a Log-Linear Demand Curve

The price elasticity of demand is constant at all points along a log-linear demand curve.

Price (dollars per baseball cap)

Quantity (baseball caps per day)

$35

$5

$10

70

DB

A

605040302010

$15

$20

$25

$30

0

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3.4 Elasticity  109

If a log-linear demand curve has been estimated, such as ln Qd = an - 1bn * ln P2, the estimated price elasticity of demand is bn and is the same at all points on the esti- mated demand curve.

Elastic, Unit-Elastic, and Inelastic Demand The price elasticity of demand measures how strongly demanders respond to a change in the price of the good. For example, economists have estimated the price elasticity of demand for coffee to be 0.25. Rearranging the formula for the price elas- ticity of demand,

e = ` Percentage change in quantity demanded Percentage change in price

`

shows that

e * (Percentage change in price) = (Percentage change in quantity demanded)

Using the rearranged formula, if the price of coffee rises by 10 percent, you can calcu- late that the percentage change in the quantity of coffee demanded is 0.25 * 10 per- cent = 2.5 percent. In other words, a 10 percent increase in the price of coffee leads to a 2.5 percent decrease in the quantity of coffee demanded. In contrast, economists have estimated the price elasticity of demand for Pepsi to be 1.55. If the price of Pepsi rises by 10 percent, then the quantity of Pepsi demanded decreases by 1.55 * 10 percent = 15.5 percent. There is a significant difference between the strength of the consumer response to a change in the price of coffee and the consumer response to a change in the price of Pepsi. The definitions of elastic demand, unit-elas- tic demand, and inelastic demand formalize this difference.

Elastic demand means that consumers respond strongly to a change in price. For a product with elastic demand, the percentage change in the quantity demanded exceeds the percentage change in the price, so the definition of the price elasticity of demand shows that it is greater than 1.00. Using this definition, we see that the de- mand for Pepsi is elastic.

Unit-elastic demand means that consumer response to a change in price is one- to-one; that is, a 10 percent increase in the price creates a 10 percent decrease in the quantity demanded. In this case, the definition of elasticity shows that the price elas- ticity of demand is equal to 1.00.

Inelastic demand means that consumers respond weakly to a change in price. The percentage change in the quantity demanded is less than the percentage change in the price, so the price elasticity of demand is less than 1.00 for a product with in- elastic demand. Using this definition, we see that the demand for coffee is inelastic.

When two demands have different elasticities, how is the difference reflected in their demand curves? Figure 3.12 answers this question for the case in which two demand curves cross. Starting from point A, the figure shows that in response to a $5 increase in the price of baseball caps, the decrease in the quantity demanded along demand curve D2 (20 caps) exceeds the decrease in the quantity demanded along demand curve D1 (5 caps). This difference in response means that the elasticity on demand curve D2 at point A is larger than the elasticity on demand curve D1 at point A. This result is precisely in line with the intuitive meaning of elasticity as responsiveness: At the point where the demand curves cross, the percentage change in price from $15 to $20 is exactly the same for both demand curves, but along the (flatter) demand curve, D2, the percentage response from consumers is stronger than along the (steeper) demand curve, D1.

8

Elastic demand Demand is elastic when the percentage change in the quantity demanded exceeds the percentage change in the price; the price elasticity of demand is greater than 1.00.

Unit-elastic demand Demand is unit elastic when the percentage change in the quantity demanded equals the percentage change in the price; the price elasticity of demand is equal to 1.00.

Inelastic demand Demand is inelastic when the percentage change in the quantity demanded is less than the percentage change in the price; the price elasticity of demand is less than 1.00.

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110  CHAPTER 3 Measuring and Using Demand

Perfectly Elastic Demand and Perfectly Inelastic Demand At the point where two demand curves cross, the flatter demand curve has a larger elasticity. This observation leads to the definitions of two extreme elasticities: per- fectly elastic demand and perfectly inelastic demand. Perfectly elastic demand means consumer response to a change in the price is the largest possible response in the quantity demanded: A rise in the price decreases the quantity demanded to zero, and a fall in the price increases the quantity demanded to infinity. The demand for milk from a particular dairy is very close to perfectly elastic. If the dairy’s managers raise its price, no one buys from the dairy because they can buy from hundreds of thousands of other dairies, so the quantity demanded falls to zero. If the dairy’s managers lower its price, everyone in the world will want to buy from it. When demand is perfectly elastic, the elasticity is defined to equal infinity 1∞ 2. A horizontal demand curve is the flattest possible demand curve, showing the largest possible response. As illustrated in Figure 3.13(a), all points on a horizontal demand curve are perfectly elastic.

Perfectly inelastic demand means consumer response to a change in the price is the smallest possible response: no change in the quantity demanded. The demand for a lifesaving drug can be perfectly inelastic: Whether managers raise the price or lower the price, consumers will buy the same quantity. When demand is perfectly inelastic, the price elasticity of demand equals 0. A vertical demand curve is the steepest possible demand curve, showing the smallest pos- sible response. As Figure 3.13(b) shows, all points on a vertical demand curve are perfectly inelastic.

Factors Affecting the Size of the Price Elasticity of Demand Skilled managers often try to change the price elasticity of demand for their product to increase their firm’s profit. But to be able to affect the price elasticity of demand, you must understand the factors involved.

Perfectly elastic demand Demand is perfectly elastic when a change in the price creates the largest possible response in the quantity demanded: A rise in the price decreases the quantity demanded to zero, and a fall in the price increases the quantity demanded to infinity.

Perfectly inelastic demand Demand is perfectly inelastic when a change in the price creates the smallest possible response: There is no change in the quantity demanded.

Figure 3.12 Elastic Demand and Inelastic Demand

At point A, where the demand curves cross, the difference in the lengths of the arrows shows that the quantity demanded along demand curve D2 responds more strongly to the price hike from $15 to $20 than the quantity demanded along demand curve D1. So, the price elasticity of demand at point A is larger on demand curve D2 than on demand curve D1.

Price (dollars per baseball cap)

Quantity (baseball caps per day)

$35

$5

$10

70605040302010

$15

$20

$25

$30

0

D2 D1

A

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3.4 Elasticity  111

Two general factors influence the size of the price elasticity of demand: the num- ber of close substitutes and the fraction of the budget spent on the product. There is no formula into which you can plug these factors to calculate a precise value. Nonetheless, these factors provide valuable insights into the size of the price elastic- ity of demand for a product and how you might be able to change it to your advantage.

The Number of Close Substitutes The larger the number of close substitutes for a product, the larger its price elasticity of demand. You probably already under- stand intuitively that the existence of a large number of close substitutes means that consumers will respond strongly to a price change. For example, New Balance athletic shoes have many substitutes, including Nike, Converse, and Puma. When the price of New Balance shoes rises, the quantity demanded will decrease sub- stantially because consumers can switch to one of the many other substitute shoes. Alternatively, when the price falls, the quantity demanded will increase as con- sumers switch away from the many other brands of shoes they had been buying to the now-cheaper New Balance shoes.

Of course, the reverse also applies: The smaller the number of close substitutes, the smaller the price elasticity of demand. The same intuition applies: When the price rises, consumers cannot decrease the quantity they demand by much because

Figure 3.13 Perfectly Elastic Demand and Perfectly Inelastic Demand

(a) Perfectly Elastic Demand At any point on the horizontal demand curve for the milk from a particular dairy demand is perfectly elastic, so the elasticity equals ∞ at all points on the demand curve.

(b) Perfectly Inelastic Demand At any point on the vertical demand curve for a lifesaving drug demand is perfectly inelastic, so the elasticity equals 0 at all points on the demand curve.

Price (dollars per gallon of milk)

Quantity (thousands of gallons of milk per month)

$1.75

$0.25

$0.50

700

D

500 600300 400100 200

$0.75

$1.00

$1.25

$1.50

0

Price (dollars per dose)

Quantity (millions of doses per year)

$140

$20

$40

7

D

5 63 41 2

$60

$80

$100

$120

0

M03_BLAI8235_01_SE_C03_pp86-137.indd 111 23/08/17 9:53 AM

112  CHAPTER 3 Measuring and Using Demand

of a lack of alternatives. And when the price falls, there is not much switching away from other substitutes precisely because there are not many substitutes. This result is why the price elasticity of demand for gasoline, a product with few substitutes, is much smaller than the price elasticity of demand for New Balance shoes, a product with many substitutes.

The general principle that the availability of more substitutes leads to a larger price elasticity of demand has three implications:

1. The more broadly defined the product, the smaller the price elasticity of de- mand. For instance, soda is a broadly defined product that includes all types of carbonated beverages, including Pepsi-Cola, Coca-Cola, and Mountain Dew. In contrast, Pepsi-Cola is narrowly defined to only that drink. Economists have estimated that the price elasticity of demand for soda is 0.80, while that for Pepsi is 1.55. Why is the price elasticity of demand for soda so much smaller than the price elasticity of demand for Pepsi? The answer is that soda has fewer substitutes than Pepsi. Fruit drinks, energy drinks, coffee, and other liquids serve as substitutes for soda. All of these other products can substitute for Pepsi, plus all other types of soda also can substitute for Pepsi. So a nar- rowly defined, specific product such as Pepsi has many more substitutes and hence a larger price elasticity of demand than a broadly defined, general product such as soda.

This distinction can save you from making erroneous decisions. For exam- ple, suppose that you are the brand manager for the Ford Focus and are con- sidering raising the price by 2 percent. To help with the decision, you want to forecast how the change in price will affect sales. Suppose that you do not have an estimate of either the demand curve or the price elasticity of demand for the Focus. Analysts have estimated the price elasticity of demand for the broader category of automobiles to be 0.9. You might be tempted to use this elasticity as your estimate of the price elasticity of demand for the Focus. If you use this number, your forecast is that sales of the Focus will decrease by 0.9 * 2 percent = 1.8 percent. But you want the elasticity for the Ford Focus, not the elasticity for automobiles in general. The Focus is a more specific product, so its price elasticity of demand is larger than the price elasticity of demand for automobiles. Indeed, the price elasticity of demand for a Ford compact car, such as the Focus, has been estimated to be 6.0, changing the forecasted decrease in sales to 6.0 * 2 percent = 12.0 percent. Using the price elasticity of demand for a general product category such as cars rather than the specific product under consideration (the Focus) could lead you to a bad decision!

2. A luxury good has a larger price elasticity of demand than does a necessity. Luxury goods have more substitutes than necessities. For instance, compare a cruise vacation to toothpaste. A cruise easily qualifies as a luxury. Most people (hopefully) classify toothpaste as a necessity. There are many more substitutes for cruises than for toothpaste. Instead of going on a cruise, peo- ple can tour Europe by rail, go on a safari in Africa, trek through Alaska, spend time at a beach house, or enjoy any number of alternatives. There are not nearly as many substitutes for toothpaste. Baking soda might qualify, but it is not a close substitute for toothpaste (and it does not taste as good!). The fact that there are more substitutes for luxuries than necessities helps explain why the price elasticity of demand for luxuries is larger than that for necessities.

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3.4 Elasticity  113

3. The more time that has elapsed since a price change, the larger the price elas- ticity of demand. This result again hinges on the number of substitutes. Consider a price hike. The quantity demanded immediately decreases a little, but many consumers who are buying the good will not immediately know of substitutes. As time passes, consumers will search for, find, and buy substitutes. This additional switch away from the now-higher-priced good makes the de- crease in its quantity demanded larger. Consequently, the price elasticity of de- mand increases in size as time passes. The effect of a price cut is analogous: Immediately after the price of an item falls, few consumers are aware of the price drop, so the increase in the quantity demanded is small. As time passes, more consumers learn of the lower price and switch from other alternatives to the good with the lower price, so its quantity demanded and its price elasticity of demand both increase. The managerial implication is clear: Advertise price reductions so that more consumers know of them immediately, thereby increas- ing the price elasticity of demand for your product. On the flip side, conceal price hikes so that fewer consumers are immediately aware of them, thereby delaying the inevitable increase in the price elasticity of demand.

The effect on the demand and the price elasticity of demand for existing products is not immediate when a firm introduces a new substitute product to the marketplace for the same reason that the effect of a price change is spread out over time: It takes consumers time to learn of the new product and its prop- erties. For example, in 2011, Bayer AG, a large German pharmaceutical company, received approval to market a first-in-its-class drug, Xarelto, to combat deep vein thrombosis (DVT). (A deep vein thrombosis occurs when a blood clot in a vein deep in the body forms. If part of the clot breaks free, it may travel to the lungs with fatal consequences.) Although other drugs existed to fight DVT, be- cause of its unique attributes, Xarelto had no close substitutes and, consequently, a relatively small price elasticity of demand. In 2014, Pfizer and Bristol-Meyers Squibb received approval to combat DVT with their similar drug, Eliquis. Because the presence of Eliquis gave Xarelto a close substitute, analysts believed that Xarelto’s market share would quickly fall and its price elasticity of demand would quickly rise. This forecast turned out to be incorrect. Xarelto’s three-year lead over Eliquis meant that physicians were familiar with Xarelto and its ef- fects. It took physicians some time to become as familiar with the new substitute, Eliquis. As time passed and physicians learned about Eliquis’s effects, Xarelto’s market-share growth slowly fell, and due to the increased knowledge and use of the new substitute, presumably its price elasticity of demand slowly rose.

As a manager, you can attempt to alter elasticity to your benefit. For example, if you are planning to boost your price, you definitely want consumers to believe that your product has no close substitutes because a lack of substitutes will lower the price elasticity of demand for your product and limit the decrease in sales from the price hike. To create this view, you want your advertisements to stress the unique properties of your product and make consumers believe that it is irreplace- able. Alternatively, you want consumers to think that your product will readily take the place of many other products if you are planning to cut your price. If consumers believe that your product can serve as a substitute for many alternatives, the price elasticity of demand for your product will be larger, which in turn means your sales increase will be larger after the price cut. If you are planning to introduce a new product, you need to get information out to potential consumers rapidly so that they can see how your product will substitute for products already on the market.

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114  CHAPTER 3 Measuring and Using Demand

The Fraction of the Budget Spent on the Product The second general factor affecting the size of the price elasticity of demand is the fraction of buyers’ bud- gets spent on the product. The larger the fraction, the larger the price elasticity of demand. Intuitively, if a product accounts for only a small fraction of consumers’ budgets, they are less likely to react to a price change. The change in the quantity demanded and the price elasticity of demand will be small. However, if the prod- uct accounts for a large fraction of consumers’ budgets, they notice and respond to the price change, which makes the price elasticity of demand larger. This effect goes a long way toward understanding the difference in the price elasticity of demand for housing (1.2) and that for salt (0.1). Of course, you need to keep in mind that salt is a larger fraction of the budget for some consumers than for others. For instance, the City of Rochester, New York, spends a bit more than 1 percent of its total budget, or near $7 million per year, on snow and ice removal; a substantial part of that amount goes toward the purchase of salt to help remove snow and ice. Salt accounts for a larger part of Rochester’s budget than for most consumers, so Rochester’s price elasticity of demand for salt is probably larger than that of most consumers.

Price Elasticity of Demand and Total Revenue Managers who know whether the demand for their product is elastic or inelastic find it easier to make good decisions. Sometimes these decisions revolve around the total revenue of their product. As you learned in Chapter 1, the total revenue of a product (TR) is the total amount collected from sales of the product; it equals the price of the product (P) multiplied by the quantity sold (Q). In equilibrium, the quantity sold equals the quantity consumers demand 1Qd2, so TR = P * Qd. Total revenue is not the same as total profit. To get the total profit, you must sub- tract the total opportunity cost from the total revenue. In some cases, however, the total revenue rather than total profit can be relevant to your decisions. Here are some examples:

• Authors and musicians receive royalties based on a percentage of the total reve- nue from their creation.

• Universities and professional sports teams often negotiate royalties based on the total revenue from sales of paraphernalia or clothing adorned with their logo.

• Small biotech companies frequently license their drugs to large pharmaceutical companies in exchange for a percentage of the total revenue from sales of the drug.

In all of these cases, understanding the relationship among total revenue, changes in price, and price elasticity of demand enhances decision making. Consider an increase in the price of a product. What will be the effect on the total revenue? Using the definition of total revenue, TR = P * Qd, the answer might seem clear: The increase in price boosts the total revenue. But that quick answer is too simple because it neglects the fact that an increase in price decreases the quantity de- manded, which offsets the effect of the higher price. The net effect of a price hike on total revenue depends on whether the increase in price or the decrease in quantity is larger. In turn, that depends on how strongly consumers respond to the increase in price: Do they respond strongly (with a substantial decrease in the quantity de- manded), or do they respond weakly (with only a minor decrease in the quantity demanded)?

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3.4 Elasticity  115

Because the price elasticity of demand measures the strength of the response, it plays a key role in determining the effect of a price change on the total revenue. Take the case of a price increase:

• Elastic demand. If the demand for the good is elastic, then the response to a price hike will be a large decrease in the quantity demanded, so that the total revenue decreases.

• Inelastic demand. If the demand for the good is inelastic, then the response to a price hike will be a small decrease in the quantity demanded, so that the total revenue increases.

• Unit-elastic demand. If the demand for the good is unit-elastic, then the response to a price hike will be a decrease in the quantity demanded by a pro- portionally equal amount, so that the total revenue does not change.

Clearly, the effect of a change in the price on total revenue depends on the price elasticity of demand. The following box summarizes this relationship in what is called the total revenue test.

If E 7 1 1 Demand is elastic (consumers respond strongly to a price change). • Price hike 1 Larger percentage decrease in quantity 1Total revenue decreases:

P c, Qd T 1 TR T • Price cut 1 Larger percentage increase in quantity 1Total revenue increases:

PT, Qd c 1 TR c If E = 1 1 Demand is unit@elastic (consumers respond one-to-one to a price change). • Price hike 1 Equal percentage decrease in quantity 1Total revenue does not

change: P c , QdT 1 TR S • Price cut 1 Equal percentage increase in quantity 1Total revenue does not

change: P T , Qd

T

1 TR S

If E 6 1 1 Demand is inelastic (consumers respond weakly to a price change). • Price hike 1 Smaller percentage decrease in quantity 1Total revenue

increases: Pc , QdT 1 TR c • Price cut 1 Smaller percentage increase in quantity 1Total revenue decreases:

P T , Qdc 1 TR T

TOTAL REVENUE TEST

Although the total revenue test can be proven mathematically, the intuition behind the test is extremely strong. (If you’re interested in the proof, see Section 3.B of the Appendix at the end of this chapter.) The test is divided into three parts:

1. Elastic demand. An increase in the price 1P T2 leads to a decrease in the quan- tity demanded 1Qd T 2. Because the demand is elastic, the percentage decrease in the quantity demanded exceeds the percentage increase in the price, so the T quantity arrow is larger than the

T

price arrow. Consequently, total revenue, P * Qd, decreases 1TRT 2 because the percentage decrease in the quantity exceeds the percentage increase in the price.

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116  CHAPTER 3 Measuring and Using Demand

2. Unit-elastic demand. The percentage increase in the price equals the percentage decrease in the quantity demanded, which makes the arrows next to P and Qd the same size. In this case, the effect on total revenue from the decrease in the quantity demanded exactly offsets the effect from the higher price, so the total revenue does not change 1TR S 2.

3. Inelastic demand. An increase in the price 1Pc 2 leads to a decrease in the quan- tity demanded 1QdT 2, but the percentage decrease in the quantity demanded is less than the percentage increase in the price, so the c price arrow is larger than the T quantity arrow. The total revenue increases 1TRc 2.

Figure 3.14(a) uses the linear demand curve from Figure 3.10 to show the relation- ship of the changes in total revenue and elasticity along a linear, downward-sloping demand curve. When demand is elastic, the range from $30 to $15 per baseball cap, lowering the price and increasing the quantity demanded increase the total revenue. When demand is inelastic, the range from $15 to $0 per cap, lowering the price and increasing the quantity demanded decrease the total revenue. As the figure illus- trates, along a linear demand curve, the total revenue equals its maximum when the price elasticity of demand equals 1.0.

Suppose that you are an executive in a biotech company that has licensed a drug to Pfizer and will receive a royalty of 10 percent of the total revenue Pfizer collects from the sale of the drug. Your goal is to have Pfizer set the price that

Figure 3.14 Relationship Between Total Revenue and Elasticity Along a Linear, Downward-Sloping Demand Curve

(a) Linear Demand Curve Moving down along a downward-sloping linear demand curve by lowering the price, the price elasticity of demand falls in value.

(b) Total Revenue When demand is elastic, moving down along the demand curve by lowering the price increases the total revenue. When demand is inelastic, however, moving down along the demand curve by lowering the price decreases the total revenue. The total revenue reaches its maximum when the price elasticity of demand equals 1.0.

Price (dollars per baseball cap)

Quantity (baseball caps per day)

$35

$5

$10

70 D

605040302010

$15

$20

$25

$30

0

A

B

e 5 5.0

e 5 2.0

e 5 1.0

e 5 0.5

e 5 0.2e . 1

e 5 1

e , 1

Total Revenue (dollars)

Quantity (baseball caps per day)

$525

$75

$150

70 TR

605040302010

$225

$300

$375

$450

0

e , 1e . 1 e 5 1

e 5 5.0

e 5 2.0 e 5 0.5

e 5 1.0

e 5 0.2

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3.4 Elasticity  117

maximizes Pfizer’s total revenue because that will maximize your royalty and profit. Knowing the price elasticity of demand for your drug is important to you. For example, if your drug is the only one to treat an illness, Pfizer has a monopoly. In other words, it is the only seller in the market. You will learn in Chapter 6 that because Pfizer has a monopoly, its profit-maximizing price for the product will fall in the elastic range of the demand. Accepting this result, you can see that when you license your drug to Pfizer, you need to push Pfizer to cut the price from what it wants to set because the total revenue test shows that when demand is elastic, a decrease in the price increases total revenue. If Pfizer’s total revenue increases, the royalty revenue your company receives will get a boost as well. Of course, Pfizer will resist lowering the price, but because you know that the demand for the drug is elastic, your biotech company will keep pressuring Pfizer.

Your marketing department estimates that at the current price and quantity, your firm’s product has a price elasticity of demand of 1.1. You run an advertising cam- paign that changes the demand, so that at the current price and quantity the elas- ticity falls to 0.8. In response to this change, would you raise the price, lower it, or keep it the same? Explain your answer.

Answer You should raise your price. Before the advertising campaign, the demand for your product was elastic, so according to the total revenue test, a price hike would lower your firm’s total revenue. After the campaign, the demand became inelastic. You now will be able to increase your firm’s profit by raising the price. Because the demand is inelastic, a price hike raises your firm’s total revenue. A price hike also decreases the quantity demanded, so your firm produces less, which decreases your costs. Raising revenue and lowering cost unambiguously boost your firm’s profit!

DECISION SNAPSHOT

Advertising and the Price Elasticity of Demand

Income Elasticity and Cross-Price Elasticity of Demand So far, you have learned about only one type of elasticity, the price elasticity of demand. Although this is the most important elasticity, there are two others to keep in mind: the income elasticity of demand and the cross-price elasticity of demand. You are unlikely to use either of these two measures often, but under- standing the different types of elasticity will help you avoid confusing them. In addition, learning about income elasticity and cross-price elasticity will help rein- force your understanding of the price elasticity of demand because all elasticities have four points in common: (1) changes are expressed as percentages, (2) fractions are used, (3) the factor driving the change is in the denominator, and (4) the factor responding to the change is in the numerator. (The Appendix at the end of this chapter presents a calculus treatment of these elasticities.)

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118  CHAPTER 3 Measuring and Using Demand

Income Elasticity of Demand The income elasticity of demand measures how strongly the quantity demanded responds to a change in consumers’ income. The income elasticity of demand 1eINC2 is defined as the percentage change in the quantity demanded divided by the per- centage change in income:

eINC = 1Percentage change in the quantity demanded2

1Percentage change in income2 The definition differs from that of the price elasticity of demand in one import-

ant respect: The price elasticity of demand uses the absolute value, but the income elasticity of demand does not. The reason for this difference is straightforward. The price elasticity of demand is always negative, so its sign is inconsequential. In con- trast, the income elasticity of demand is positive for a normal good and negative for an inferior good. Recall that an increase in income (a positive change in income) leads to an increase in demand for a normal good (which, for a given price, means a positive change in the quantity demanded). Therefore, the income elasticity of de- mand for a normal good equals one positive number divided by another, so the re- sulting elasticity is positive. In contrast, an increase in income leads to a decrease in demand for an inferior good. Therefore, the income elasticity of demand for an infe- rior good equals a negative number divided by a positive number, and the resulting elasticity is negative. Because the sign of the income elasticity of demand indicates whether the good is normal or inferior, the absolute value is not used.

Goods with income elasticities that exceed 1.0 are called luxury goods. Air travel, Caribbean cruises, and fine dining are examples of luxury goods. If you are a man- ager of a company producing a luxury good, such as steak dinners, you must keep an eye on forecasts of how income is changing. Any change in income will affect the demand for your product, and the change in demand will be larger than the change in income. So the effect on your business will be very important.

Goods with income elasticities between zero and 1.0 are called necessities. Groceries, gasoline, and shampoo are examples of necessities. If you are a manager of a company producing a necessity, changes in consumers’ income are not as important

to you. Any change in income will affect the demand for your product, but the change will be smaller than the change in income. It will affect your business, but the effect will be minor.

Table 3.2 summarizes the key points about the income elasticity of demand, including its formula and the meaning of a positive or negative sign.

Cross-Price Elasticity of Demand The cross-price elasticity of demand measures how strongly the quantity demanded responds to a change in the price of a related product. The cross-price elasticity of demand 1eCROSS2 is equal to the percentage change in the quantity demanded di- vided by the percentage change in the price of the related good:

eCROSS = 1Percentage change in the quantity demanded2

1Percentage change in the price of the related good2 The cross-price elasticity of demand is similar to the income elasticity of

demand—and different from the price elasticity of demand—with regard to

Cross-price elasticity of demand A measure of how strongly the quantity demanded changes when the price of a related product changes; it equals the percentage change in the quantity demanded divided by the percentage change in the price of the related product.

Table 3.2 Income Elasticity of Demand

• eINC = 1Percentage change in the quantity demanded2

1Percentage change in income2 • eINC is positive for a normal good.

• eINC is negative for an inferior good.

Income elasticity of demand A measure of how strongly the quantity demanded responds to a change in consumers’ income; it equals the percentage change in the quantity demanded divided by the percentage change in income.

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3.4 Elasticity  119

absolute value. The cross-price elasticity of demand does not use the absolute value because the sign of the elasticity again provides information about the rela- tionship of the products. Consider substitutes. Nike athletic shoes are a substitute for New Balance athletic shoes. A rise in the price of the substitute good, Nike athletic shoes, leads to an increase in demand (and, for any price, an increase the quantity demanded) for New Balance athletic shoes. For substitutes, the cross- price elasticity of demand equals one positive number divided by another, so the resulting elasticity is positive. For complementary goods, such as hot dogs and hot dog buns at a grocery store, an increase in the price of a complement leads to a decrease in the quantity demanded of the first good. For complements, the cross- price elasticity of demand equals a negative number divided by a positive number, so the cross-price elasticity of demand is negative for complements.

Table 3.3 summarizes the key points about the cross-price elasticity of demand, including its formula and the meaning of a positive or negative sign.

The Price Elasticity of Demand for a Touch-Screen Smartphone

When Apple introduced the iPhone in 2007, it was one of the first smartphones to have a touch screen. You are a manager at a smartphone company similar to Apple and your company has quickly introduced its own smartphone with a touch screen.

a. Suppose your marketing department tells you that the demand curve for your smartphone is Qd = 9,900,000 - 19,000 * P2. The price is $650, and the predicted quantity demanded is 4,050,000. At that price and estimated quantity, what is the price elasticity of demand for your smartphone?

b. At a sales meeting, some of the participants ask you what would happen to total revenue if you raised the price by 2 percent. Do not calculate the change in revenue; instead, just indicate whether your total revenue would rise, fall, or not change.

c. It’s now a few years later, and other companies, like HTC and Samsung, have introduced smartphones with touch screens. How did introduction of these new phones affect the price elasticity of demand for your touch-screen smartphone? Explain your answer.

Answer

a. The price elasticity of demand can be calculated using the estimated demand function and Equation 3.5. Using this equation, the price elasticity of demand equals

� -9,000 * 1$650/4,050,0002 � = 1.44 b. At this point on the demand curve, the demand is elastic. The total revenue test shows

that when the demand is elastic, an increase in price decreases total revenue. So if you raised the price of your smartphone by 2 percent, your total revenue would decrease.

c. The new smartphones with touch screens are substitutes for your smartphone. The presence of more substitutes increases the price elasticity of demand, so as time passed after the new phones were introduced, the price elasticity of demand for your smartphone increased.

SOLVED PROBLEM

Table 3.3 Cross-Price Elasticity of Demand

• eCROSS = 1Percentage change in the quantity demanded2

1Percentage change in the price of the related good2 • eCROSS is positive for substitute goods.

• eCROSS is negative for complementary goods.

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120  CHAPTER 3 Measuring and Using Demand

3.5 Regression Analysis and Elasticity Learning Objective 3.5 Use regression analysis and the different elasticity measures to make better managerial decisions.

Regression analysis and the different elasticity measures are important to managers because they help quantify decision making. As a manager, you will face situations in which you need to know the exact amount of a change in the price of an input, the precise change in your cost when you change your production, or the actual decrease in quantity demanded when you raise the price of your product. Regression analysis and the application of the different elasticity measures can help you answer these and many other important questions.

Using Regression Analysis Using the results from regression analysis is an essential task in many managerial positions. Analysts can use regression analysis for much more than estimating a demand curve. For example, you can use it to estimate how your costs change when production changes. We explain this important concept, called marginal cost, in Chapter 4 and use it in all future chapters. Large companies with demand that depends significantly on a specific influence often use regression analysis to forecast changes in such factors as personal income (important to automobile manufacturers such as General Motors and Honda) or new home sales (important to home improve- ment stores such as Home Depot and Lowe’s).

The ultimate goal of regression analysis is to help you make better decisions. For example, as a manager at the high-end steak restaurant chain, you can use an esti- mated demand function to help you make both immediate decisions about the price to set and long-term decisions about whether to open a new location. Suppose that an analyst for your firm has used regression to determine that the nightly demand for your chain’s steak dinners depends on the following factors:

1. The price of the dinners, measured as dollars per dinner 2. The average income of residents living within the city, measured as dollars per

person 3. The unemployment rate within the city, measured as the percentage unemploy-

ment rate 4. The population within 30 miles of the restaurant

Suppose that Table 3.4 includes the estimated coefficients and their standard er- rors, t-statistics, and P-values.4 The R2 of the regression is 0.72, so the regression pre- dicts the data reasonably well. In the table, the t-statistics for all five coefficients are greater than 1.96, and accordingly all five P-values are less than 5 percent (0.05). Therefore, you are confident that all the variables included in the regression affect the demand for steak dinners. The coefficient for the price variable, −12.9, shows that a $1 increase in the price of a dinner decreases the quantity demanded by -12.9 * $1, or 12.9 dinners per night. Similarly, the coefficient for the average income variable, 0.0073, shows that a $1,000 increase in average income increases the demand by 0.0073 * 1,000, or 7.3 dinners per night. The coefficient for the unemployment rate

MANAGERIAL APPLICATION

4 Often regression results are written with the standard errors in parentheses below the estimated coefficients: Qd = 139.2 - 112.9 * PRICE2 + 10.0073 * INCOME2 - 110.0 * UNEMPLOYMENT2+ 10.0005 * POPULATION2 (11.9) (1.8) (0.0012) (3.2) (0.0002)

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3.5 Managerial Application: Regression Analysis and Elasticity  121

variable, -10.0, shows that a one percentage point increase in the unemployment rate decreases the demand by -10.0 * 1, or 10 dinners per night. And the coefficient for the population variable, 0.0005, shows that a 1,000-person increase in population increases the demand by 0.0005 * 1,000, or 0.5 dinners per night.

Short-Run Decisions Using Regression Analysis Although a more detailed explanation of how managers determine price must wait until Chapter 6, intuitively it is clear that demand must play a role. The estimated demand function can help determine what price to charge in different cities because you can use it to estimate the nightly quantity of dinners your customers will demand in those cities. Suppose that one of the restaurants is located in a city of 900,000 people, in which aver- age income is $66,300 and the unemployment rate is 5.9 percent. If you set a price of $60 per dinner, you can predict that the nightly demand for steak dinners equals

Qd = 139.2 - 112.9 * $602 + 10.0073 * $66,3002 - 110.0 * 5.92 + 10.0005 * 900,0002 or 240 dinners per night. You can now calculate consumer response to a change in the price. For example, if you raise the price by $1, then the quantity of dinners de- manded decreases by 12.9 per night, to approximately 227 dinners.

Long-Run Decisions Using Regression Analysis You can also use the estimated demand function to forecast the demand for your product. Such forecasts can help you make better decisions. For example, you and the other executives at your steak chain might be deciding whether to open a restaurant in a city of 750,000 residents, with average income of $60,000 and an unemployment rate of 6.0 percent. Using the estimated demand function in Table 3.4 and a price of $60 per dinner, you predict demand of about 118 meals per night. Suppose this quan- tity of sales is too small to be profitable, but you expect rapid growth for the city: In three years, you forecast the city’s population will rise to 950,000, average income will increase to $70,000, and the unemployment rate will fall to 5.8 percent. Three years from now, if you set a price of $60 per dinner, you forecast the demand will be 293 dinners per night. This quantity of dinners provides support for a plan to open a restaurant in three years. You might start looking for a good location!

Other companies can use an estimated demand function to forecast their future input needs. General Motors, for example, can use an estimated demand function for their automobiles to forecast the quantity of steel it expects to need for next year’s production. This information can help its managers make better decisions about the contracts they will negotiate with their suppliers.

Table 3.4 Estimated Demand Function for Steak Dinners

The table shows the results of a regression of the demand for meals at an upscale steak restaurant, with the estimated coefficients for the price, average income in the city in which the restaurant is located, unemployment rate in the city, and population of the city.

Coefficient Standard Error t Stat P-value Lower 95% Upper 95%

Constant 139.2 11.9 11.7 0.00 117.3 163.1

Price of dinner −12.9 1.8 7.2 0.00 −9.4 −16.4

Average income 0.0073 0.0012 6.1 0.00 4.9 9.7

Unemployment rate −10.0 3.1 3.1 0.00 −3.9 −16.5

Population 0.0005 0.0002 2.5 0.02 0.0001 0.0009

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122  CHAPTER 3 Measuring and Using Demand

5 This estimate is from Lihong McPhail and Bruce Babcock, “Impact of US Biofuel Policy on US Corn and Gasoline Price Variability,” Energy, January 2012, p. 509.

Using the Price Elasticity of Demand There might be situations in which you need information about a demand but can- not obtain what you need from regression analysis, perhaps because you lack the necessary data. In such cases, you might be able to take advantage of preexisting estimates of the price elasticity of demand, based on either your previous experience or one of the many available estimates in print or on the Internet.

Suppose that your career leads you to an executive position with a company similar to Pacific Ethanol, an ethanol producer with plants located in the western United States. Because your company uses field corn to make ethanol, corn is a significant expense. (Field corn—also called cow corn—is less sweet than the corn people eat.) You read a report predicting that bad weather during the growing season will decrease the supply of field corn by 3 percent. As you learned in Chapter 2, a decrease in supply will raise the price; with this information, you can immediately forecast that the price of corn will rise. For planning purposes, however, you need a more precise forecast: By how much will the price of corn rise? You lack the data needed to estimate a demand curve for corn, but estimates of the price elasticity of demand for corn are easy to obtain. According to one such estimate, the price elasticity of demand for field corn is 0.2.5 Using this estimate, you can forecast that the percentage rise in the price of corn will equal (3 percent decrease in quantity)>10.22 = 15 percent. You now know that you must either prepare for a large increase in your costs or try to moderate the increase, perhaps by signing contracts to lock in the price of corn at a lower level.

In later chapters, you will learn that you also can use the price elasticity of demand to help you make pricing decisions (see Sections 6.2, 6.3, and 10.1). In the meantime, it should be obvious that the price elasticity of demand is useful to man- agers because they can use it to determine the change in the quantity demanded with a change in price.

Using the Income Elasticity of Demand Through the Business Cycle The income elasticity of demand is similarly useful in making better managerial decisions. For example, suppose that the income elasticity of demand for new auto- mobiles is 1.9. Because it is a positive number, new automobiles are a normal good— demand increases when the economy is expanding and people’s incomes are growing, and demand decreases when the economy is in a business cycle recession and people’s incomes are falling. Because the value exceeds 1, the swings in demand for automobiles are larger than the changes in income. If you are a manager at Kia Motors Corporation (the South Korean automotive company), when you make deci- sions about your future production plans, you must keep in mind that rapid growth in demand for automobiles in a growing economy might be followed by an equally rapid decrease in demand in response to a recession.

For a contrasting example, say that you are a manager at FirstGroup plc (the British-based owner of Greyhound Lines, which offers inter-city bus travel). The income elasticity of demand for intercity bus travel is negative because it is an inferior good. Your planning must take into account the decrease in demand for your product in a growing economy and the increase in demand during a recession. The magnitude of the income elasticity of demand will provide information about the sizes of the changes in demand, and you can use that information to improve your decisions.

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Revisiting How Managers at the Gates Foundation Decided to Subsidize Antimalarial Drugs

As noted at the beginning of the chapter, the manag-ers at the Bill and Melinda Gates Foundation want to use their funds in the best way possible. Because wast- ing their resources means that people could die unneces- sarily, managers at the foundation want to fund the most cost-effective programs. To achieve that goal, they must determine the quantitative impact of the proposals pre- sented to them.

In the case of the proposals to subsidize antimalarial drugs in Kenya and other nations, the managers were unlikely to have an estimated demand curve for the drugs in these countries because of data limitations. Instead, they proba- bly relied on estimates of the price elasticity of demand to determine the increase in the quantity of drugs demanded.

The subsidy programs lowered the price of these drugs between 29 percent and 78 percent (the fall in price differed from nation to nation and from drug to drug). Overall, the average decrease in price was roughly 50 percent. Because there are few substitutes, the demand for pharmaceutical drugs is price inelastic. The price elas- ticity of demand for pharmaceutical drugs for low-income Danish consumers is estimated to be 0.31. Denmark and

Kenya differ in an important respect: Low-income consum- ers in Kenya have much lower incomes than their coun- terparts in Denmark. Consequently, the expenditure on drugs in Kenya is a much larger fraction of consumers’ income, which means that the price elasticity of demand for drugs in Kenya is larger than in Denmark. If the man- agers at the Bill and Melinda Gates Foundation estimated that the price elasticity of demand for drugs in Kenya was about twice that in Denmark-—say, 0.60-—they could then predict that lowering the price of the drugs by 50 percent would increase the quantity demanded by 50 percent * 0.60 = 30 percent.

The Gates Foundation funded the proposals to sub- sidize antimalarial drugs. The actual outcome was that the quantity of the drugs demanded in the different na- tions increased by 20 to 40 percent. The quantitative estimate was right in line with what occurred. Using the price elasticity of demand to estimate the impact of the drug subsidy proposals allowed the managers at the foundation to compare them to competing proposals and to make decisions that saved the maximum number of lives.

Summary: The Bottom Line 3.1 Regression: Estimating Demand • Regression analysis is a statistical tool used to estimate

the relationships between two or more variables. • Regression analysis assumes that the function to be es-

timated has a random element. The estimated coeffi- cients minimize the sum of the squared residuals between the actual values of the dependent variable and the values predicted by the regression.

3.2 Interpreting the Results of Regression Analysis

• The coefficients estimated by a regression change when the data change. The statistical programs used in regression analysis calculate confidence intervals for each estimated coefficient. For the 95 percent confi- dence interval, the value of the true coefficient falls within the interval 95 percent of the time.

• The P-value indicates whether an estimated coefficient is statistically significantly different from zero. If the P- value is 5 percent (0.05) or less, then you can be 95 percent confident that the true coefficient is not equal to zero.

• The R2 statistic, which measures the overall fit of the regression, varies between 100 percent (the predicted values capture all the variation in the actual dependent variable) and 0 (the predicted values capture none of the variation in the actual dependent variable).

3.3 Limitations of Regression Analysis • Managers should examine regressions reported to

them to be certain that all the relevant variables are included.

• Managers should determine whether a regression’s functional form (curve or straight line) is the best fit for the data.

3.4 Elasticity • The price elasticity of demand measures how strongly

the quantity demanded responds to a change in the price of a product. It equals the absolute value of the percentage change in the quantity demanded divided by the percentage change in the price.

Summary: The Bottom Line  123

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124  CHAPTER 3 Measuring and Using Demand

• If the price elasticity of demand exceeds 1.0, consum- ers respond strongly to a change in price, and demand is elastic. If the price elasticity of demand equals 1.0, demand is unit elastic. If the price elasticity of demand is less than 1.0, consumers respond weakly to a change in price, and demand is inelastic.

• The more substitutes available for the product and the larger the fraction of the consumer’s budget spent on the product, the larger the price elasticity of demand.

• The income elasticity of demand equals the percentage change in the quantity demanded divided by the per- centage change in income. It is positive for normal goods and negative for inferior goods.

• The cross-price elasticity of demand equals the per- centage change in the quantity demanded of one good

divided by the percentage change in the price of a re- lated good. It is positive for products that are substi- tutes and negative for those that are complements.

3.5 Managerial Application: Regression Analysis and Elasticity

• Regression analysis can estimate a firm’s demand function and other important relationships. You can use the estimated functions to make forecasts and pre- dictions that improve your decisions.

• When there are not enough data to estimate a demand function, you can use the price elasticity of demand, the income elasticity of demand, and/or the cross- price elasticity of demand to estimate or forecast the effect of changes in market factors.

Key Terms and Concepts Confidence interval

Critical value

Cross-price elasticity of demand

Elastic demand

Elasticity

Income elasticity of demand

Inelastic demand

Perfectly elastic demand

Perfectly inelastic demand

Price elasticity of demand

P-value

Regression analysis

R2 statistic

Significance level

t-statistic

Unit-elastic demand

Questions and Problems All exercises are available on MyEconLab; solutions to even-numbered Questions and Problems appear in the back of this book.

3.1 Regression: Estimating Demand Learning Objective 3.1 Explain the basics of regression analysis.

1.1 In the context of regression analysis, explain the meaning of the terms dependent variable, indepen- dent variable, explanatory variable, univariate equa- tion, and multivariate equation.

1.2 Why does regression analysis presume the pres- ence of a random error term?

1.3 Explain why minimizing the sum of the squared residuals is a reasonable objective for regression analysis.

3.2 Interpreting the Results of Regression Analysis Learning Objective 3.2 Interpret the results from a regression.

2.1 Your marketing research department provides the following estimated demand function for your

product: Qd = 500.6 - 11.4P + 0.5INCOME, where P is the price of your product and INCOME is average income. a. Is your product a normal good or an inferior

good? Explain your answer. b. The standard error for the price coefficient

is 2.0. What is its t-statistic? What can you conclude about the coefficient’s statistical significance?

c. The standard error for the income coeffi- cient is 0.3. What is its t-statistic? What can you conclude about the coefficient’s statisti- cal significance?

2.2 What does the R2 statistic measure? Why is it important?

2.3 The estimated coefficient for a variable in a regression is 3.5, with a P-value of 0.12. Given these two values, what conclusions can you make about the estimated coefficient?

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3.3 Limitations of Regression Analysis Learning Objective 3.3 Describe the limita- tions of regression analysis and how they affect its use by managers.

3.1 You are a manager at a company similar to KB Home, one of the largest home builders in the United States. You hired a consulting firm to estimate the demand for your homes. The con- sultants’ report used regression analysis to esti- mate the demand. They assumed that the demand for your homes depended on the mortgage interest rate and disposable income. The R2 of the regression they report is 0.24 (24 percent). What suggestions do you have for the consultants?

3.2 Your research analyst informs you that “I always estimate log-linear regressions.” Do you think the analyst’s procedure is correct? What would you say to the analyst?

3.3 You are an executive manager for HatsforAll, a major producer of hats. You are studying a pre- liminary report submitted by a research firm you hired. The report includes a regression that estimates the demand for your hats. The re- search firm used 20 years of data on sales of your hats and included two independent vari- ables: the annual average price of your hats and the annual average winter temperature in your marketing areas. (The theory behind the tem- perature variable is that consumers are more likely to buy hats when the temperature is colder.) The estimated coefficient for the price variable is −5.8, with a standard error of 0.8, and the estimated coefficient for the tempera- ture variable is −20.8, with a standard error of 15.6. Based on the results of survey cards in- cluded with the hats, you are confident that higher-income people buy more hats. You are writing a memo to the research firm regarding the report. What additional information will you request from the research firm, and what changes will you recommend it make?

3.4 Elasticity Learning Objective 3.4 Discuss different elasticity measures and their use.

4.1 The short-run price elasticity of demand for oil is 0.3. If new discoveries of oil increase the quan- tity of oil by 6 percent, what will be the resulting change in the price of oil?

4.2 Complete the following table.

Elasticity

Percentage Change in

Price

Percentage Change in Quantity

Demanded

a. __ 8 percent 12 percent b. 1.4 6 percent _____ c. 0.6 6 percent _____ d. 1.2 _____ 6 percent e. 0.4 _____ 6 percent

4.3 The slope of a linear demand curve is −$2 per unit. a. What is the price elasticity of demand when

the price is $300 and the quantity is 100 units? b. What is the price elasticity of demand when

the price is $250 and the quantity is 125 units? c. What is the price elasticity of demand when

the price is $100 and the quantity is 200 units? d. As the price falls (causing a downward

movement along the demand curve), how does the price elasticity of demand change?

4.4 Your marketing research department estimates that the demand function for your product is equal to Qd = 2,000 - 20P. What is the price elasticity of demand when P = $60?

4.5 Your marketing research department estimates that the demand function for your product is equal to Qd = 2,000 - 20P. What is the price elasticity of demand when P = $40?

4.6 Your marketing research department estimates that the demand function for your product is equal to ln Qd = 7.5 - 2.0ln P. What is the price elasticity of demand when P = $60?

4.7 As a brand manager for Honey Bunches of Oats cereal, you propose lowering the price by 4 percent. What will you tell your supervisor about what you expect will be the impact on sales in the short run and in the long run? Explain your answer.

4.8 You own a small business and want to increase the total revenue you collect from sales of your product. a. If the demand for your product is inelastic,

what can you do to increase total revenue? b. If the demand for your product is elastic,

what can you do to increase total revenue? c. If the demand for your product is unit elas-

tic, what can you do to increase total revenue?

Questions and Problems  125

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126  CHAPTER 3 Measuring and Using Demand

4.9 You are a literary agent for an author who writes very popular mystery novels. As the agent, you receive 0.5 percent of the total revenue from sales of the books. You are currently in negotia- tions with Amazon about the price Amazon will charge for your author’s e-books. You believe that your author’s books are unique—no one else writes similar stories. What implication does this belief have for your estimate of the price elasticity of demand for your author’s books and for your negotiations with Amazon?

4.10 As a manager for the fresh chicken division of a firm like Tyson Foods, Inc., you know that the price elasticity of the total market demand for broiler chickens is 0.5. When one of your assis- tants suggests raising the price of your chicken by 10 percent, asserting that such a move would in- crease revenue, how do you respond, and why?

4.11 Only the price elasticity of demand uses the absolute value. Why don’t the other elasticities (income elasticity of demand and cross-price elasticity of demand) also use the absolute value?

4.12 Economists estimate that the income elasticity of demand for clothing and footwear is 0.96. As in- comes grow, what happens to the fraction of in- come spent on clothing and footwear? Explain your answer.

4.13 Say that as a manager at a company supplying processed chicken, you are aware that a rise in the cost of feeding steers is predicted to lead to a 15 percent rise in the price of beef. Your analysts have estimated the cross-price elasticity between the demand for chicken and the price of beef is 0.12. You and a customer are negotiating the price at which you will sell them chicken for the next year. What do you predict will be the im- pact on the demand for chicken from the rise in the price of beef, and how does this estimate af- fect your negotiating position?

3.5 Managerial Application: Regression Analysis and Elasticity Learning Objective 3.5 Use regression analysis and the different elasticity measures to make better managerial decisions.

5.1 You are managing a division of a large company. The marketing department submits a report to you about the demand for the product you man- age. The report includes the following estimated demand function:

Qd = 2,910.0 - 11.3P + 0.050INCOME - 3.0Pother (100.4) (3.2) (0.012) (1.0)

where P is the price of your product, INCOME is average income, Pother is the price of a related product, and the numbers in parentheses are the standard errors of the estimated coefficients di- rectly above them. The R2 statistic for the regres- sion is 0.84 (84 percent). a. What are your general comments about the

regression, such as its fit and the significance of the coefficients? As a manager, would you use this estimated demand function to help you make decisions? Explain your answer.

b. Is the product a normal good? Explain your answer.

c. Is the related product a complement or a substitute for your product? Explain your answer.

d. The current price of your product is $200, average income is $50,000, and the price of the related product is $300. What is the quantity demanded of your product?

e. Based on the prices and income in part d, what is the price elasticity of demand for your product? Round your answer to one decimal point.

f. If you raise the price of your product, what do you predict will happen to the total revenue?

5.2 Using disposable personal income (people’s in- come after paying taxes) as their measure of in- come, General Motors’ economists estimate that the income elasticity of demand for its cars is 1.9. The economists forecast that disposable per- sonal income will grow 3.8 percent next year. What will be the effect on the demand for General Motors’ cars?

5.3 Your marketing research department estimates that the log-linear demand function for your prod- uct is ln Qd = 9.3 - 1.6ln P. The standard error of the coefficient for ln P is 0.3, and the 95 percent confidence interval runs from -2.2 to -1.0. a. At a price of $50, what is the predicted price

elasticity of demand? Calculate the 95 percent confidence interval for the elasticity using the 95 percent confidence interval for the estimated coefficient.

b. At a price of $30, what is the predicted price elasticity of demand? Calculate the 95 percent confidence interval for the elasticity using the 95 percent confidence interval for the estimated coefficient.

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5.4 Say that you work for U.S. Steel Corporation. Energy accounts for a significant fraction of U.S. Steel’s costs. One of its sources of energy is natu- ral gas. Because of new methods of production, such as hydraulic fracking, the quantity of natu- ral gas is increasing. Suppose that forecasters predict the quantity of natural gas will increase by 10 percent and you know the price elasticity of demand for natural gas is 0.4. U.S. Steel will be very interested in how much the price of nat- ural gas will change. What is your prediction for the change in the price of natural gas?

5.5 You are a midlevel manager for a seafood restau- rant. You and your supervisor discuss new regu- lations that decrease the quantity of cod caught on Georges Bank by 55 percent. Your restaurant fea- tures Georges Bank cod, so your supervisor asks you for a quick estimate of the impact of the new regulations on its price. You know that the price elasticity of demand for Georges Bank cod is 2.0. a. Will the new regulations shift the demand

curve for cod? Will they shift the supply curve? Explain your answers.

b. What will you report to your supervisor? What managerial suggestions will you make?

5.6 The table below has data for the price of pizzas and the quantity demanded at each price. a. Use these data to estimate the demand curve

for pizza. You want to report and discuss the estimated coefficients. Are they what you expected? How well does your estimated re- gression fit the data? Provide a figure if you think it would be useful.

5.7 The St. Louis Cardinals’ website has data on play- ers’ batting averages, and the Deadspin website has data on the players’ salaries. (For example, the 2015 batting salaries are at http://deadspin .com/nl-central-chicago-cubs-jon-lester-20-000- 000-edwin-ja-1695058450.) Excluding pitchers, presumably a higher batting average leads to a higher salary. a. Using regression, determine whether this

hypothesis is correct for players on the opening day payroll for the St. Louis Cardinals in 2015. Explain your regression results.

b. It may be that a player’s salary depends on his batting average and the number of his home runs. Using regression, determine whether this hypothesis is correct for the players on the opening day payroll for the St. Louis Cardinals in 2015. Explain your re- gression results.

b. Your manager knows that the elasticity of demand can help you make good decisions. So once you have your demand curve, cal- culate the elasticity at a price of $10, $15, $20, $25, and $30. Carefully describe how you calculated the elasticity. How does the elastic- ity change along the demand curve? Using the estimated demand curve, over what price range is the demand elastic? At what price is the demand unit elastic? Over what price range is the demand inelastic?

Quantity (pizzas per evening)

Price (dollars)

Quantity (pizzas per evening)

Price (dollars)

Quantity (pizzas per evening)

Price (dollars)

69 $30 92 $18 141 $12

42 29 125 17 141 12

66 28 140 16 163 11

57 28 106 16 154 11

78 27 115 15 141 11

72 25 104 15 151 10

81 24 148 14 151 10

83 23 143 14 147 10

70 22 124 14 135 9

101 21 138 13 160 9

93 20 129 13 163 8

100 19 131 13 163 8

107 18 138 12 172 7

Accompanies problem 5.6.

Questions and Problems  127

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128  CHAPTER 3 Measuring and Using Demand

3.1 Bret’s Accounting & Tax Services is a small but locally well-known accounting firm in Sioux City, IA, that completes taxes for individuals. Every year firms like Bret’s decide how much they will charge to complete and file an individ- ual tax return. This price determines how many tax returns firms complete each year. Suppose that you are an office manager for a firm like Bret’s Accounting & Tax Services and you are trying to determine what your firm should charge next year for tax returns. Use the data provided to complete the following: a. Graph the data using a scatter plot. Using the

Insert Trendline function in Excel, determine whether you should use linear or log-linear regression. (Place the graph beneath the data; be sure to label both axes.)

b. Using Excel’s Regression Analysis function, run a regression, and answer the following ques- tions about your output. (Place your regression results beneath the graph from part a.)

c. What is your estimated demand function? (Round the estimated coefficients to two decimal places.)

d. What is the R2? (Report this as a percentage; round to two decimal places.)

e. Based on the R2, do you think this regression can be used for analysis?

f. How many returns do you expect to be com- pleted if the firm charges $85 per return?

g. What is the elasticity at this point on the demand curve?

h. At this price, are you on the elastic, inelastic, or unit-elastic portion of your demand curve?

i. Do you recommend an increase, a decrease, or no change in the price with this information?

3.2 Hawaiian Shaved Ice, in Newton Grove, NC, sells shaved ice and snow cone equipment and supplies for individual and commercial use. Suppose that you purchased a commercial-grade machine and supplies from a company similar to Hawaiian Shaved Ice to open a shaved ice stand on a beach busy with tourists. Because this is a new business, you’ve tried a number of prices and run a few specials to try to attract customers. As such, you have 20 days’ worth of data to ana- lyze and help you set a more permanent price.

a. Graph the data provided using a scatter plot. Using the Insert Trendline function in Excel, determine whether you should use linear or log-linear regression. (Place the graph beneath the data; be sure to label both axes.)

b. Using Excel’s Regression Analysis function, run a regression, and answer the following ques- tions about your output. (Place your regression results beneath the graph from part a.)

c. What is your estimated demand function? d. Discuss the fit and significance of the

regression.

MyLab Economics Auto-Graded Excel Projects

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3.3 Ben and Jerry’s is a popular brand of ice cream based in South Burlington, VT. The company is known for its delicious and cleverly named fla- vors and its commitment to social responsibility. Suppose that the marketing department for a firm like Ben and Jerry’s estimates monthly demand for a pint of ice cream to be Q = 1000 - 150P. a. Using the table provided and Excel func-

tions, calculate quantity demanded for each of the prices given.

b. Using the prices provided and quantities demanded that you calculated in part a, cal- culate the elasticity of demand for each of the prices in the table.

c. Comment on how elasticity changes as you move along the demand curve.

d. Are there prices between $3 and $6 that you are certain the company should not charge based on the elasticities you observe? Why or why not?

e. If the goal of this firm is to maximize reve- nue, what price do you recommend it charge for a pint of ice cream?

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Decision-Making Using Regression

Introduction Upper-level managers frequently make important long- run strategic decisions about acquisitions, mergers, plant or store locations, pricing, financing, and marketing. Indeed, a major focus of this book is to explain how man- agers can use economic principles as a guide to making these types of decisions. But even the best guidance can fail without adequate information and data analysis.

Company analysts often use regression analysis to help them provide quantitative information to manage- rial decision makers. In this chapter, you learned how re- gression analysis can help managers estimate demand functions. But regression can be used to help managers answer other questions, such as these: How many more units of a product will we sell if our store stays open an extra hour each day? Is San Diego a good location to open a new store? How will consumers react if we change the packaging of our product? In this case study, we explore how regression analysis can help provide invaluable in- formation about another important managerial issue, whether to remodel the company’s stores and/or change how the company prices its products.

Regression Example Regression can help managers make the decisions faced by companies that are debating whether to remodel their stores and/or their operations. Companies such as restau- rant chains continually struggle to retain their market share by remaining fresh and relevant for consumers. Most restaurant chains undertake constant innovation, moving specials on and off their menus as well as tweak- ing and refining their more permanent offerings. Occa- sionally, however, upper-level managers decide that some of their restaurants need renovation. Take, for example, Olive Garden, a division of Darden with more than 800 restaurant locations. In 2013, the new president of Olive Garden, Dave George, announced that Olive Garden would remodel and modernize its interiors.

Suppose that you work in the research department for a similar restaurant chain. Your chain has a new presi- dent, and your president also is considering a new style of remodeling for your restaurants. Remodeling is expen- sive, so the new president asks your research team to determine if the expense is justified by the projected increased in the chain’s profit.

To obtain the information needed to make this type of decision, a firm often remodels a few stores and then

130

CASE STUDY

1 This situation is similar to what Darden’s analysts faced in 2013 because Olive Garden had started remodeling its stores’ ex- teriors and some of the interiors to present a different view of Italy. That approach, however, was not what the incoming presi- dent, Mr. George, envisioned. His goal was modernization, not changing the geographic region the stores presented.

uses regression analysis to compare the profitability of the remodeled stores to that of stores that are not remodeled. Suppose, however, that your chain faces a more compli- cated situation: Under the previous president, the chain had already remodeled some locations but in a way that differs from your new president’s vision.1 So you have two types of restaurants—already remodeled and not previously remodeled. The regression analysis needs to consider this factor.

To use regression, your chain needs to remodel sev- eral restaurants according to the new president’s vision. Which restaurants are remodeled is unimportant because your regression should be able to predict the profitability regardless of location. After the remodeling, your group must collect data over several months to measure the profitability of all your restaurants. Ideally, you would collect the economic profits of the restaurants. In practice, however, their economic profit is impossible to measure, so you will need to use their accounting profits as a proxy for their economic profits. Your research group will use these data as the dependent variable in the regression.

Your team of analysts needs to determine how the new remodeling scheme affects profitability. But other factors also affect profitability. A restaurant’s profit equals its total revenue minus its total cost, so you and the other analysts need to determine what variables affect total rev- enue and total cost:

• Total revenue. The higher the demand for meals at your restaurants, the greater the total revenue. So the regression should include independent variables that affect the demand for dining at your restaurants. For example, your group might decide to include two in- dependent variables that affect demand and thereby total revenue: (1) the population of the county or lo- cality in which the restaurant is located and (2) in- come in that county or locality. When these variables are included in the regression, the estimated coeffi- cients for both these variables are expected to be pos- itive—higher population and higher income both in- crease demand and thereby increase the restaurant’s total revenue and raise its profit.

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SUMMARY  131

• Total cost. The higher the total cost, the lower the profit. So your team should include independent variables in the regression that affect a restaurant’s cost. For example, your group might settle upon two variables: (1) the rent paid for the restaurant, which will vary among locations, and (2) the legal mini- mum wage employees receive, which will also vary among locations. When these variables are included in the regression, the estimated coefficients for both of them are expected to be negative—a higher rent and a higher minimum wage both increase the restaurant’s cost and thereby reduce its profit.

In addition to the factors that affect total revenue and total cost, the regression needs to take account of whether the restaurant was remodeled according to the past president’s scheme, remodeled according to the new president’s ideas, or not remodeled at all. To do so, your team needs to include indicator variables (colloquially called “dummy variables”) as additional independent variables. Indicator variables equal 1 when a condition is met and equal 0 otherwise. For example, one indicator variable should equal 1 if the restaurant had previously been remodeled and 0 if it had not been remodeled. Call this variable OLDREMODEL. For the purposes of deter- mining the profitability of the new style of remodeling, the crucial indicator variable measures whether the loca- tion has been remodeled according to the new scheme. This variable equals 1 for restaurants that are newly remodeled and 0 for the other restaurants. Call this vari- able NEWREMODEL. The estimated coefficient of each indicator variable measures the effect of whatever condi- tion is being met.2 That means that the coefficient for the variable NEWREMODEL is key because when the variable equals 1, the restaurant has been newly remodeled along the lines suggested by the new president. The change in profit for a restaurant going from no remodeling at all to the new remodeling equals the estimated coefficient of NEWREMODEL—call it gn—multiplied by the value of the

variable when the location is newly remodeled, which is 1, or gn * 1 = gn.3

There are other factors you and your group could in- clude that affect the total revenue and total cost, but let’s limit the discussion to what we have discussed. Using these variables, to predict the profitability of a restaurant in your chain, your team would estimate the regression as

PROFIT = a + 1b * POPULATION2 + 1c * INCOME2 - 1d * RENT2 - 1e * MINIMUMWAGE2 + 1 f * OLDREMODEL2+1g * NEWREMODEL2

in which a, b, c, d, e, f, and g are the coefficients the regres- sion will estimate.

Once your team has estimated the regression, you can use what you have learned in Chapter 3 to judge the adequacy of the regression: Are the estimated coefficients statistically different from zero? Is the fit of the regression high? Or do you and your group need to either add or re- move some variables? Once you are satisfied with the re- gression, you can use it to determine the profitability of the proposed new remodeling. In particular, the estimated gn coefficient measures the change in profit from the new remodeling. If this estimated coefficient is positive and significantly different from zero, you can present it to your new president as an estimate of the profit from re- modeling a previously unremodeled store according to the new style and allow the president to use it when de- ciding whether to proceed with the new remodeling.

Your Decisions Regression analysis can be used in any industry, not just the restaurant industry. Take, for example, the retail industry. In November 2011, Ron Johnson was hired to be the new CEO of JCPenney. Less than two months later, Mr. Johnson announced the following sweeping changes:

1. JCPenney’s pricing had relied on heavy discounting and extensive use of coupons; Mr. Johnson immedi- ately changed the pricing policy to adopt “full-but- fair prices” with no discounts or coupons.

2. JCPenney had offered a large selection of middle-of- the-road store brands; Mr. Johnson discontinued the store brands in favor of selling more “trendy,” high-fashion brands.

2 For technical reasons, when a set of conditions taken together equals the entire set of observations, it is not possible to use an indicator variable for each type of condition; one type must not have an indicator variable. For example, in the analysis discussed above, you cannot use an indicator variable that equals 1 if the location had been previously remodeled, another indicator vari- able that equals 1 if the location is newly remodeled, and yet a third indicator variable that equals 1 if the location has not been remodeled. You cannot use all three of these indicator variables because taken together these three conditions equal the entire set of observations. Consequently, in the regression discussed in the example, there is no indicator variable for the stores that have not been remodeled.

3 More specifically, the NEWREMODEL indicator variable’s coeffi- cient, gn, measures the profit from the new remodeling relative to whichever condition has not been given an indicator variable. In the example at hand, gn measures the restaurant’s change in profit from being newly remodeled compared to not being remodeled at all.

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132  CHAPTER 3 Measuring and Using Demand

3. JCPenney’s customer base was generally older and middle to lower income; Mr. Johnson moved to es- tablish smaller “stores within a store” with more expensive merchandise to target younger, higher- income customers.

Mr. Johnson immediately started to implement his new policies without any testing. Unfortunately for both him and the company, customers rejected his changes: JCPenney’s sales dropped about 30 percent, its profit turned to billions of dollars of losses, and in April 2013, the board of directors fired Mr. Johnson as CEO.

Suppose you work in the research department of a retail department store chain that is considering three similar changes—ending discounts, offering trendy brands, and creating stores within the store. Your chain, however, decides to test these ideas before rolling them out chain-wide. So your supervisor asks you to write a proposal that will allow your company’s executives to determine the profitability of these possible changes. You will use regression analysis to decide on the profitability of the changes.

Prepare a proposal that answers the following questions:

1. The changes can be implemented separately, all to- gether, or in combinations of two, so how do you want to test the three changes? Be sure to explain why you made your decision.

2. If you want to compare the profitability of stores in different locations, explain what variables you expect to use. Be certain to mention variables other than those discussed above in the restaurant example that might affect the stores’ profitability. Carefully explain what effect you expect from each variable you in- clude. For each variable, do you expect that the esti- mated coefficient will be positive or negative? Mention the source from which you plan to obtain the data you will use.

3. Will you use any indicator variables? If so, what will they be?

4. Is there any feature (or features) about the specifica- tion or functional form of the regression that needs additional explanation?

5. After you estimate the regression, how do you plan to decide whether the estimated regression is ade- quate? How might the regression results be inade- quate? What do you plan to do if the results are inadequate?

6. Once you have an acceptable regression, explain how you plan to use the results to determine the profit- ability of the changes.

Sources: Steve Denning, “J.C. Penney: Was Ron Johnson Wrong?” Forbes.com, April 9, 2013, http://www.forbes.com/sites/ stevedenning/2013/04/09/j-c-penney-was-ron-johnsons- strategy-wrong/#32427add283c; James Surowiecki, “The Turnaround Trap,” New Yorker, March 25, 2013.

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A. Regression Analysis and Elasticity  133

CHAPTER 3 APPENDIX

The Calculus of Elasticity

Many of the elasticity results discussed in this chapter, including the elasticity formulas for linear and log-linear demand functions and the total revenue test, can be derived using calcu- lus. Indeed, we can start by giving the definition of the price elasticity of demand 1e2 from Equation 3.2 (Section 3.4),

e = ∞ a∆Q

d

Qd b

a∆P P

b ∞

a precise calculus interpretation:

e = ∞ adQ

d

Qd b

adP P

b ∞ A3.1

where the discrete Δ changes are now differential d changes.

A. Price Elasticity of Demand for a Linear and a Log-Linear Demand Function Some algebra using the definition of the price elasticity of demand in Equation A3.1 gives another measure of elasticity:

e = ∞

dQd

Qd

dP P

∞ = ` adQ d

Qd b * a P

dP b ` = ` dQ

d * P Qd * dP

` = ` dQ d * P

dP * Qd ` = ` adQ

d

dP b * a P

Qd b ` A3.2

If you use a general specification of the demand function, Qd = f1P2, then dQ d

dP = f′1P2,

where f′1P2 is the derivative of the demand function with respect to the price. Substituting f′1P2 into Equation A3.2 shows that the price elasticity of demand equals

e = ` adQ d

dP b * a P

Qd b ` = ` f′1P2 * a P

Qd b ` A3.3

Equation A3.3 has the following interpretation: At any price and for any demand function, the price elasticity of demand equals the derivative of the demand function at that price multiplied by the price divided by the quantity demanded at that price.

We can use Equation A3.3 to determine the equations for the price elasticity of demand for two common demand functions, a linear demand function and a log-linear demand func- tion. For a linear demand function—say, Qd = a - 1b * P2, where a and b are coefficients— the derivative of the quantity with respect to the price is dQ

d

dP = -b. Using Equation A3.3, for a linear demand function the price elasticity of demand equals

e = ` b * a P Qd

b `

133

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134  CHAPTER 3 APPENDIX The Calculus of Elasticity

which is shown as Equation 3.4 in the chapter (see Section 3.4). For a log-linear demand function—say,

ln Qd = a - 1b * ln P2 A3.4 where ln represents the natural logarithm—the derivative of the quantity with respect to the price is1

dQd

dP = -b * aQ

d

P b

Accordingly, using Equation A3.3 once again shows that, for a log-linear demand function, the price elasticity of demand equals

e = ` a - b * aQ d

P b b * a P

Qd b ` = b

precisely as stated in the chapter. In other words, for a log-linear demand function, the price elasticity of demand is the same for all prices and equals b, the coefficient multiplying the logarithm of the price in Equation A3.4.

B. Total Revenue Test Calculus also helps prove the total revenue test presented in the chapter (see Section 3.4). Recall that the total revenue test shows how the total revenue changes when the price changes; that is, it measures dTR>dP. The total revenue test includes three assertions: Demand is elastic when e is greater than 1, unit-elastic when e equals 1, and inelastic when e is less than one.

1. Elastic demand 1E + 1 2 : • If the price rises, the total revenue decreases, which means that dTR>dP is negative. • Conversely, if the price falls, the total revenue increases, which (again) means that

dTR>dP is negative. 2. Unit-elastic demand 1E = 1 2 :

• If the price rises or falls, the total revenue does not change, which means that dTR>dP is equal to zero.

3. Inelastic demand 1E * 1 2 : • If the price rises, the total revenue increases, which means that dTR>dP is positive. • Conversely, if the price falls, the total revenue decreases, which (again) means that

dTR>dP is positive. Total revenue equals the price of the product (P) multiplied by the quantity sold (Q), and

the quantity sold equals the quantity demanded by consumers (Qd):

TR = P * Qd

The quantity demanded is given by Qd = f1P2, so total revenue equals TR = P * f1P2 A3.5

Taking the derivative of total revenue in Equation A3.5 with respect to the price by using the product rule gives

dTR dP

= 3P * f′1P24 + f1P2 A3.6

1 Taking the total derivative of ln Qd = a - 1b * ln P2 gives 11>Qd) * dQd = -b * 11>P2 * dP. Multiplying both sides of the equality by Qd and dividing both sides by dP yields dQd>dP = -b * 1Qd>P2.

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CHAPTER 3 APPENDIX The Calculus of Elasticity  135

In Equation A3.6, f1P2 = Qd. Using this equality and rearranging the terms in the right side of Equation A3.6 yields

dTR dP

= Qd + 3f′1P2 * P4 A3.7

Next, multiply the second term (the term in Equation 3.7 in the brackets) on the right side

of Equation 3.7 by 1 in the form of aQ d

Qd b :

dTR dP

= 3Qd4 + c aQ d

Qd b * 1f′1P2 * P2 d

Finally, factor Qd out of both terms, and then rearrange the terms to give

dTR dP

= Qd * e 314 + c a 1 Qd

b * 1f'1P2 * P2 d f = Qd * e 314+ c af′1P2 * P Qd

b d f A3.8

The term c f′1P2 * P Qd

d is the same as the price elasticity of demand in Equation A3.3 except that there is no absolute value sign. Recall that we use the absolute value sign because otherwise the price elasticity of demand would be negative, since the law of demand means

that f′1P2, which equals dQ d

dP , is negative. Consequently, the c f′1P2 * P

Qd d term in

Equation A3.8 has the same numeric value as the price elasticity of demand but is negative, so

c f′1P2 * P Qd

d = -e. Using this equality, we can rewrite Equation A3.8 as

dTR dP

= Qd * 31 - e4 A3.9

Equation A3.9 shows how the total revenue changes when the price changes. In it, the

quantity demanded, Qd, is always positive, so the sign of dTR dP

depends on the 31 - e4 term. Using this result, we can now prove the total revenue test:

1. Elastic demand 1E + 1 2 : • If e 7 1, then 1 - e is negative, so from Equation A3.9, dTR>dP is negative.

2. Unit-elastic demand 1E = 1 2 : • If e = 1, then 1 - e equals 0, so from Equation A3.9, dTR>dP is equal to zero.

3. Inelastic demand 1E * 1 2 : • If e 6 1, then 1 - e is positive, so from Equation A3.9, dTR>dP is positive.

C. Income Elasticity of Demand and Cross-Price Elasticity of Demand It is probably no surprise that both the income and the cross-price elasticities of demand can be defined using calculus. If the demand function is Qd = f1P, INCOME, Pj2, where P is the price of the good, INCOME is consumers’ average income, and Pj is the price of a substitute or complement, then the income and cross-price elasticities of demand are

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In both of the definitions, we take a partial derivative because the demand function is multivariate; that is, the demand function has more than one independent variable. Even so, as Table A3.1 shows, the meanings of the signs of the income and cross-price elasticities do not change from what was explained in the chapter.

Table A3.1 Signs of Income Elasticity and Cross-Price Elasticity of Demand

Income elasticity of demand

• If ∂Qd>∂INCOME is positive then eINC is positive, and the product is a normal good. • If ∂Qd>∂INCOME is negative then eINC is negative, and the product is an inferior good. Cross-price elasticity of demand

• If ∂Qd>∂Pj is positive then eCROSS is positive, and the products are substitutes. • If ∂Qd>∂Pj is negative then eCROSS is negative, and the products are complements.

Calculus Questions and Problems All exercises are available on MyEconLab; solutions to even-numbered Questions and Problems appear in the back of this book.

A3.1 The hourly demand for music downloads is given by

Qd = 500 - 100P

where Qd is the number of songs demanded per hour and P is the price of downloading a song. a. Suppose that P = $3. At this price, what does

the price elasticity of demand equal? What is the total revenue?

b. At what price does e = 1? What is the total rev- enue when the price is $2.50?

c. Explain whether your results to parts a and b are consistent with the total revenue test.

A3.2 The weekly demand for sandwiches at a local sand- wich shop is given by

Qd = 2,000 - 5P + 2Pj - 0.01INCOME

where Qd is the number of sandwiches demanded per week, P is the price of a sandwich, Pj is the price of a related product, and INCOME is the average monthly income of consumers.

a. Suppose that P = $10, Pj = $50, and INCOME = $5,000. What is the value of the cross-price elasticity of demand? Is the related product a substitute or a complement?

b. Suppose that P = $10, Pj = $50, and INCOME = $5,000. What is the value of the income elasticity of demand? Are sandwiches a normal good or an inferior good?

A3.3 The hourly demand for corndogs at the local state fair is estimated to be

Qd = 360P-2

where Qd is the number of corndogs demanded per hour and P is the price of a corndog. a. Using the estimated demand function for corn-

dogs, calculate the price elasticity of demand as a function of the price of a corndog.

b. Using the demand function for corndogs, the quantity demanded is 90 corndogs when the

136  CHAPTER 3 APPENDIX The Calculus of Elasticity

eINC =

a 0Q d

Qd b

a 0INCOME INCOME

b = a 0Q

d

0INCOME b * a INCOME

Qd b

eCROSS =

a 0Q d

Qd b

a 0Pj Pj

b = a 0Q

d

0Pj b * a

Pj

Qd b

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price is $2 per corndog, and the quantity demanded is 40 corndogs when the price is $3 per corndog. Does the total revenue from sell- ing corndogs rise or fall as the number of corn- dogs sold increases?

c. Is your answer to part b consistent with the total revenue test? Explain.

A3.4 The monthly demand for bus rides in Miami, Flor- ida, depends on the price of a train ride, the price of a bus ride, and the average monthly income of rid- ers. Some consumers might choose to ride the train instead of the bus, while other riders might use both forms of transportation to get to their final destination. The demand function for bus rides is

Qd = 9,750 - 500P + 250Pj + 5INCOME

where Qd is the number of bus rides demanded per month, P is the price of a bus ride, Pj is the price of a train ride, and INCOME is the average monthly income of riders. a. Suppose that P = $1.50, Pj = $4.00, and

INCOME = $3,000. What is the monthly quan- tity of bus rides demanded?

b. Suppose that P = $1.50, Pj = $4.00, and INCOME = $3,000. What is the value of the cross-price elasticity of demand? Based on your answer, are train rides and bus rides substitutes or complements?

c. Suppose that P = $1.50, Pj = $4.00, and INCOME = $3,000. What is the value of the in- come elasticity of demand? Based on your an- swer, are train rides an inferior or a normal good?

A3.5 The monthly demand for personal pizzas depends on the price of a personal pizza and the price of a separate related good. The demand function for personal pizzas is

Qd = 480 - 5P + 10Pj

where Qd is the number of personal pizzas demanded per month, P is the price of a personal pizza, and Pj is the price of the related good. a. Suppose that P = $6 and Pj = $9. What does

the cross-price elasticity of demand equal? b. Based on the answer to part a, is the related

good a substitute or a complement to pizza?

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138  

4

Pizza Hut Managers Learn That Size Matters

In 2014, Pizza Hut had about 6,300 restaurants in the United States. Although this number is impressive, exec- utive managers at Pizza Hut realized that they had a prob- lem. Most of the existing locations featured both delivery and dine-in services, so they were large restaurants with correspondingly high costs. Potential franchisees became unwilling to open new restaurants because their high costs made them unprofitable. From 2001 to 2014, the number of Pizza Hut restaurants in the United States actu- ally decreased from 7,700 to 6,300 because franchisees closed more restaurants than they opened.

After crunching some data, Pizza Hut’s research department calculated that the fraction of their pizza sales

involving home delivery had fallen. Delivery is the most popular way for consumers to buy pizza, so Pizza Hut’s executive managers needed to boost delivery sales. They also recognized a cost problem: Conventional Pizza Hut restaurants were too large to make focusing primarily on home delivery profitable. What could Pizza Hut’s manag- ers do to increase the number of their stores, and thereby their profit, in the face of these challenges?

This chapter explains the relationship between the costs of inputs, such as labor and capital, and the amount of output. At the end of the chapter, you will learn how Pizza Hut’s executives could have evaluated these factors in creating a plan to improve their company’s operation.

Sources: Annie Gasparro, “Pizza Hut Scales Down to Boost Delivery,” Wall Street Journal, October 2, 2012; Annie Gasparro, “Yum Pizza Hut Pares Outlet size; Delivery Is Focus,” Marketwatch, October 3, 2012; Rick Hynum, “The 2015 Pizza Power Report,” PMQ Pizza Magazine, December 2014; A World of Yum! (2005 YUM Annual Report).

Production and Costs

Learning Objectives After studying this chapter, you will be able to:

4.1 Explain the relationship between a firm’s inputs and its output as well as calculate the marginal product of an input.

4.2 Use the cost-minimization rule to choose the combination of inputs that produces a given quantity of output at the lowest cost.

4.3 Distinguish between fixed cost and variable cost and calculate average total cost, average variable cost, average fixed cost, and marginal cost.

4.4 Derive the long-run average cost curve and explain its shape. 4.5 Apply production and cost theory to make better managerial decisions.

C H

A P

T E

R

Introduction Successful businesses must respond to consumers’ demands for goods and services. The amount of a good or service a firm produces depends on the demand for that good or service and the opportunity costs of producing it.1 The costs depend on four factors:

1. The quantity of inputs, such as labor and capital, utilized 2. The cost of each input

1 For the sake of brevity, we usually drop the modifier opportunity in front of the word cost, but keep in mind that as a manager you must always be concerned with opportunity cost rather than accounting cost.

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4.1 Production  139

3. The production technology utilized 4. The managers’ efforts to minimize the cost of production

The chapter begins with an analysis of the firm’s production function, which is the relationship between the firm’s inputs and its output. For simplicity, the discussion assumes that managers know their firm’s production function. Unfortu- nately, managers often begin with only a vague idea. Discovering the best way to organize inputs to produce a good or service can be a challenging trial-and- error process. This chapter can help you develop a strategy to work through this trial-and-error process and make the managerial decisions that lead to the most efficient production.

Next, you will learn about costs by deriving and illustrating a firm’s cost curves. Because the firm incurs costs for its use of inputs, the cost curves are closely related to the firm’s production technology and the productivity of the inputs. The cost curves are the foundation for the next several chapters, which provide valuable insights into managers’ profit-maximizing decisions about the amount of output to produce and the price to charge.

To help you understand the important concepts of production and costs, Chapter 4 includes five sections:

• Section 4.1 explores the production function, the difference between the short run and the long run, and the definitions of the marginal product of labor and capital.

• Section 4.2 describes how to determine the combination of inputs that produces the desired quantity of output at the minimum cost.

• Section 4.3 explains how costs change in the short run when production changes. • Section 4.4 examines how costs change in the long run when production changes. • Section 4.5 discusses how you can apply production and cost theory to make better man-

agerial decisions.

4.1 Production Learning Objective 4.1 Explain the relationship between a firm’s inputs and its output as well as calculate the marginal product of an input.

Suppose that you are a general manager of an Italian restaurant, like Olive Garden, and you report to a district manager. One of your goals is to produce your output (Italian dinners) as efficiently as possible, which generally means producing the dinners at the lowest possible cost. If you minimize the cost of producing the out- put, you will be well on your way to maximizing the profit of your restaurant. To make the best decisions about costs, you must understand some basic elements of production.

Production Function When a firm produces a good or service, it combines inputs, called factors of produc- tion, according to a precise procedure or “recipe,” called a production function. At your Italian restaurant, inputs consist of

• The workers you hire, such as chefs and servers • Raw materials, such as lettuce and chicken • Capital equipment, such as grills and ovens • Intermediate goods, such as olive oil and flour

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140  CHAPTER 4 Production and Costs

The production function is the relationship between different amounts of a firm’s inputs and the maximum quantity of output it can produce with those inputs. Mathematically, the production function is written as Q = f1X1, X2, c, Xn2, where

• Q is the quantity of output • Xs are the inputs • f is the function, or “recipe,” that converts the inputs into output

The function, f, incorporates the current state of technology. Changes in technol- ogy change the production function and generally enable firms to produce more output using the same or even smaller quantities of inputs.

A production function that uses many inputs can be complex. For simplicity, let’s focus on a simple firm that uses only two inputs, labor and capital equipment. This firm’s two-input production function can be written as Q = f1L, K2, where Q is the quantity of output, f is the production function, L is the quantity of the labor input, and K is the quantity of the capital input. This simplified two-input produc- tion function will provide lessons and insights that you can apply to real-world pro- duction decisions involving many more than two inputs.

Short Run and Long Run Within a given period of time, it is more difficult for a firm to obtain and use addi- tional units of some inputs than others. For instance, at your Italian restaurant, it would be very expensive, if not impossible, to increase the size of the dining area by 20 percent in the space of a week. During that same week, however, you could easily hire an additional server. On the other hand, if you had a year to make changes, it would be easy to both increase the size of your dining area and hire another server. Economists define two periods of time that reflect these differences: the short run and the long run. The short run is the period of time during which at least one input is fixed, so that a firm cannot vary the quantity of that input. Using the two-input production function with capital and labor as the only inputs, in the short run capital is the fixed input and labor is the variable input. For a restaurant, the size of the dining room (capital) is a fixed input in the short run. The long run is a period of time long enough that no input is fixed, allowing a firm to vary the quantity of all the inputs it uses. Because managers can change the amounts used, in the long run both capital (expansion of the dining area) and labor (the addition of a server) are variable inputs.

The long run varies widely among firms. It might take a firm like Darden, the parent company of Olive Garden, two years to obtain the permits and construct a new Olive Garden restaurant. By comparison, it might take as long as six years for a computer chip–producing company like Intel to obtain permits, construct a new manufacturing facility, and then certify it.

Long-run decisions are often more difficult or more costly to reverse—the cost of building an unnecessary factory dwarfs the cost of hiring an unnecessary worker. So decisions about the long run are more strategic in nature. Generally, upper-level management or executives make long-run decisions. Short-run decisions are often more tactical, however, and can be made by midlevel managers.

With more than two inputs, the complexity of the production function increases because it takes different amounts of time for different inputs to become variable. For example, at your restaurant, it is possible to change the number of servers within a week, but it could take two months to hire a new skilled chef, three months to add a new oven, and two years to remodel the entire restaurant. As this example shows,

Production function The relationship between different amounts of a firm’s inputs and the maximum quantity of output it can produce with those inputs.

Short run The period of time during which at least one input is fixed, so that a firm cannot vary the quantity of that input.

Long run A period of time long enough that no input is fixed, allowing a firm to vary the quantity of all the inputs it uses.

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4.1 Production  141

you can make more profound changes as time passes, which is reflected in differ- ences in the short-run production function and the long-run production function.

Short-Run Production Function The previous section pointed out that firms can vary the quantity of labor (number of servers) more quickly than capital (expansion of the dining area), which for the short run makes capital a fixed input and labor a variable input. So the short-run pro- duction function, when there is at least one fixed input, is

Q = f1L, K2 where the bar over K signifies that the quantity of capital is fixed.

You can get a feeling for this short-run production function for your Italian restaurant by examining the hypothetical data and graph in Figure 4.1. Figure 4.1(a) assumes that the restaurant’s capital—the size of the dining room, number of ovens, and number of booths—is fixed and equal to 5 units of capital. The curve labeled PF in Figure 4.1(b) is the short-run production function for 5 units of capital, plotted from the data in Figure 4.1(a). The PF curve illustrates the relationship between the quantity of labor (the number of workers) on the horizontal axis and quantity of out- put (the number of dinners per day) on the vertical axis.

To derive the data and then the graph in Figure 4.1, you need to determine the relationship between the number of dinners produced and the number of employ- ees. Conceptually, you could experiment by starting with one employee per shift and then adding extra workers, while keeping track of the quantity of dinners served. The production data in Figure 4.1 represent these hypothetical findings. As you can

Output (dinners per day)

Labor (workers)

350

50

100

121110987654321

150

200

250

300

0

PF

Capital, K (units of capital)

Labor, L (workers)

Output, Q (dinners per

day)

5 0 0

5 1 10

5 2 30

5 3 60

5 4 110

5 5 170

5 6 220

5 7 260

5 8 290

5 9 310

5 10 320

5 11 310

Figure 4.1 The Short-Run Production Function

The data represent the short-run production function for 5 units of capital.

The figure graphs the data from part a and shows the short- run production function, PF.

(a) Production Data (b) Short-Run Production Function

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142  CHAPTER 4 Production and Costs

see from the data and curve in Figure 4.1, the output begins to decrease with the 11th worker. No manager would add more workers when doing so decreases output, so there is no need to include data beyond 11 workers.

For small quantities of labor, output responds dramatically to changes in labor. Why? Suppose you start with a single worker. This worker would need to seat the customers, take the orders, cook the food, serve the food, collect the payment, and bus the tables. As you add more workers, they waste less time scurrying around from one place to another, allowing them to be more efficient and produce more output (dinners) and thereby serve more customers. In addition, greater specialization of labor is possible. Some workers specialize in cooking, others in serving the custom- ers, and still others in busing the tables. Specialization also increases the output (the dinners). Both the more efficient use of labor and the increase in specialization mean that as the managers hire more labor, each additional worker increases the firm’s out- put by more than the previous worker. As more labor is used, however, eventually output increases more slowly in response to increases in the number of workers because the opportunity for additional gains diminishes. Finally, as the managers add more and more workers, the congestion of workers becomes so severe that the restaurant reaches its maximum output. In Figure 4.1, the maximum output is 320 dinners per day. Any further additions to the workforce—say, going from 10 to 11 workers per shift—actually decrease the quantity of output.

Marginal Product The production function highlights a crucial decision for managers: determining the optimal quantity of an input to employ. This decision depends on the input’s pro- ductivity and its cost compared to other inputs’ productivities and costs. The rele- vant measure of productivity is the input’s marginal product, which is the change in total output that results from changing the input by one unit while keeping the other inputs constant.

Using this definition, the marginal product of labor (MPL) is the change in total output that results from changing labor by one unit while keeping the other inputs constant. It equals

MPL = 1Change in output2 1Change in labor2 =

1∆Q2 1∆L2

In this equation, the delta symbol (Δ) means “change in,” Q is output, and L is labor.

Figure 4.2(a) shows the marginal product of labor from the same data included in Figure 4.1(a). To calculate the marginal product of labor, divide the change in the number of dinners by the change in the number of workers. For example, the marginal product of labor of increasing the number of workers from 6 to 7 equals

1260 dinners - 220 dinners2 17 workers - 6 workers2 = 40 dinners per worker

which means that increasing the number of workers from 6 to 7 enables your Italian restaurant to produce an additional 40 dinners per day. In Figure 4.2(a), this mar- ginal product is located between 6 and 7 workers. The remaining results in the third column of Figure 4.2(a) are calculated in the same way.

Figure 4.2(b) shows the behavior of the MPL curve: As the number of workers increases, the marginal product of labor starts small, rises, hits a maximum, and then decreases. This is a graphic example of the economics of the situation. When only a

Marginal product The change in total output that results from changing an input by one unit while keeping the other inputs constant.

Marginal product of labor The change in total output that results from changing labor by one unit while keeping the other inputs constant.

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4.1 Production  143

Labor, L (workers)

Output, Q (dinners per day)

Marginal Product of Labor

(dinners per worker)

MPL

Marginal product (dinners per worker)

Labor (workers)

70

0

10

20

121110987654321

30

40

50

60

210

0 0 10

20

30

50

60

50

40

30

20

10

-10

1 10

2 30

3 60

4 110

5 170

6 220

7 260

8 290

9 310

10 320

11 310

Figure 4.2 The Marginal Product of Labor

The marginal product of labor equals 1Change in Q2 (Change in L) .

The third column shows the marginal product of labor obtained by dividing the change in output (column 2) by the change in labor (column 1). For example, the marginal product of labor of increasing employment from 4 to 5 workers equals 1170 dinners - 110 dinners2 15 workers - 4 workers2 = 60 dinners per worker.

The figure plots the marginal product of labor (MPL) for each worker using the data from part a.

(a) Marginal Product of Labor Data (b) Marginal Product of Labor Curve

few workers are employed, hiring another worker results in increased specialization and increases the efficiency of all of the workers, leading to a large increase in out- put—that is, a large MPL. Eventually, the marginal product of labor hits its maxi- mum, which occurs at 4½ workers in Figure 4.2(b). Then as managers hire more workers, congestion sets in, and there is a smaller increase in output from hiring another worker. Of course, the number of workers and the numerical value of the maximum marginal product of labor differ from company to company, but the gen- eral appearance of the curve is similar to the one shown in Figure 4.2(b).

Figure 4.3 shows the relationship between the production function and the mar- ginal product of labor curve by illustrating both in the same diagram. As labor increases from 1 worker to 4½ workers, the production function rises and becomes steeper—each additional worker increases output by more than the previous worker—so the marginal product of labor increases in this range. The range over which the marginal product of labor increases is defined as the range with increasing marginal returns to labor.

For the range of workers between 4½ and 10, the production function still rises, but it becomes less steep—each additional worker increases output by less than the previous worker—so the marginal product of labor decreases in this range. The range over which the marginal product of labor decreases but remains positive is defined as the range with decreasing marginal returns to labor.

Increasing marginal returns to labor The range of labor input over which the marginal product of labor increases.

Decreasing marginal returns to labor The range of labor input over which the marginal product of labor decreases but remains positive.

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144  CHAPTER 4 Production and Costs

Finally, for all workers beyond 10, the production function falls—each addi- tional worker decreases output. Consequently, the marginal product of labor is nega- tive in this range. The range over which the marginal product of labor is negative is defined as the range with negative marginal returns to labor.

The concept of marginal product applies to other inputs besides labor. Each input has its own marginal product, equal to the change in output that results from changing that input by one unit while keeping all the other inputs constant. For example, in the long run, managers can change the quantity of capital, so at that point the marginal product of capital (MPK) is equal to

MPK = ∆Q ∆K

More realistic production functions include more than two inputs, but the mar- ginal products for all other inputs are calculated in the same way. The inputs will have the same three ranges described above: initially increasing marginal returns followed by decreasing marginal returns and ending with negative marginal returns.

The marginal product for each input is important knowledge for managers because it helps determine the cost-minimizing combination of inputs. Unfortu- nately, as a manager, you will never know the precise production function or the precise marginal product of your inputs. You can estimate approximate values using records of changes in output resulting from changes in the use of an input, perhaps by using regression analysis as explained in Chapter 3 (see Section 3.1). Alternatively, you might use your best managerial judgment to estimate the marginal product. Regardless of how you obtain your estimate, as you will learn in Section 4.2, know- ing the marginal product is essential to accomplishing the goal of minimizing your firm’s costs.

Negative marginal returns to labor The range of labor input over which the marginal product of labor is negative.

Figure 4.3 Increasing, Decreasing, and Negative Marginal Returns to Labor

The range over which the marginal product of labor increases, from 0 to 4½ workers in the figure, has increasing marginal returns to labor. The range over which the marginal product of labor decreases but is positive, 4½ to 10 workers in the figure, has decreasing marginal returns to labor. The range over which the marginal product of labor decreases and is negative, more than 10 workers in the figure, has negative marginal returns to labor.

Output and marginal product

Labor (workers)

350

50

250

100

121110987654321

150

200

250

300

0

MPL

Increasing marginal returns

to labor

Negative marginal returns to labor

Decreasing marginal returns to labor

PF

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4.1 Production  145

The Impact of Changes in Technology A change in technology shifts the production function. Typically, advances in tech- nology allow the firm to produce more output from the same quantity of inputs. For example, suppose that a new convection oven technology doubles the number of dinners your Italian restaurant can produce at each quantity of workers. As illus- trated in Figure 4.4(a), the technological advance shifts the production function upward. Technological advances also generally increase the marginal product of labor. The technological advance that doubles the number of dinners shifts the mar- ginal product of labor curve upward, as shown in Figure 4.4(b).

Long-Run Production Function In the long run, all inputs are variable, so managers can change the quantity of all of the inputs. For a two-input production process, you can write the long-run production func- tion, when all inputs are variable, as Q = f1L, K2, where both labor, L, and capital, K, can be changed. The long-run production function is more difficult to illustrate in a figure because even with just two inputs the figure needs to be three-dimensional to take account of the two inputs and one output. Instead of trying to illustrate a long-run production function, Table 4.1 presents a portion of the long-run production function using data from the Italian restaurant example.

Output (dinners per day)

Labor (workers)

700

100

200

121110987654321

300

400

500

600

0

PF1

PF0

Marginal product (dinners per worker)

Labor (workers)

140

20

220

40

121110987654321

60

80

100

120

0

MP1 MP0

Figure 4.4 The Effects of a Technological Advance

(a) The Effect of a Technological Advance on the Production Function

(b) The Effect of a Technological Advance on the Marginal Product of Labor Curve

An improvement to technology shifts the production function upward, from PF0 to PF1.

An improvement to technology shifts the marginal product of labor curve upward, in the figure from MP0 to MP1, though in general the unit of labor with the maximum marginal product will change.

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146  CHAPTER 4 Production and Costs

For any given amount of capital, such as the 4 units shown in Table 4.1, the mar- ginal product of labor follows the same pattern described earlier: It rises to a maxi- mum during a range with increasing marginal returns and then falls during a range with decreasing marginal returns. Although there are not enough data in the table to show its entire pattern, the marginal product of capital follows the same behavior: It rises to a maximum during a range with increasing marginal returns and then falls during a range with decreasing marginal returns. For example, holding employment constant at 5 workers, the marginal product of capital when capital is increased from 4 to 5 units is

1170 dinners - 130 dinners2 15 units of capital - 4 units of capital2 = 40 dinners per unit of capital

Then the marginal product of capital when capital is increased from 5 to 6 units is

1230 dinners - 170 dinners2 16 units of capital - 5 units of capital2 = 60 dinners per unit of capital

These two marginal products of capital fall within the increasing marginal returns range, but if you continued to calculate the marginal product of capital for larger and larger amounts of capital, eventually it would hit a maximum and then begin to decrease.

Using the marginal product along with the prices of the different inputs enables you to make decisions that minimize the cost of producing your firm’s product. The next section explains how to make these decisions.

Table 4.1 The Long-Run Production Function

These data represent the long-run production function.

Production Data

Capital, K

(units of capital)

Labor, L

(workers)

Output, Q

(dinners per day)

Capital, K (units of

capital)

Labor, L

(workers)

Output, Q

(dinners per day)

Capital, K

(units of capital)

Labor, L

(workers)

Output, Q

(dinners per day)

4 0 0 5 0 0 6 0 0

4 1 8 5 1 10 6 1 12

4 2 26 5 2 30 6 2 34

4 3 50 5 3 60 6 3 72

4 4 85 5 4 110 6 4 140

4 5 130 5 5 170 6 5 230

4 6 170 5 6 220 6 6 300

4 7 205 5 7 260 6 7 350

4 8 235 5 8 290 6 8 390

4 9 250 5 9 310 6 9 420

4 10 240 5 10 320 6 10 440

4 11 230 5 11 310 6 11 450

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4.2 Cost Minimization  147

4.2 Cost Minimization Learning Objective 4.2 Use the cost-minimization rule to choose the combination of inputs that produces a given quantity of output at the lowest cost.

When a firm uses an input, it incurs a cost. Regardless of whether you are managing a for-profit firm, a not-for-profit organization, a government agency, or an NGO, your goal should be to use the mix of inputs that minimizes the cost of producing the desired quantity of the good or service. You will constantly face decisions about the amount of each input to use when producing your product. For instance, if you are a general manager at a restaurant, should you hire another server and let a table busser go, or should you purchase another dish-washing machine and fire a dish- washer? If you are a manager at a nonprofit like the American Red Cross, should you buy another emergency response vehicle and fire five disaster workers and two CPR trainers? As the choices faced by these managers demonstrate, all the different types of organizations use multiple inputs. For simplicity, however, the text discus- sion continues to use the two-input production function, Q = f1L, K2. Learning how to minimize cost with only two inputs will help you understand the process for the real-world case of many inputs.

As you have already learned, some inputs are fixed in the short run. You cannot change the quantity of fixed inputs, so you must focus on minimizing the cost of the variable inputs to optimize production and minimize the total cost. To demonstrate how to choose the quantities of variable inputs to minimize costs, assume that you are dealing with the long run so that both inputs (labor and capital) are variable. Although the demonstration uses labor and capital, the results apply to any combi- nation of variable inputs.

Marginal Product of Labor at a Bicycle Courier Service

You are a manager at a firm like Snap Delivery, a bicycle courier service in New York City. You estimate that if you hire 10 couriers, you can deliver 180 packages a day and if you hire 11 couriers, you can deliver 198 packages a day. You also estimate that the price you can charge for the delivery of each package will be $25. What is the marginal product of labor for the 11th courier? What is the effect of the price on the marginal product of labor?

Answer

The marginal product of labor is equal to the change in the output divided by the change in labor, or

MP L = ∆Q ∆L

The total output using 11 couriers is 198 packages, and the total output using 10 couriers is 180 packages. So the change in output, ∆Q, that occurs by adding the 11th courier is 198 packages - 180 packages, or 18 packages. The change in employment, ∆L, is 1 worker, so the marginal product of the 11th courier is 118 packages2 >11 worker2, or 18 packages. The price of the delivery plays no role in determining the marginal product because the marginal product is based solely on the change in output and the change in input.

SOLVED PROBLEM

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148  CHAPTER 4 Production and Costs

The decision to use an additional unit of an input—say, hire a worker—has two immediate effects:

1. The firm’s output increases. Recall that the marginal product of labor is the amount by which production increases, so hiring another worker increases the firm’s output by MPL units.

2. The firm’s total cost increases. Assume that the cost of hiring a worker is the wage rate (W), the amount that the worker must be paid. In reality, firms must also pay taxes, unemployment insurance, and possibly fringe benefits. More- over, merely employing another worker usually does not increase production on its own because additional raw materials must often be purchased. For example, when you hire another cook for your restaurant, you might also need to pur- chase more flour to enable that worker to boost production of pasta and bread. For simplicity, consider all of these costs (taxes, fringe benefits, unemployment insurance, and price of other necessary materials) as part of the wage rate, W.

Cost-Minimization Rule To derive the cost-minimization rule, start by combining the marginal product of labor and the wage rate into one term, MPLW . This term measures the change in output that results from a $1 change in the quantity of labor employed. For example, if the wage of a restaurant worker is $100 and the marginal product of the worker is 20 dinners, then

MPL W

= 20 dinners

$100 = 0.2 dinners per dollar

In other words, as the restaurant’s general manager, for each additional dollar spent on labor you gain 0.2 dinners. Alternatively, for each decrease of a dollar spent on labor you lose 0.2 dinners.

Similar calculations hold for any input. For example, if R is the cost of using an additional unit of capital equipment,2 then MPKR is the change in production from a $1 change in the quantity of capital used.

Using both of these fractions, you arrive at the cost-minimization rule: To mini- mize cost, a firm should use the combination of labor and capital that produces the desired amount of output and is such that MPLW =

MPK R .

To minimize cost, a firm should use the combination of labor and capital that produces

the desired amount of output and is such that MP LW = MP K

R .

COST-MINIMIZATION RULE

2 Both the services from and the expenditures for a piece of capital equipment typically accrue for many periods. This fact complicates the proper measurement of the cost of capital. Chapter 16 covers these issues in detail. This chapter sidesteps this difficulty by assuming that both MPK and R are measured correctly.

Why does this equality minimize cost? It minimizes cost because if the two terms are not equal, a manager can adjust the quantity of inputs used and lower the cost without changing the total quantity produced. Let’s see how these adjustments work:

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4.2 Cost Minimization  149

• If MPLW 7 MPK

R , the quantity of inputs can be changed to lower the firm’s cost.

For example, suppose that MPLW = 6 units per dollar and MPK

R = 2 units per dollar. At these values, reducing the amount spent on capital by $3 decreases produc-

tion by 6 units 12 units * $32, and increasing the amount spent on labor by $1 increases production by 6 units. Combining these changes leaves the quantity

produced unchanged but lowers the cost by $2 1$3 - $12. More generally, whenever MPLW 7

MPK R , you can lower the total cost by increasing the amount of

labor used and decreasing the amount of capital used. As you make these changes, the increase in the quantity of labor decreases the marginal product of labor, and the decrease in the quantity of capital increases the marginal product

of capital, thereby driving the inequality MPLW 7 MPK

R toward the cost-minimizing

equality, MPLW = MPK

R . But as long as MPL W exceeds

MPK R , increasing the amount of

labor used and decreasing the amount of capital used lowers the total cost.

• If MPKR 7 MPL W , the cost can once again be reduced by adjusting the quantity of

inputs employed. In this case, however, you would increase the quantity of capital and decrease the quantity of labor. Suppose that MPKR = 8 units per dollar and

MPLW = 1 unit per dollar. At these values, reducing the amount spent on labor by $8 decreases production by 8 units 11 unit * $82, and increasing the amount spent

on capital by $1 increases production by 8 units. Combining these changes again leaves the quantity produced unchanged but lowers the cost, this time by $7 1$8 - $1). As you make this change, the increase in the quantity of capital decreases the marginal product of capital, and the decrease in the quantity of labor increases

the marginal product of labor, driving the inequality MPKR 7 MPL W toward the cost-

minimizing equality, MPLW = MPK

R . As long as MPK

R exceeds MPL W , increasing the amount

of capital used and decreasing the amount of labor used lowers the total cost.

The cost-minimizing lesson from these examples is straightforward: Increase spending on the input with the larger output per dollar, and reduce spending on the input with the lower output per dollar.

Generalizing the Cost-Minimization Rule The cost-minimization rule generalizes beyond the example of two inputs. To mini- mize the cost of producing the desired quantity of output with more than two inputs requires that

MP1 P1

= MP2 P2

= MP3 P3

= c MPn Pn

4.1

In Equation 4.1, MP1 is the marginal product of the first input and P1 is the price of the first input, MP2 is the marginal product of the second input and P2 is the price of the second input, and so on. For example, if the first input is labor, then MP1 is the marginal product of labor, MPL, and P1 is the wage rate, W.

The intuition behind Equation 4.1 and that behind the two-input cost-minimization rule are identical. When MPi is the marginal product of input i and Pi is its price, then the term MPiPi equals the change in output from changing spending on input i by $1. According to the cost-minimization rule, these terms must be equal for all inputs, so the change in output from changing spending by $1 on any input must be equal for all inputs. If these quantities are not equal, the manager can lower costs by buying

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150  CHAPTER 4 Production and Costs

4.3 Short-Run Cost Learning Objective 4.3 Distinguish between fixed cost and variable cost and calculate average total cost, average variable cost, average fixed cost, and marginal cost.

Effective managers make decisions based on understanding how their firm’s costs change when the production of output changes. This section begins by examining

Cost Minimization at a Construction Firm

As a construction manager for a firm like KB Home, you employ carpenters and carpen- ter assistants. You pay your carpenters $800 per week and your carpenter assistants $500 per week. The marginal product of a carpenter is construction of 2 rooms per week, and the marginal product of a carpenter assistant is construction of 1 room per week. Are you minimizing your costs? Explain your answer.

Answer

Cost minimization requires that

MP CARPENTER WCARPENTER

= MPASS‘T CARPENTER WASS‘T CARPENTER

But using the data in the problem shows that

2 rooms per week $800 per week

≠ 1 room per week

$500 per week

so you are not minimizing your costs. Spending an additional dollar on a carpenter increases your construction of rooms by more than spending that dollar on a carpenter assistant, so increasing the number of carpenters and decreasing the number of carpenter assistants will decrease your cost. You can verify this conclusion by noticing that hiring an additional carpenter for ½ of a week enables you to construct 1 room at a cost of $400, while laying off a carpenter assistant for a week decreases your construction by 1 room but saves you $500 in cost. Combining these changes leaves the number of rooms you construct the

same, but your costs fall by $100. As long as the MP CARPENTERWCARPENTER and MPASS‘T CARPENTER WASS‘T CARPENTER

terms are not

equal, you can decrease your cost by using more of the input with the larger change in production per dollar and less of the input with the smaller change in production per dollar.

SOLVED PROBLEM

more of the inputs that give the manager more output (those with high MPP ) and buying fewer of the inputs that give the manager less output (those with low MPP ). No matter how many inputs managers use in the production process, whenever the change in output from spending $1 on one input differs from that for another input, managers can lower the total cost by using more of the input with the larger change in output and less of the input with the smaller change.

Successful managers make decisions that minimize the cost of producing a given quantity of output. They also know how costs change when the quantity of output changes. You will begin to learn about this important topic in the next section on short-run changes in cost.

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4.3 Short-Run Cost  151

short-run costs. As you learned in Section 4.1, the short run is the time period during which at least one input is fixed. To capture this difference between inputs, again use the two-input short-run production function, Q = f1L, K2. Recall that the bar over K signifies that the quantity of capital is fixed. This two-input short-run production function means that managers can change the quantity produced only by changing the quantity of the variable input, labor. In reality, managers can change the quantity produced by adjusting the amount(s) of any of a larger number of variable inputs. But as usual, once you understand the two-input production function, you can apply this simplified approach to more realistic situations.

Fixed Cost, Variable Cost, and Total Cost Regardless of the number of inputs, all the inputs can be sorted into one of two cate- gories: fixed or variable. The sum of the costs paid for all fixed inputs is called the fixed cost (FC). Fixed cost does not change with changes in output because the quan- tity of fixed inputs cannot be changed. The sum of the costs paid for all variable inputs is called the variable cost (VC). Variable cost changes with changes in output because managers must change the quantity of variable inputs in order to change output. Since every input falls into one of the two groups (fixed inputs or variable inputs), the total cost (TC) of the inputs equals the sum of the fixed costs (for the fixed inputs) and the variable costs (for the variable inputs), or

TC = FC + VC

Table 4.2 relates a firm’s production function to its costs. The first three col- umns of Table 4.2 are from the production function shown in Table 4.1 when your Italian restaurant uses 6 units of capital (K). The fixed input is capital, so the cost of the capital is the fixed cost. Suppose that the cost of each unit of capital, which might represent rental payments on the building, interest payments due on the capital equipment, or the economic depreciation of the capital, is $83.33. The fixed cost (FC) for all 6 units is $500, 6 units of capital multiplied by $83.33 per unit of capital. The variable input is labor, so the cost of the labor is the variable cost. Suppose that the cost of each unit of labor (the sum of the wage rate plus other costs of hiring a worker) is $100. In the first row of Table 4.2, when no work- ers are hired, the variable cost is $0. In the second row, when one worker is hired, the variable cost is $100. In the third row, when two workers are hired, the variable cost is $200.

Table 4.2 illustrates a fundamental difference between fixed cost and variable cost: The fixed cost remains constant when output changes, but the variable cost changes with a change in output. This difference reflects the distinction between a fixed input and a variable input. In the short run, a firm cannot change the amount of its fixed input(s), so the fixed cost remains constant—fixed—when output changes. But to change its output, the firm must change the amount of its variable input(s), so when output changes, so does the variable cost.

Table 4.2 shows two other significant aspects of total cost:

1. Even when output is zero—that is, even when the firm is closed—the firm still incurs a cost. In particular, the firm still must pay its fixed costs. Although the variable costs are zero when the firm is closed, the total cost is not zero.

2. When output changes, the total cost changes. When output increases, the total cost increases. When output decreases, the total cost decreases. This relationship is due entirely to the changes in the variable costs when output changes.

Fixed cost The sum of the costs paid for all fixed inputs; fixed cost does not change when output changes.

Variable cost The sum of the costs paid for all variable inputs; variable cost changes when output changes.

Total cost The sum of the fixed cost and the variable cost; TC = FC + VC .

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152  CHAPTER 4 Production and Costs

Sunk Cost Versus Fixed Cost In Chapter 1 you learned about sunk costs, costs that you cannot recover because they have been paid or incurred in the past. Costs that have already been paid do not change when output changes. Consequently, all sunk costs are fixed costs, but not all fixed costs are sunk costs. For example, your restaurant might have a month-to-month rental agreement that specifies rent on the site of $200 per day. The rent is a fixed cost because it pays for a fixed input and does not change with the number of dinners produced. But the rent is not a sunk cost because the restaurant pays it month by month.

Average Fixed Cost, Average Variable Cost, and Average Total Cost The next three columns of Table 4.2 have data related to three more cost concepts: average fixed cost, average variable cost, and average total cost. The definitions of these three cost concepts are similar. Average fixed cost (AFC) is the fixed cost (FC) divided by the amount of output (Q), or, in algebraic terms, AFC = FCQ . The average variable cost (AVC) is the variable cost (VC) divided by the amount of output, or AVC = VCQ . Finally, the average total cost (ATC) is the total cost (TC) divided by the

amount of output, or ATC = TCQ . Average total cost also equals the sum of the average fixed cost and the average

variable cost: ATC = AFC + AVC. This alternative expression is derived from the definition of total cost: TC = FC + VC. Divide both sides of the total cost definition by the quantity (Q), and the result is

TC Q

= FC Q

+ VC Q

1 ATC = AFC + AVC

Average fixed cost Fixed cost divided by the amount of output; AFC = FCQ .

Average variable cost Variable cost divided by the amount of output; AVC = VCQ .

Average total cost Total cost divided by the amount of output; ATC = TCQ .

Table 4.2 Short-Run Production Function and Cost Data

The table presents a short-run production function and the resulting costs. The cost of a unit of labor is $100, and the cost of a unit of capital is $83.33. Because marginal cost is calculated for a change in output, each MC is placed midway between two rows, indicating that it applies to the change in output between the rows.

Capital, K

Labor, L

Output, Q

Fixed Cost, FC

Variable Cost, VC

Total Cost, TC

Average Fixed Cost, AFC

Average Variable

Cost, AVC

Average Total Cost, ATC

Marginal Cost, MC

6 0 0 $500 $0 $500 X X X $8.33

4.55

2.63

1.47

1.11

1.43

2.00

2.50

3.33

5.00

10.00

6 1 12 500 100 600 $41.67 $8.33 $50.00

6 2 34 500 200 700 14.71 5.88 20.59

6 3 72 500 300 800 6.94 4.17 11.11

6 4 140 500 400 900 3.57 2.86 6.43

6 5 230 500 500 1,000 2.17 2.17 4.35

6 6 300 500 600 1,100 1.67 2.00 3.67

6 7 350 500 700 1,200 1.43 2.00 3.43

6 8 390 500 800 1,300 1.28 2.05 3.33

6 9 420 500 900 1,400 1.19 2.14 3.33

6 10 440 500 1,000 1,500 1.14 2.27 3.41

6 11 450 500 1,100 1,600 1.11 2.44 3.56

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4.3 Short-Run Cost  153

Figure 4.5 shows how the average fixed cost, average variable cost, and average total cost change when quantity increases or decreases. The behavior of the AFC curve is unique: The average fixed cost constantly falls as the quantity increases.3 In Figure 4.5, the average fixed cost (the blue curve) falls from $14.71 when 34 dinners are produced to $1.11 when 450 dinners are produced. As additional dinners beyond 450 are produced, the average fixed cost continues to fall.

The shapes of the AVC curve and the ATC curve are more complicated. As Table 4.2 and Figure 4.5 show, both of these costs start out large, decrease until they hit a minimum, and then increase. The U shape is typical of the AVC curve (in red) and the ATC curve (in green) for any type of firm, not just a restaurant. Of course, different firms reach the minimum points on the curves at different amounts of production.

The explanation of the U shape must wait until the next section, which covers mar- ginal cost. For now, note that in Figure 4.5 the vertical distance between the two curves becomes smaller as output increases. The equation ATC = AFC + AVC shows why. Rearranging it to ATC - AVC = AFC shows that the difference between the average total cost and the average variable cost is the average fixed cost. As you just learned, the average fixed cost becomes smaller as output increases. With average fixed cost becoming smaller, the difference between the average total cost and average variable cost becomes smaller, which means that the AVC curve approaches the ATC curve.

Marginal Cost As a manager, knowing your average total cost and average variable cost can be helpful in making decisions, but knowing yet another cost, the marginal cost, is sig- nificantly more important. Like all marginal concepts, the marginal cost focuses on changes. The marginal cost (MC) is the change in the total cost brought about by a

Marginal cost (MC ) The change in total cost (TC ) divided by the change in output (Q ); MC = ∆TC∆Q .

3 As output increases, fixed cost does not change. Consequently, for the average fixed cost, as output increases the numerator does not change and the denominator increases, so the fraction falls in value.

Cost (dollars per dinner)

Output (dinners per day)

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

$14.00

$16.00

$18.00

$20.00

47542537532527522517512575250

ATC AVC

AFC

Figure 4.5 AFC, AVC, and ATC Curves

The three cost curves are derived from the data in Table 4.4. Both the AVC and the ATC curves are U-shaped. The vertical distance between the AVC and ATC curves becomes smaller as the quantity increases.

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154  CHAPTER 4 Production and Costs

The marginal cost shows the change in total cost when output changes. Because the fixed cost does not change when output changes, it has no effect on the marginal cost.

The last column in Table 4.2 shows the marginal cost for your Italian restaurant. Because marginal cost is calculated for a change in output, each MC listing in the table is placed midway between two rows, indicating that it applies to the change in output between the rows. For example, when output increases from 300 to 350 units, the total cost increases from $1,100 to $1,200, so the marginal cost equals $10050 = $2.00 per dinner.

Figure 4.6 shows the MC curve calculated from the data in Table 4.2, along with the AVC curve and the ATC curve. In Figure 4.6, the marginal cost values are plotted midway between the relevant quantities, indicating that the marginal cost applies to the change in output between these quantities. For example, the marginal cost of increasing production from 34 to 72 dinners, $2.63, is plotted at 53 dinners, midway between 34 and 72 dinners.

Figure 4.6 shows that the marginal cost initially falls and then rises as the quan- tity increases. The general U shape of the MC curve is common to all firms. In fact, the U shape of the MC curve is the consequence of how the marginal product of the variable inputs changes as output changes.

Suppose that labor is the only variable input. The cost of hiring an additional worker is W, and the increase in output is MPL. Consequently, the cost of producing one more unit of output—the marginal cost—by hiring an additional worker is equal to WMPL. For example, using the data in Table 4.2, hiring the first restaurant worker increases the production of dinners from 0 dinners to 12 dinners, so the marginal product of this worker is 12 dinners. At a wage rate of $100, the marginal cost of

Fat Tire Tours is a Paris-based company selling “skip-the-line” tours to the Eiffel Tower and other Paris landmarks. Suppose that you manage a similar company and each year your company sells tours to 60,000 sightseers, with a marginal cost of $47 per tour. In addition, suppose that last year the monthly insurance premium you paid to insure against accidents was $6,000. This year the insurance company increases the premium to $9,000. How would this change affect your company’s marginal cost?

Answer It may surprise you that the change in the insurance premium has no effect on the marginal cost. In other words, the marginal cost does not change. The marginal cost measures how the total cost changes when output changes (when the number of tours changes). The insurance premium is a fixed cost. The premium does not change when your company sells more or fewer tours. Accordingly, the (fixed) insurance premium has no effect on the marginal cost.

DECISION SNAPSHOT

Input Price Changes and Changes in the Marginal Cost of an Eiffel Tower Tour

change in output and is defined as MC = ∆TC∆Q , where, as usual, the symbol delta (Δ) means “change in.” Marginal cost is most meaningful when calculated for small changes in output. When output increases by a single unit, the marginal cost is the additional cost incurred to produce the additional unit. Conversely, when output decreases by a single unit, the marginal cost is the decrease in cost from not producing the unit. You will see throughout this text that the marginal cost plays a vital role in decision making.

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4.3 Short-Run Cost  155

producing one more dinner between 0 and 12 dinners is $10012 dinners = $8.33 per dinner. The marginal product of the second worker is 22 dinners, so the marginal cost of

producing one more dinner between 12 and 34 dinners is $10022 dinners = $4.55 per dinner. The larger the marginal product, the smaller the marginal cost. Over the range of output with increasing marginal returns to labor, the marginal product increases, so the marginal cost decreases and the MC curve slopes downward. Eventually, as more workers are hired, the range with decreasing marginal returns to labor is reached, and the marginal product starts to decrease. For example, the 11th worker has a marginal product of only 10 dinners, so the marginal cost of producing one

more dinner here is $10010 dinners = $10.00 per dinner, much larger than the marginal cost when hiring the first or second worker. Once the marginal product starts to decrease, the marginal cost of an additional dinner increases, so over this range of output the MC curve slopes upward.

The following box summarizes the general relationship between the marginal product of labor and marginal cost.

• Over the range of output where the marginal product of labor increases, the marginal cost decreases.

• At the level of output where the marginal product of labor is at its maximum, the marginal cost is at its minimum.

• Over the range of output where the marginal product of labor decreases, the marginal cost increases.

RELATIONSHIP BETWEEN THE MARGINAL PRODUCT OF LABOR AND MARGINAL COST

Cost (dollars per dinner)

Output (dinners per day)

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

$8.00

$9.00

$10.00

$11.00

47542537532527522517512575250

ATC

AVC

MCThe MC curve intersects the ATC and AVC curves at their minimum points.

Figure 4.6 MC, ATC, and AVC Curves

The figure shows three cost curves from Table 4.2. The values for the MC curve are plotted midway between the relevant quantities. The MC curve intersects the AVC curve and the ATC curve at their minimums.

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156  CHAPTER 4 Production and Costs

Marginal/Average Relationship Figure 4.6 illustrates another notable result: The MC curve intersects the AVC curve and the ATC curve at their minimum points, an example of a more general relation- ship called the marginal/average relationship. The marginal/average relationship has two parts:

• If the marginal ________ is greater than the average ________, then the average ________ increases.

• If the marginal ________ is less than the average ________, then the average ________ decreases.

As the blanks imply, this relationship applies anytime a marginal and an aver- age are involved. For example, every student is familiar with this general relation- ship: If the grade you receive in an additional class (a marginal class) exceeds your grade point average (GPA), then your GPA will rise. Conversely, if the grade you receive in an additional class is less than your GPA, then your GPA will fall. What is true for grades is also true for costs: If the marginal cost of another unit is greater than the average cost, then the average cost will rise. If the marginal cost of another unit is less than the average cost, then the average cost will fall.

These results mean that the MC curve must intersect the AVC curve and the ATC curve at their minimums. In Figure 4.6, examine the relationship between average variable cost and marginal cost when your Italian restaurant produces less than 325 dinners. Over this range of production, the marginal cost of another dinner is less than the average variable cost, so producing an additional dinner means a decrease in the average variable cost. As the figure shows, the AVC curve slopes downward.

Now look at this same relationship when the production exceeds 325 dinners. Over this range of output, the marginal cost of another dinner is greater than the average variable cost, so producing another dinner increases the average variable cost. As Figure 4.6 shows, the AVC curve slopes upward. Combining these two results demonstrates that the AVC curve slopes downward until it reaches 325 din- ners, after which it slopes upward. Therefore, average variable cost must equal its minimum at 325 dinners, the quantity where it intersects the MC curve. The same reasoning leads to the conclusion that the MC curve intersects the ATC curve at its minimum.4

In Figure 4.6, the AVC curve is flat at its minimum value, between 300 and 350 dinners. If Table 4.2 had a finer division for the labor input—for instance, increasing the numbers of workers fractionally by hiring part-time labor—then the curves might not have long, straight sections. Even with hiring fractional numbers of work- ers, however, some firms’ production techniques are such that their average cost curves still have long flat sections at their minimums.

Competitive Return This section has developed cost theory with the assumption that a firm uses only two inputs. Realistically, of course, any firm will use many more inputs. When considering costs such as the average total cost or marginal cost, it is essential that you include the opportunity costs of all of the inputs. As you learned in Chapter 1, one key input is the assets made available by the firm’s owners, such

4 We formally prove this result using calculus in Section 4.C of the Appendix at the end of this chapter.

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4.3 Short-Run Cost  157

as the funds supplied to a large corporation by its investors. The opportunity cost of the owners’ resources is the return these resources would earn if invested in the next best alternative use (the competitive return). As an opportunity cost of the business, the competitive return is included among all the other costs, such as wages and rent, when calculating the average total cost, average variable cost, and marginal cost.

Shifts in Cost Curves Understanding how cost changes when output changes will help you make optimal managerial decisions. The cost curves just presented provide a good framework for organizing your thoughts. But you must also understand the factors that change costs and shift the cost curves because shifts in cost curves can change business deci- sions. Three factors shift the cost curves: (1) changes in the prices of the inputs, (2) changes in technology that alter the production function, and (3) economies and diseconomies of scope.

The Effect of Changes in Input Prices on the Cost Curves Costs change and cost curves shift if the price of an input changes. The curves that shift depend on the type of input that changes in price. For example:

• If the price of a fixed input (such as the rent on a firm’s store or factory) rises, then the fixed cost increases, and the FC curve shifts upward. Because the fixed cost is part of the total cost, the average total cost increases, and the ATC curve also shifts upward. Neither the AVC nor the MC curve shifts, because the fixed cost does not affect the variable or marginal costs. Figure 4.7 shows the effect an increase in the fixed cost has on the ATC, AVC, and MC curves for your Italian restaurant.

Cost (dollars per dinner)

Output (dinners per day)

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

$8.00

$9.00

$10.00

$11.00

47542537532527522517512575250

ATC0

ATC1

AVC

MC

Figure 4.7 Effect of an Increase in Fixed Cost

An increase in the fixed cost shifts the ATC curve upward. It does not shift the AVC and MC curves.

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158  CHAPTER 4 Production and Costs

• If the price of a variable input (such as the wage rate) rises, then the variable cost increases, and the AVC and ATC curves both shift upward. The MC curve also shifts upward. Figure 4.8 shows the effect of an increase in the variable cost for your restaurant.

The Effect of Changes in Technology on the Cost Curves Changes in technology shift both the production function and the cost curves. Some- times technological change means that fewer inputs are necessary to produce the same quantity of output. For example, Toyota has redesigned its assembly lines from a straight line to a U shape. The U shape allows the workers to accomplish more work in the same time on each vehicle, decreasing the number of workers that Toy- ota must use to produce a car. Airbus provides another example: The company used to install overhead bins directly part-by-part in the plane. It now assembles the bins outside of the plane and then installs them in one piece. This change has decreased the time and labor spent installing bins. These types of technological changes reduce the cost for each unit of output produced and shift the AVC, ATC, and MC curves downward.

Learning-by-doing is an important source of technological change. Learning- by-doing refers to the idea that as a firm produces more of a particular product, its workers become better at the production process, thereby lowering costs. Com- puter chips are a prime example. Computer chip–manufacturing firms like Intel produce computer chips on large wafers, approximately 12 inches in diameter. Each wafer has many chips etched into it, but minuscule errors result in some of the chips malfunctioning. As a firm produces the same wafer week after week and month after month, its technicians learn how to increase the yield of good chips. The knowledge gained from learning-by-doing is a technological change that shifts the cost curves downward.

Cost (dollars per dinner)

Output (dinners per day)

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

$8.00

$9.00

$10.00

$11.00

47542537532527522517512575250

ATC0

ATC1

AVC0

AVC1

MC0

MC1

Figure 4.8 Effect of an Increase in Variable Cost

An increase in the variable cost shifts the ATC, AVC, and MC curves upward.

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4.3 Short-Run Cost  159

A firm like Intel can use its learning curve, a curve that shows how the average total cost of a chip falls as the firm produces more wafers, to help predict its average total cost of a particular chip. Figure 4.9 shows such a learning curve. After the firm has produced 100,000 wafers, the average total cost of this chip is $70, but the aver- age total cost falls to $50 and then $30 after 200,000 and then 500,000 wafers have been produced.

The flip side of learning-by-doing is forgetting-by-not-doing. Forgetting- by-not-doing refers to a situation in which workers forget the most efficient way of

Suppose that you are an executive at a steel mill owned by Shagang Group, one of China’s top five steel producers. Heating iron and other ores to high tempera- tures is one of the first steps in steel making. The heat to melt the ores often comes from burning coal. How does an increase in the price of iron affect your average total cost and marginal cost? How does an increase in the price of coal affect your average total cost and marginal cost? Finally, how does an increase in the wage paid your employees affect your average total cost and marginal cost?

Answer Increases in the prices of all three inputs increase your average total cost. All three inputs—iron, coal, and workers—are variable inputs. More iron, more coal, and more workers are necessary to produce more steel. Increases in any of these three prices increase your marginal cost.

DECISION SNAPSHOT

Changes in Input Prices and Cost Changes at Shagang Group

Average cost of a computer chip (dollars per chip)

Cumulative quantity of wafers (wafers)

$10

$20

$30

$40

$50

$60

$70

$80

$90

$100

6005004003002001000

Figure 4.9 A Learning Curve for a Computer Chip

The learning curve shows how the average total cost of a chip falls as the firm reaps learning-by-doing economies from producing more wafers.

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160  CHAPTER 4 Production and Costs

doing an activity because of a decrease in production, causing the company’s cost curves to shift upward. There is evidence that learning-by-doing can be important in many industries and for many firms. There is less evidence supporting the perils of forgetting-by-not-doing, though in recent years NASA had to spend significant sums of money to rediscover how to produce huge rockets, such as the Saturn V rocket (the rocket that sent astronauts to the moon). Because no one had made such huge rockets for decades, NASA engineers had effectively forgotten how to produce them.

Often technological changes are embedded in capital. In other words, new capi- tal is required to implement technological change. For example, JCPenney, a mid- level U.S. retailer, and Burberry, a high-end U.K. retailer, have recently changed the procedure by which customers use credit and debit cards to purchase their products. Previously, customers lined up at fixed cash registers, but these companies decided to equip their associates with mobile iPod and iPad checkout devices. This techno- logical change altered the type and the quantity of capital required at their stores.

The Effect of Economies and Diseconomies of Scope on the Cost Curves Firms that produce more than one good are called multiproduct firms. Producing multiple goods can have varied effects on a firm’s costs. We discuss two: economies of scope and diseconomies of scope. The first lowers the firm’s costs and shifts its cost curves downward, and the second raises the firm’s costs and shifts its cost curves upward.

1. Economies of scope occur when the total cost of producing two or more goods is lower if they are produced within one firm than if they are produced sepa- rately by two different firms. For example, Intel and other chip-manufacturing firms produce computer chips and spend billions of dollars researching methods of shrinking the transistors used on each chip. When Intel started to produce chips for wireless communication, it used the same research to shrink the tran- sistors on these chips. Spreading the cost of the research across the different types of chips means Intel’s total cost is lower when compared to the total costs of two independent firms, each one specializing in the production of one type of chip and separately performing the research to shrink transistors.

Cost complementarities are a special case of economies of scope. Cost comple- mentarities occur when the production of one good makes the marginal cost of producing another good at the same firm lower compared to the marginal cost of a firm that produces only the second good. For example, refineries produce kerosene by heating petroleum until it evaporates and then allowing it to cool. They collect the kerosene as it condenses from the petroleum vapor at tempera- tures between 600°F and 350°F. Refineries also produce gasoline, in this case by simply letting the vapor cool some more and collecting the gasoline when it condenses at temperatures between 210°F and 140°F. By producing kerosene and gasoline, the petroleum is heated only once to a very high temperature to collect the kerosene, so there is no need to incur a separate cost of heating the petroleum to collect gasoline, thereby making the marginal cost of producing gasoline lower than it would be at a firm that refined petroleum and produced only gasoline.

2. Diseconomies of scope occur when the total cost of producing two goods is higher if they are produced within one firm than if they are produced sepa- rately by two different firms. In this case, the total cost of producing any of the goods increases as the firm produces more types of goods. For example,

Economies of scope The total cost of producing two goods is lower if they are produced within one firm than if they are produced separately by two different firms.

Diseconomies of scope The total cost of producing two goods is higher if they are produced within one firm than if they are produced separately by two different firms.

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4.3 Short-Run Cost  161

Calculating Different Costs at a Caribbean Restaurant

The following table includes the various costs involved in operating a restaurant like Bahama Breeze, an American restaurant chain that serves Caribbean-inspired dishes. Supposing all the workers are paid the same wage, fill in the missing numbers.

SOLVED PROBLEM

Capital, K

Labor, L

Output, Q

Fixed Cost,

FC

Variable Cost, VC

Total Cost,

TC

Average Fixed Cost,

AFC

Average Variable Cost,

AVC

Average Total Cost, ATC

Marginal Cost, MC

2 0 0 X X X $20.00

2 1 10 200 $35.00 2 2 40 18.75 2 3 90 2 4 150 5.33 2 5 220 2 6 300 1.17 2 7 350 5.00 2 8 390

5.00

2 9 420 2 10 440 4.54 2 11 450 350 20.00

Answer

The completed table is on the next page. The fixed cost is the same for all quantities, so it is $350 for all the rows. The second row in the table shows that the variable cost is $200 per worker, so the variable cost equals $200 per worker multiplied by the number of workers. The total cost is equal to the sum of the fixed cost and the variable cost. The average fixed cost equals the fixed cost divided by the output, the average variable cost equals the variable cost divided by the output, and the average total cost equals the total cost divided by the output. Finally, the marginal cost equals the change in the total cost divided by the change in the output.

McDonald’s executive managers apparently determined that McDonald’s was suffering from diseconomies of scope because the firm had allowed its menu to get too large. The managers decided to simplify the menu by reducing the number of different items McDonald’s sells. The reduction in the number of menu items decreased McDonald’s total cost of producing the products they continued to sell.

So far, you have learned how short-run costs change when output changes. As a manager, you must also be concerned with the impact of your decisions in the long run. As you learned earlier in this chapter, you can make more profound changes in the operation of your business in the long run, such as remodeling to increase the size of the dining area or the kitchen in your Italian restaurant. Such changes are costly and not easily reversed, both of which are excellent reasons to learn about long-run cost curves, the topic of the next section.

(Continues )

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162  CHAPTER 4 Production and Costs

4.4 Long-Run Cost Learning Objective 4.4 Derive the long-run average cost curve and explain its shape.

The long run is important for planning purposes because in the long run managers can adjust the scale of the firm’s operations by changing not only the amount of labor employed but also the amount of capital (and all other inputs). Managers’ long-run decisions about the scale of their operations are very important. For exam- ple, if Darden’s regional managers were to approve a remodeling plan that makes some Olive Garden restaurants too large for the most profitable operation, the firm would need to live with this mistake for years.

Long-Run Average Cost In the long run, managers can adjust the scale of production by changing some or all inputs. For simplicity, assume once again that the firm uses only two inputs, capital (K) and labor (L), to produce its output (Q). With this assumption, the long-run pro- duction function is Q = f1L, K2. In the long run, managers can change the quantities of both inputs. Efficient managers select the amounts of capital and labor that mini- mize the average cost of its output.

Table 4.3 presents some more production data for your Italian restaurant. In this long- run case, all inputs are variable. So unlike Table 4.1(a), which examined the short run and therefore had only one quantity of capital, included in Table 4.3 are three different quantities of capital. From these data, you can calculate three sets of average total costs— one for 4 units of capital, one for 6 units of capital, and one for 8 units of capital. Assum- ing again that one unit of capital costs $83.33 and one unit of labor costs $100, Table 4.4 shows the average total costs in the short run for the three different amounts of capital. The columns in the tables are shaded to help you to see the linkage between the tables.

The Long-Run Average Cost Curve Part of a manager’s job is to determine the combination of inputs that minimizes the average total cost of its output. As a manager, you will make day-to-day deci- sions that minimize your short-run average cost, but the long-run decision about

Capital, K

Labor, L

Output, Q

Fixed Cost,

FC

Variable Cost, VC

Total Cost,

TC

Average Fixed Cost,

AFC

Average Variable

Cost, AVC

Average Total

Cost, ATC

Marginal Cost, MC

2 0 0 $350 $0 $350 X X X $20.00

6.67 4.00

3.33 2.86 2.50 4.00 5.00 6.67

10.00

20.00

2 1 10 350 200 550 $35.00 $20.00 $55.00 2 2 40 350 400 750 8.75 10.00 18.75 2 3 90 350 600 950 3.89 6.67 10.56 2 4 150 350 800 1,150 2.33 5.33 7.66 2 5 220 350 1,000 1,350 1.59 4.55 6.14 2 6 300 350 1,200 1,550 1.17 4.00 5.17 2 7 350 350 1,400 1,750 1.00 4.00 5.00 2 8 390 350 1,600 1,950 0.90 4.10 5.00 2 9 420 350 1,800 2,150 0.83 4.29 5.12 2 10 440 350 2,000 2,350 0.80 4.54 5.34 2 11 450 350 2,200 2,550 0.78 4.89 5.67

SOLVED PROBLEM (continued )

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4.4 Long-Run Cost  163

Table 4.3 The Long-Run Production Function

All inputs are variable in the long-run production function.

Capital, K

(units of capital)

Labor, L

(workers)

Output, Q

(dinners per day)

Capital, K

(units of capital)

Labor, L

(workers)

Output, Q

(dinners per day)

Capital, K

(units of capital)

Labor, L

(workers)

Output, Q

(dinners per day)

4 0 0 6 0 0 8 0 0

4 1 8 6 1 12 8 1 14

4 2 26 6 2 34 8 2 40

4 3 50 6 3 72 8 3 90

4 4 85 6 4 140 8 4 170

4 5 130 6 5 230 8 5 290

4 6 170 6 6 300 8 6 370

4 7 205 6 7 350 8 7 440

4 8 235 6 8 390 8 8 500

4 9 250 6 9 420 8 9 550

4 10 240 6 10 440 8 10 580

4 11 230 6 11 450 8 11 600

Table 4.4 Short-Run Average Total Costs

The table shows the average total costs for different amounts of capital.

4 Units of Capital 6 Units of Capital 8 Units of Capital

Output, Q

Average Total

Cost, ATC

Output, Q

Average Total

Cost, ATC

Output, Q

Average Total

Cost, ATC

0 X 0 X 0 X

8 $54.17 12 $50.00 14 47.62

26 20.51 34 20.59 40 21.67

50 12.67 72 11.11 90 10.74

90 8.63 140 6.43 170 6.27

130 6.41 230 4.35 290 4.02

170 5.49 300 3.67 370 3.42

210 5.04 350 3.43 440 3.11

240 4.82 390 3.33 500 2.93

250 4.93 420 3.33 550 2.85

240 5.56 440 3.41 580 2.87

230 6.23 450 3.56 600 2.94

the quantity of capital to use determines what choices are available on any given day. Figure 4.10 illustrates the three sets of short-run average total cost data from Table 4.4. The figure shows that the amount of capital that minimizes the average cost depends on the scale of output—that is, quantity of dinners produced. For example, if you project that your Italian restaurant will serve 80 dinners per day, using 4 units of capital will have the lowest average total cost, approximately $9 per

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164  CHAPTER 4 Production and Costs

Cost (dollars per dinner)

Output (dinners per day)

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

$8.00

$9.00

$10.00

$11.00

560480400320240160800

ATC8 ATC6

ATC4

A

B

Figure 4.10 Using Short-Run Average Total Cost Curves to Create a Long-Run Average Cost Curve

The three short-run average total cost curves have been created using data from Table 4.4. The subscript of each curve denotes the amount of capital used. The LAC curve will run along the ATC4 curve until point A, then along the ATC6 curve until point B, and then along the ATC8 curve.

dinner. If instead you forecast that the restaurant will serve 240 dinners per day, 6 units of capital minimizes the average total cost, and 8 units of capital is optimal at 440 dinners per day.

You can use this type of analysis to determine the minimum average total cost of producing any quantity of output. The long-run average cost is defined as the mini- mum average total cost of producing any given quantity of output when all inputs can be changed.

The long-run average cost (LAC) curve shows how the long-run average cost depends on the level of output. In Figure 4.10, if the only quantities of capital that can be used are 4, 6, and 8 units, the LAC curve runs along the ATC4 curve to point A, then along the ATC6 curve to point B, and finally along the ATC8 curve.

Figure 4.10 shows the long-run average cost with only three possible amounts of capital for your Italian restaurant. In contrast, Figure 4.11 shows a more general case, in which the managers can use many possible amounts of capital (and other fixed inputs), thereby creating many short-run ATC curves. Only a few of the many possi- ble curves are illustrated in the figure. The point on each short-run ATC curve that is the minimum average total cost of producing an amount of output becomes a point on the LAC curve. In other words, in Figure 4.11 the short-run blue ATC curves are combined to trace the red LAC curve.

Note that it is only on the horizontal section of the LAC curve that the actual minimum points of the individual (short-run) ATC curves fall on the LAC curve. For example, take point B on ATC1. To produce 200 units, the managers could produce at point B, which is the minimum-cost point on ATC1. If they do so, the average cost is $12.00. However, the managers could use more capital and produce at point C on ATC2, for an average cost of $9.00. Even though the firm is not producing at the min- imum point on ATC2, its average cost is still lower than at the minimum point on ATC1, which is why point C is on the LAC curve and point B is not.

The quantity at which the long-run average cost first reaches its minimum is called the minimum efficient scale. In Figure 4.11, the minimum efficient scale is 300 units per day.

Long-run average cost The minimum average total cost of producing any given quantity of output when all inputs can be changed.

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4.4 Long-Run Cost  165

Figure 4.11 illustrates the importance of your decision about the quantity of capital (and other fixed inputs) to utilize. If you use too much capital (for your restaurant, increasing your dining area too much) or too little capital (not expanding your kitchen when you increase the size of the dining area), your firm faces higher costs for an extended period of time until you can correct your mistake. Because the stakes are high, long-run decisions about the quantity of capital are usually made by higher-level executives.

The LAC curve also contains some insight about your optimal response to a perma- nent change in the quantity produced. Suppose that your firm initially produces 75 units and you had made short-run decisions that minimized costs, so production occurred at minimum cost at point A on the long-run average cost curve in Figure 4.11. If the firm’s sales expand to 200 units, in the short run you can increase the quantity of the variable inputs so the firm moves down along short-run average total cost curve ATC1 to point B, decreasing the firm’s average cost to $12.00. In the long run, you can lower the average cost still more by changing inputs that are fixed in the short run. You can increase the firm’s capital, move along the LAC curve to point C (which is on short-run average total cost curve ATC2), and lower the firm’s average cost from $12.00 to $9.00.

This same result—increasing the quantity of capital in the long run—can be obtained using the cost-minimization analysis presented in Section 4.2. At point A in Figure 4.11, the managers are minimizing the firm’s costs by producing 75 units of output, so at this point MPLW =

MPK R . Moving from point A to point B requires the firm to

hire more variable inputs, such as labor. Using more labor decreases the marginal product of labor, MPL. The fall in the marginal product of labor means that at point B the cost-minimization equality has changed to an inequality, MPLW 6

MPK R . As you

learned in Section 4.2, this inequality indicates that you can lower the total cost by increasing the quantity of capital and moving to average total cost curve ATC2, though, of course, this change cannot be made until the long run.

Long-Run Marginal Cost To determine the cost of each additional unit of output in the long run, you must use the long-run marginal cost. The long-run marginal cost (LMC) is the cost of produc- ing an additional unit of output when all inputs are variable. The long-run marginal cost corresponds to the least costly of all the possible ways to increase output.

Long-run marginal cost The cost of producing an additional unit of output when all inputs are variable.

Cost (dollars per unit)

Output (units per day)

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

$14.00

$16.00

$18.00

1,0009008007006005004003002001000

ATC1

ATC2 ATC3 ATC4 ATC5

ATC6

A

B

C

LAC

Figure 4.11 Long-Run Average Cost Curve

The long-run average cost curve, the red curve labeled LAC, shows the minimum average total cost to produce different quantities of output. The LAC curve is comprised of the points on the short-run ATC curves that are the minimum average total cost for each different amount of output.

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166  CHAPTER 4 Production and Costs

The relationship between the long-run marginal cost and the long-run average cost is the same as the relationship between the short-run marginal cost and the short-run average total cost. As Figure 4.12 shows, when the long-run marginal cost is less than the long-run average cost, the LAC curve slopes downward. When the long-run marginal cost is greater than the long-run average cost, the LAC curve slopes upward. When the long-run marginal cost equals the long-run average cost, the long-run average cost is at its minimum. In Figure 4.12, along the horizontal sec- tion of the LAC curve, the range where the long-run average cost is at its minimum, the long-range marginal cost lies directly on the LAC curve. Indeed, whenever the LAC curve is horizontal—which occurs if the long-range average cost is constant when changing production—it is always equal to the long-range marginal cost.

Economies of Scale, Constant Returns to Scale, and Diseconomies of Scale A firm’s LAC curve typically has three segments: one with economies of scale, one with constant returns to scale, and one with diseconomies of scale. Figure 4.13 iden- tifies the segments for a bakery like Texas Star Bakery, which manufactures delicious loaves of bread. These different returns to scale reflect features of the firm’s technology.

The region with economies of scale is one in which the long-run average cost falls when output increases, so the LAC curve is downward sloping. In this range, when a firm increases all of its inputs by the same percentage, the firm’s production process is such that its output increases by an even larger percentage. Economists say the firm has increasing returns to scale. Increasing returns to scale lead to econo- mies of scale. For example, if a firm increases its use of all inputs by 10 percent at the same time, its cost rises by 10 percent. If the firm’s output increases by more than 10 percent, however, then the average cost falls.

The range with constant returns to scale is one in which the long-run average cost does not change when output increases, so the LAC curve is horizontal. In this case, when a firm increases all of its inputs by the same percentage, the technology is such that its output increases by the same percentage. Therefore, a 10 percent

Economies of scale The long-run average cost falls when output increases; the downward-sloping segment of the long-run average cost curve.

Constant returns to scale The long-run average cost does not change when output increases; the horizontal segment of the long-run average cost curve.

Cost (dollars per unit)

Output (units per day)

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

$14.00

$16.00

$18.00

1,0009008007006005004003002001000

LACLMC

Figure 4.12 Long-Run Average Cost and Long- Run Marginal Cost Curves

The LMC curve shows the marginal cost of producing an additional unit of output when all inputs are variable. When the LMC curve lies below the LAC curve, the LAC curve slopes downward; when it lies on top of the LAC curve, the LAC curve is horizontal; and when it lies above the LAC curve, the LAC curve slopes upward.

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4.4 Long-Run Cost  167

increase in all inputs results in a 10 percent increase in the firm’s cost and in its out- put, so the firm’s average cost does not change.

Finally, the segment with diseconomies of scale is one in which the long-run average cost rises when output increases, so the LAC curve is upward sloping. Over this range of the LAC curve, when a firm increases all of its inputs by the same per- centage, its output increases by a smaller percentage. The firm has decreasing returns to scale. Decreasing returns to scale lead to diseconomies of scale: If the firm increases all of its inputs by 10 percent, again raising its cost by 10 percent, its output increases by less than 10 percent, so the average cost rises.

The Challenges of Economies of Scale Economies of scale are often the result of increased specialization. As a firm’s pro- duction expands, it buys more specialized equipment. For instance, consider again the humble loaf of bread. A bakery starting out with a small scale of production, such as at point A in Figure 4.13, makes the loaves by hand. A chef measures and combines all ingredients, kneads the dough, lets it rise, shapes it into a loaf, bakes the loaf in the oven, wraps it, and moves it to the front of the store, where a clerk sells it. The average cost of producing a loaf is high. In the long run, as the bakery expands in size and increases the scale of its production, ultimately the bread is made almost exclusively by machine. Workers pour flour, water, yeast, and other ingredients into enormous vats, where large mixers combine the ingredients and knead the dough. Workers then wheel the vats of dough to huge machines that do the rest: proof the dough (let it rise), shape it into loaves, bake the loaves, slice them, wrap them, and then deliver them to workers who place the loaves in boxes ready to be shipped nationwide. The scale of production is immensely larger than that of the small bakery, and with the increased capital in the form of specialized machinery, the firm has moved along its LAC curve and gained economies of scale.

Executives managing firms in which economies of scale are important must always be alert to the growth of competitors. If competitors increase their scale of

Diseconomies of scale The long-run average cost rises when output increases; the upward-sloping segment of the long-run average cost curve.

Cost (dollars per loaf of bread)

Output (loaves of bread per day)

$0.25

$0.50

$0.75

$1.00

$1.25

$1.50

$1.75

$2.50

$2.25

$2.00

1,0009008007006005004003002001000

LAC

C

B

A

Economies of scale

Diseconomies of scale

Constant returns to scale

Figure 4.13 Regions of the Long-Run Average Cost Curve

The three segments of the LAC curve are • Economies of scale:

The long-run average cost falls when output increases

• Constant returns to scale: The long-run average cost does not change when output increases

• Diseconomies of scale: The long-run average cost rises when output increases

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168  CHAPTER 4 Production and Costs

operations, they gain the advantage of lower costs. If your firm lags behind the com- petition and your rivals use their cost advantage to lower their prices, your outlook can quickly become dire. In addition, if the source of economies of scale lies in the utilization of specialized equipment, as a manager you must make certain that your firm is using the specialized equipment appropriate to its scale of production.

Constant Returns to Scale Eventually, economies of scale taper off and reach a region of the LAC curve with constant returns to scale, such as at point B in Figure 4.13. For firms in many indus- tries, the region with constant returns to scale is quite large. Some firms’ LAC curves are effectively L-shaped: One segment has economies of scale and a second has per- sisting constant returns to scale. Regression results for firms in a large variety of industries show that their LAC curves have constant returns to scale. Paper mills, insurance companies, and producers of glass containers, construction equipment, and men’s footwear seem to have little in common, but their LAC curves all display extended regions with constant returns to scale.

Managers of firms in industries producing in the region of constant returns to scale need not fear that competitors will gain a cost advantage by increasing the scale of their operations. They cannot relax completely, however, because they must constantly be on the alert in order to minimize cost.

The Challenges of Diseconomies of Scale With increases in scale come increases in complexity, bureaucracy, and the size of a firm’s labor force. All of these factors may eventually cause the average cost to increase when a firm increases production. As the firm becomes large and complex, decision making suffers because information must be filtered through layers of man- agement before a decision can be made and then communicated back through the same channels before any action can be taken. As the bureaucracy builds and the labor force increases in size, managers and workers have increasing opportunities to focus on their own self-interest and office politics, rather than spending their time advancing the firm’s interest. In the largest organizations, wasteful duplication of effort can easily occur, with one group of managers and/or workers hard at work, blissfully unaware that another group elsewhere in the firm is diligently working on the same task. The slowdown and loss of quality in decisions, the pursuit of advance- ment by engaging in office politics, and the growing likelihood of duplication of effort all mean that as the firm increases its scale of production, its average cost rises.

Executives managing a firm that suffers from diseconomies of scale, such as a firm at point C in Figure 4.13, face difficult decisions. To lower the firm’s costs, the managers must decrease the scale of operations, creating a movement down along its LAC curve to a scale of production with lower average cost. Decreasing produc- tion means decreasing the amount of inputs. In the popular vernacular, the manag- ers must downsize the firm. Downsizing is never easy because of the human cost inflicted on the downsized workers, but at times, these decisions are necessary. In some cases, the only way to assure the firm’s survival is to reduce its costs. Of course, when decreasing inputs, the managers must be careful to follow the rules you have learned about cost minimization.

Changes in the Long-Run Average Costs In Section 4.3, you learned that a fall in the price of an input, a technological change, and learning-by-doing lower a firm’s average total costs and thereby shift its short- run ATC curve downward. Anything that shifts the short-run ATC curve also shifts

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4.4 Long-Run Cost  169

the LAC curve. For example, a fall in the price of an input decreases the short-run average total cost and shifts the short-run ATC curves downward. It also decreases the long-run average cost and shifts the LAC curve downward.

Changes in the price of inputs and changes in technology are likely to affect all competitors’ costs more or less equally. Learning-by-doing, however, may result in an important competitive advantage. As a manager, you must realize that accepting an apparently unprofitable contract might actually wind up being profitable if it enables your workers to learn by doing. Such a contract could lower your long-run production costs below those of your competitors.

Long-Run Average Cost

In the table below, identify points on the firm’s LAC curve. Then graph the LAC curve. Over what ranges of output are there economies of scale? Constant returns to scale? Diseconomies of scale?

SOLVED PROBLEM

2 Units of Capital 4 Units of Capital 6 Units of Capital 8 Units of Capital

Output, Q

Average Total Cost,

ATC

Output, Q

Average Total Cost,

ATC

Output, Q

Average Total Cost,

ATC

Output, Q

Average Total Cost,

ATC

5 $40 5 $60 5 $80 5 $100

10 20 10 30 10 50 10 70

15 15 15 10 15 25 15 50

20 20 20 15 20 9 20 30

25 40 25 35 25 5 25 15

30 70 30 60 30 20 30 5

35 110 35 90 35 40 35 15

40 160 40 130 40 80 40 30

Answer

2 Units of Capital 4 Units of Capital 6 Units of Capital 8 Units of Capital

Output, Q Average

Total Cost, ATC

Output, Q

Average Total Cost,

ATC

Output, Q

Average Total Cost,

ATC

Output, Q

Average Total Cost,

ATC

5 $40 5 $60 5 $80 5 $100

10 20 10 30 10 50 10 70

15 15 15 10 15 25 15 50

20 20 20 15 20 9 20 30

25 40 25 35 25 5 25 15

30 70 30 60 30 20 30 5

35 110 35 90 35 40 35 15

40 160 40 130 40 80 40 30

(Continues)

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170  CHAPTER 4 Production and Costs

Cost (dollars per unit)

Quantity (units)

$5

$10

$15

$20

$25

$30

$35

$40

$45

$50

5 10 15 20 25 30 35 40

LAC

450

The points on the LAC curve are in red in the table and are graphed in the figure, which shows the LAC curve. For each quantity, these points have the lowest average total cost. From 5 units to 25 units, there are economies of scale because the long-run aver- age cost falls between these levels of output. There are constant returns to scale between 25 units and 30 units because the long-run average cost is constant between these levels of output. There are decreasing returns to scale after 30 units because the long-run average cost rises after this quantity.

4.5 Using Production and Cost Theory Learning Objective 4.5 Apply production and cost theory to make better managerial decisions.

Costs serve as a fundamental factor in virtually every business decision you will encounter in your career. Consequently, the material in this chapter serves as the foundation for the economic models presented in many of the later chapters. Even before you proceed to those chapters, some noteworthy lessons emerge that can be extremely helpful in making decisions.

Effects of a Change in the Price of an Input Suppose that you are a manager at a firm like Sticky’s Finger Joint, a fast-food restaurant in New York specializing in unique, delicious chicken fingers. As an alert manager, one of your goals is to minimize the impact of a change in input price on

MANAGERIAL APPLICATION

SOLVED PROBLEM (continued)

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4.5 Managerial Application: Using Production and Cost Theory  171

the cost of producing a given output. Recall the cost-minimization equation for two inputs: MPLW =

MPK R . The City of New York has passed regulations that will require the

minimum wage you pay your workers to rise, eventually reaching $15 per hour on July 1, 2021. Suppose that the wage rate will rise from its current level—say, W—to a

higher level—say, W∼. The increase in the wage rate changes the equality to MPL W∼

6 MPKR . Section 4.2 showed that with this inequality your restaurant can lower costs by using less labor and more capital. More generally, according to the cost-minimization equation, the marginal products of all inputs divided by their costs should be equal, not just capital and labor. So when the cost of any variable input rises, cost-minimizing managers decrease the quantity of that input and increase the quantities of the other variable inputs to maintain the equality.

Of course, in the short run, it might be impossible for you to change the quantity of capital, but in the long run, you can do so. Accordingly, you might decide to decrease your order staff by creating self-order kiosks, where customers can use tab- lets to order and pay for their items. Or you might cut back on the number of cooks by purchasing fryers that automate more of the cooking process.

This general conclusion—that managers should decrease use of an input that rises in cost and increase use of other inputs—probably does not come as a sur- prise. The issue is determining the magnitude of the changes. Unfortunately, there is no easy, cut-and-dried method to determine precisely how much to change the inputs, but keep in mind the intuition behind the cost-minimization rule. In partic- ular, you learned in Section 4.2 that cost minimization requires that the change in out- put from spending one more dollar on one input must equal the changes in output from spending one more dollar on the other inputs. When the price of an input changes, ask yourself, “How much more output would I obtain if I spent one more dollar on that input?” Then ask yourself the same question for another input. Comparing the two answers will guide you to lower the total cost by using less of the input that produces less output and more of the other input. If you continue to make changes until your answers are all the same, you will have responded cor- rectly to the change in the price of an input. Of course, the difficult part of this procedure is determining the marginal products of the inputs. As a manager, you may be forced to come up with educated estimates of the marginal products. Thinking about how output changes when spending an additional dollar on an input can help you refine your estimates. If you are working for a company with research analysts, you may be able to call on them to use regression analysis (explained in Section 3.1) to provide you with estimates of the marginal products.

Economies and Diseconomies of Scale Suppose that you are an executive at a firm like Groupon, an online deal company that offers to sell consumers discount coupons for different products if enough con- sumers sign up for the deal. There is no simple, instantaneous way to determine where on its LAC curve your firm is producing. However, you can infer whether it is operating on the LAC curve where there are economies of scale or diseconomies of scale by thinking about the short-run average total cost:

• Economies of scale. If your firm is producing at a point such as point A in Figure 4.14, where the firm can lower the short-run average total cost by increasing the scale of production—say, from 50,000 deals per year to 100,000—then you can infer that it is producing at a point on the LAC curve with economies of scale.

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172  CHAPTER 4 Production and Costs

• Diseconomies of scale. If your firm is producing at a point such as point C in Figure 4.14, where the short-run average total cost can be lowered by decreasing the scale of production—say, from 450,000 deals per year to 400,000—you can conclude that it is producing at a point on the LAC curve with diseconomies of scale.

• Constant returns to scale. If your firm is producing at a point such as point B in Figure 4.14, where you cannot decrease your short-run average total cost by either increasing or decreasing the scale of production, you can deduce that the firm is producing at a point with constant returns to scale.

Once you know the segment of the LAC curve on which your firm is operat- ing—economies of scale, constant returns to scale, or diseconomies of scale—you can make much better decisions than managers who either lack this information or choose to ignore it. For example, if your firm is producing 450,000 deals per year at point C on its LAC curve, you know that decisions designed to expand output might fail. Because your firm is producing at a point with diseconomies of scale, the expansion will raise its long-run average costs. Indeed, you may want to con- tract your scale of business in order to lower your long-run average costs. If instead your firm is producing 50,000 deals per year at point A, you should be more inclined to make decisions that increase the scale of output. Because the firm is producing at a point with economies of scale, the increase in production will lower its long-run average costs. As it happens, initially Groupon was producing at a point such as A because it expanded rapidly. But apparently its managers expanded too much. Groupon wound up offering approximately 450,000 deals per year, but Groupon’s executives then announced that they planned to reduce its scale of operations and would cease operating in 12 countries, offering deals in 15 countries instead of 27.

Cost (dollars per deal o�ered)

Output (thousands of deals o�ered per year)

$2.50

$5.00

$7.50

$10.00

$12.50

$15.00

$17.50

$25.00

$22.50

$20.00

500450400350300250200150100500

LAC

C

B

A

Economies of scale

Diseconomies of scale

Constant returns to scale

ATC4

ATC1 ATC7

Figure 4.14 Determining the Returns to Scale

A manager can determine if the firm is producing at a point on its LAC curve with economies of scale, constant returns to scale, or diseconomies of scale by considering the effect of a change in production on the short-run average total cost. • If increasing production lowers the short-run

average total cost (point A), then the firm is producing at a point with economies of scale.

• If decreasing production lowers the short-run average total cost (point C), then the firm is producing at a point with diseconomies of scale.

• If increasing or decreasing production does not change the short-run average total cost (point B), then the firm is producing at a point with constant returns to scale.

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Revisiting How Pizza Hut Managers Learned That Size Matters  173

Revisiting How Pizza Hut Managers Learned That Size Matters

A t the beginning of the chapter, you read about a challenge facing managers at Pizza Hut: How could they increase the number of stores and thereby boost their profit? You can now apply the concepts of this chapter to explain how those managers answered that question.

The hypothetical data in Figure 4.15 show Pizza Hut’s problem. Pizza Hut’s standard restaurants were large and designed to feature both dine-in and delivery services. In Figure 4.15, the average total cost curve of these large stores is ATC0. For simplicity, assume that ATC0 means Pizza Hut is operating where it has constant returns to scale, but note that the results would be the same if Pizza Hut was operating where it had economies or diseconomies of scale. In Figure 4.15, the lowest average total cost ($3 per pizza) occurs at production of 700 pizzas per day on ATC0. A delivery-only restaurant, however, sells fewer pizzas—say, 350 per day. As the black dot on ATC0 at the quantity of 350 pizzas shows, the average total cost for a large restaurant that sells only 350 pizzas per day is $8 per pizza, which is much too high to be profitable.

Pizza Hut’s executive managers realized that they needed to develop a new concept: a restaurant that would have lower average total cost when producing 350 pizzas per day and would concentrate on home delivery. Pizza Hut’s managers designed a smaller store for delivery only, with no dine-in services. The smaller store used less capital, less land, and fewer other inputs. The new design was appropriate for a smaller scale of production because the designers planned a restaurant that would have lower average total costs when producing fewer pizzas per day. The smaller restaurant’s average total cost curve is ATC1 in Figure 4.15. Its average total cost when producing 350 pizzas per day is only $3 per pizza, a cost that would enable franchisees to make a profit selling

350 pizzas. After Pizza Hut began offering this new concept, the franchisees gobbled them up: The number of Pizza Hut restaurants stopped decreasing and started to increase, thereby increasing Pizza Hut’s profit.

Cost (dollars per pizza)

Output (pizzas per day)

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

$8.00

$9.00

$10.00

1,0009008007006005004003002001000

ATC1 ATC0

LAC

Figure 4.15 Determining the Returns to Scale for Pizza Hut

Pizza Hut designs its large restaurants to support both home delivery and dine-in services, which requires producing and selling 700 pizzas per day. The average total cost curve for a large restaurant is ATC0, so the average total cost of 700 pizzas is $3.00. A restaurant that provides delivery only sells a smaller number of pizzas—say, 350 per day. Along ATC0, the average total cost of producing 350 pizzas per day is $8.00. Pizza Hut’s managers designed a smaller restaurant optimized to sell only 350 pizzas. The smaller restaurant has average total cost curve ATC1 and an average total cost of only $3.00 for 350 pizzas.

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174  CHAPTER 4 Production and Costs

Summary: The Bottom Line 4.1 Production • The production function is the relationship between

different amounts of a firm’s inputs and the maximum quantity of output it can produce with those inputs.

• The short run is the period of time during which at least one input is fixed, so that a firm cannot vary the amount of that input. The long run is a period of time long enough that no input is fixed, allowing a firm to vary the amounts of all the inputs it uses.

• The marginal product of an input is the change in out- put that results from changing the input by one unit while keeping other inputs constant.

4.2 Cost Minimization • The cost-minimization rule shows that costs are mini-

mized when managers use the combination of inputs that produces the desired quantity of output and for

which MP1P1 = MP2 P2 =

MP3 P3 = c .

4.3 Short-Run Cost • The total cost (TC) is equal to the fixed cost (FC) plus

the variable cost (VC): TC = FC + VC. • The average fixed cost (AFC) equals the fixed cost divided

by the output (Q): AFC = FC>Q. The average variable cost (AVC) equals the variable cost divided by the out- put: AVC = VC>Q. The average total cost (ATC) equals the total cost divided by the output: ATC = TC>Q.

• The marginal cost (MC) equals the change in total cost divided by the change in output: MC = ∆TC>∆Q.

• Both the ATC curve and the AVC curve are U-shaped. The MC curve intersects the minimum points on the AVC and ATC curves.

• Changes in the prices of inputs and changes in tech- nology alter the costs and shift the cost curves.

4.4 Long-Run Cost • The long-run average cost (LAC) is the minimum aver-

age cost of producing any given quantity of output when all inputs can be changed. The LAC curve is U-shaped.

• If increasing output lowers a firm’s LAC, the firm has economies of scale, and the LAC curve is downward sloping. If the firm’s long-run average cost does not change as output increases, the firm has constant returns to scale, and its LAC curve is horizontal. If increasing output raises a firm’s LAC, the firm has diseconomies of scale, and the LAC curve is upward sloping.

4.5 Managerial Application: Using Production and Cost Theory

• If the price of an input changes, you can use the cost-minimization rule to adjust the quantity of inputs and lower your costs.

• If you are producing at a point on the LAC and an increase in output lowers short-run average total cost, your firm is operating in a region with economies of scale. If you are producing at a point on the LAC and a decrease in output lowers short-run average total cost, your firm is operating in a region with diseconomies of scale. If you are producing at a point on your LAC and your firm cannot lower its average total cost by either increasing or decreasing its production, it is operating in a region with constant returns to scale.

• If your firm is operating on its LAC curve in a region with increasing returns to scale, you can decrease its average cost by increasing production.

• If your firm is operating on its LAC curve in a region with decreasing returns to scale, you can decrease its average cost by decreasing production.

Key Terms and Concepts Average fixed cost

Average total cost

Average variable cost

Constant returns to scale

Decreasing marginal returns to labor

Diseconomies of scale

Diseconomies of scope

Economies of scale

Economies of scope

Fixed cost

Increasing marginal returns to labor

Long run

Long-run average cost

Long-run marginal cost

Marginal cost

Marginal product

Marginal product of labor

Negative marginal returns to labor

Production function

Short run

Total cost

Variable cost

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Questions and Problems

4.1 Production Learning Objective 4.1 Explain the relation- ship between a firm’s inputs and its output as well as calculate the marginal product of an input.

1.1 What is the difference between the short run and the long run? As a manager producing 3,000 units of output, if you can lower your cost, will you be able to lower it more in the short run or the long run? Explain your answer.

1.2 As a manager, how would you expect the mar- ginal product of labor to change as you hire more workers?

1.3 “A firm will never find it optimal to employ so much of an input that its marginal product is negative.” Is this statement true or false? Explain your answer.

1.4 A technological change increases the amount of output that a firm can produce from a given quantity of inputs. It increases the marginal product of labor for each quantity of labor and shifts the marginal product of labor curve upward. How does this technological change affect the marginal product of capital?

4.2 Cost Minimization Learning Objective 4.2 Use the cost- minimization rule to choose the combination of inputs that produces a given quantity of output at the lowest cost.

2.1 The production of ABC, Inc.’s output requires only two inputs. Its manager says, “Because the two input prices are equal, to minimize cost I employ equal quantities of the two inputs.” Is the manager correct? Explain your answer.

2.2 The wage rate of high-skilled labor is $40 per hour, and the wage rate of low-skilled labor is $15 per hour. The marginal product of high- skilled labor is 60 units per hour, and the mar- ginal product of low-skilled labor is 15 units per day. Is a firm operating under these conditions minimizing its cost? If not, what should the firm do? Explain your answers.

2.3 As a production manager, your job depends on your ability to minimize the cost of production. You hire a consulting firm, and its report sug- gests that you have plenty to worry about: The

cost of capital is $200 per hour, the wage paid to your workers is $16 per hour, the marginal product of capital is 10 units per hour, and the marginal product of labor is 32 units per hour. What is the consulting firm going to recom- mend, and why?

2.4 You are an executive for a firm like VCA Antech, which operates over 600 animal hospitals in the United States. Each hospital is treating the desired number of cases per day. At each hospital, you estimate that hiring another veterinarian enables the location to treat 20 additional cases per day and firing one decreases the number of cases treated by 20 per day. Hiring another veterinary assistant enables the location to treat 10 more cases per day, and firing one decreases the number of cases treated by 10 per day. Finally, hiring another veterinary technician enables the location to treat 15 more cases per day, and firing one decreases the number of cases treated by 15 per day. A veterinar- ian is paid $300 per day, a veterinary assistant is paid $100 per day, and a veterinary technician is paid $150 per day. Are your hospitals minimizing the cost of treatment? If so, explain why. If not, identify the change(s) that you should make.

2.5 As a manager for a nonprofit like Doctors With- out Borders, you are charged with determining what supplies to send to South Sudan. You can send different boxes of medicine. The marginal product is the number of lives saved. Suppose that the cost of a box of medicine to treat cere- bral malaria is $40 and will save 10 lives. The cost of a box of medicine to treat diarrhea is $60 and will save 20 lives. Which box will you ship first? Explain your answer.

2.6 Suppose that your manufacturing firm has the following production function with three inputs:

Q = F1X1, X2, X32 where X1, X2, and X3 are the three inputs. As

a manager, how will you determine the cost- minimizing quantities of X1 and X2 if the quantity of X3 is fixed?

4.3 Short-Run Cost Learning Objective 4.3 Distinguish between fixed cost and variable cost and calculate average total cost, average variable cost, average fixed cost, and marginal cost.

Questions and Problems  175

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176  CHAPTER 4 Production and Costs

3.2 Why is a firm’s short-run average total cost curve typically U-shaped?

3.3 How does marginal cost differ from average total cost?

3.4 As a manager, you know that as your firm uses more of a variable input, the marginal product of the input decreases. What conclusion can you draw about the behavior of the marginal cost curve?

3.5 What is the competitive return for the resources the owners provide? Why is it included as part of a firm’s costs?

3.6 Quick-service restaurants like Burger King (also called fast-food restaurants) typically employ many minimum wage workers. If the govern- ment raises the minimum wage, what happens to a Burger King’s cost curves?

3.7 Clerical workers form a union that successfully raises its members’ wages. What happens to the short-run average total cost curve and long-run average cost curve of a firm that hires clerical workers? What happens to the firm’s marginal costs?

3.8 Energizer Holdings initially produced only its namesake batteries. Over the years, it acquired

other divisions that produced personal care products such as razors (Schick) and sunscreen (Hawaiian Tropic and Banana Boat). The execu- tives at Energizer Holdings decided that they would split the company into two independent firms, one producing batteries and the other the personal care products, because they thought the split would lower the two firms’ costs. Using the concepts presented in this chapter, explain the executives’ reasoning.

3.9 Apple Inc.’s research and development for its iPhone eventually helped the firm develop its first iPad. How did Apple’s production of iPads affect its costs?

4.4 Long-Run Cost Learning Objective 4.4 Derive the long-run average cost curve and explain its shape.

4.1 Explain the relationship between the short-run average total cost and the long-run average cost. Include a figure in your answer.

4.2 The table shows production data for three quantities of capital. Suppose that each unit of capital costs $1,000 and each unit of labor costs $200.

3.1 Assuming that all units of labor are paid the same wage rate, complete the table below.

Labor, L Capital, K Output, Q Average

Total Cost, ATC

Capital, K Output, Q Average

Total Cost ATC,

Capital, K Output, Q Average

Total Cost, ATC

0 2 0 X 3 0 X 4 0 X

1 2 100 3 160 4 210

2 2 800 3 1,200 4 1,350

3 2 1,300 3 1,800 4 2,200

4 2 1,475 3 2,100 4 2,600

5 2 1,500 3 2,200 4 2,700

6 2 1,510 3 2,220 4 2,710

Capital, K Labor, L Output, Q Fixed Cost, FC Variable Cost, VC

Total Cost, TC

Average Fixed

Cost, AFC

Average Variable

Cost, AVC

Average total cost,

ATC

Marginal Cost, MC

2 0 0 $400 X X X

2 1 100 $400

2 2 800

2 3 1,200

2 4 1,500

2 5 1,700

2 6 1,800

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a. Complete the table. b. If you estimate that your production will be

1,300 units, how much capital do you want to use?

c. If you estimate that your production will be 2,100 units, how much capital do you want to use?

d. Over what approximate range of production would you use 2 units of capital? Explain your answer.

4.3 If doubling all inputs increases output by 70 per- cent, what can you conclude about the shape of the long-run average cost curve?

4.4 Your company has a long-run average cost curve that has a range of output with economies of scale, followed by a range with constant returns to scale, and then followed by a range with diseconomies of scale. You know that you are producing at a point where you have constant returns to scale. You want to lower your average cost. Can you do so by increasing your output by using more labor? By using more capital? By using more labor and more capital? Explain your answers.

4.5 Suppose that the only inputs your company uses are labor and capital. a. Explain how it is possible to simultaneously

have negative marginal returns to labor and increasing returns to scale.

b. As a manager in this situation, what changes would you make to minimize your average total cost in the short run?

c. What changes would you make to minimize your average total cost in the long run?

4.5 Managerial Application: Using Production and Cost Theory Learning Objective 4.5 Apply production and cost theory to make better managerial decisions.

5.1 A firm uses only labor (L) and capital (K) as inputs and is minimizing the cost of producing Q1 units of output by using L1 worth of labor and K1 worth of capital. How should the firm respond to an increase in the price of capital? Be sure to explain your answers for both the short run and the long run.

5.2 A large architectural firm has just landed a con- tract to build a hospital. Eight architects currently work 40 hours per week in this firm, and all are available to work full-time on this project. The managers estimate that they need 400 archi- tect-hours per week for 20 weeks to complete this project. Architects earn $500 per 40-hour week. Suppose that there is a fixed cost of hiring an architect of $2,000. (This cost reflects the advertis- ing costs, interviewing costs, and so forth.) a. The firm’s current architects are willing to

work overtime to complete this project if they receive 1.5 times their usual wage rate for any hours in excess of 40 hours per week. How much would the managers pay in overtime wages for the project?

b. Alternatively, the firm can handle this proj- ect by hiring new workers (for 20 weeks only) and having all architects work 40 hours per week. How many new architects would the firm need to hire?

c. Should the managers hire new architects or ask the firm’s current architects to work overtime? Explain your answer.

5.3 Suppose that the government offers to pay a firm that hires low-skilled labor a subsidy. In particular, for each low-skilled worker hired, the government will pay a part of the wage rate. How would this program affect the firm’s hiring decisions?

5.4 The Monroe County Public Defender’s Office in New York has a budget of approximately $8 mil- lion and employs nearly 70 attorneys and 25 staff people. The courts have imposed new require- ments for representation: Indigent people must now be represented at their first hearing. The Public Defender has given you the task of deter- mining how many new attorneys to hire while simultaneously minimizing the cost. Suppose that you can hire Special Assistant Public Defenders at a salary of $12,000 per month, Senior Assistant Public Defenders at a salary of $10,000 per month, and Assistant Public Defend- ers at a salary of $6,000 per month. You know that you will need to provide representation for 700 new cases per month. The precceding table shows how many cases each class of attorney can

Questions and Problems  177

Special Assistant Public Defender

Additional Cases Handled

(per month)

Senior Assistant Public Defender

Additional Cases Handled

(per month)

Assistant Public Defender

Additional Cases Handled

(per month)

1 240 1 200 1 140

2 200 2 160 2 120

3 160 3 110 3 60

Accompanies problem 5.4.

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178  CHAPTER 4 Production and Costs

handle. How many Special Assistant, Senior Assistant, and Assistant Public Defenders will you hire? Explain your answer.

long-term, fixed-price contract for your product that would significantly increase the size of your firm. If you sign the contract and do not expect the prices of your inputs to change, do you think your profit will be larger in the short run or the long run?

MyLab Economics Auto-Graded Excel Projects 4.1 Cakes by Monica (a bakery under the umbrella

of the Café Brulé restaurant) in Vermillion, SD, makes cupcakes for customers to purchase both in the store and in bulk orders for birthday par- ties and weddings. Suppose that in the short run Cakes by Monica has a fixed amount of capital but can easily hire college students from the University of South Dakota to increase production as needed. A pro- duction schedule is provided for you where Q is dozens of cupcakes. a. Using the schedule provided, calculate the

marginal product of labor when K = 3. b. Using your calculations, for which workers

are there increasing, decreasing, and nega- tive marginal returns to labor?

c. Suppose Cakes by Monica decides to add another unit of capital in the long run. Find the marginal product of the 4th unit of capi- tal and the marginal product of labor when K = 4.

d. Create a graph of the marginal product of labor for K = 3 and K = 4.

e. Using your graph and the data, how does the addition of another unit of capital affect the productivity of labor?

4.2 Sugar Plum Oak is a company based in Norfolk, NE, that produces handmade Amish furniture. One of its signature items is handmade rocking chairs. The table provides weekly cost data for handmade rocking chairs. a. Using the total cost schedule provided, calcu-

late total and average fixed cost and variable cost, average total cost, and marginal cost.

b. Use Excel to graph the ATC, AVC, and MC curves. What does the distance between the ATC and AVC curves represent?

c. Using the same graph, where does the MC curve intersect the ATC curve? What does this point mean to the firm from a cost perspective?

Accompanies problem 4.1.

5.5 Your company is producing at a point on its long- run average cost curve with economies of scale. As a manager, you have the opportunity to sign a

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179

CHAPTER 4 APPENDIX

Demonstrating some of the production and cost results discussed in the chapter using calculus can help reinforce your understanding. We start with the definition of marginal product.

A. Marginal Product You have learned that the marginal product of an input is the change in total output that results from changing the input by one unit while keeping other inputs constant. As you will see in many of these appendices, all “marginal” concepts have calculus interpretations that revolve around “changes,” and marginal product is no exception. If a firm’s production func- tion is Q = f1L, K2, where Q is the quantity produced, L is labor input, K is capital input, and f is the function that relates the inputs to the output, then the marginal product of labor is equal to

MPL = 0f1L, K2

0L A4.1

and the marginal product of capital is equal to

MPK = 0f1L, K2

0K A4.2

In both cases, we take the partial derivative because the production function depends on more than one variable and the concept of marginal product studies the change in output that results from changing one input while keeping the others constant. In this case, the variables are the inputs labor and capital.

Equations A4.1 and A4.2 use a general specification for the production function. Often economists use a specific production function—in, particular, Q = ALaKb. This production function is called a Cobb–Douglas production function after the first two researchers to use it. In it, A, a, and b are parameters that determine some of the properties of the production func- tion. A is a scale parameter because it has a direct effect on the quantity produced. a and b are both less than one and influence the relative importance of labor and capital in production. Using the power rule to take the partial derivative of the Cobb–Douglas production function with respect to labor, the marginal product of labor equals

MPL = aALa - 1Kb

and taking the partial derivative with respect to capital, the marginal product of capital is equal to

MPK = bALaKb-1

To explore the Cobb–Douglas production function in more detail, we can specify some values for the A, a, and b parameters and then observe how the marginal product of labor changes when labor changes and when capital changes. Figure A4.1 shows two MPL curves for A = 50, a = 0.7, and b = 0.3 for two levels of capital: K = 4 and K = 6. These curves show that the Cobb–Douglas production function misses the region with increasing mar- ginal returns to labor because the MPL curves always slope downward. They also, however, demonstrate that when the quantity of capital increases, the MPL curve shifts upward, which means that for any quantity of labor, the marginal product of labor is larger with more capital.

The Calculus of Cost

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You can check that the MPK curves are similar: They always slope downward as capital increases, and they shift up when labor increases.

B. Cost Minimization The marginal products of labor and capital play an important role in minimizing the total cost of producing a given quantity of output. Suppose that the firm produces a fixed amount of output, Q. The production function, Q = f1L, K2, shows that any number of combinations of labor and capital can be used to produce this quantity of output. The firm’s managers, of course, want to use the combination of labor and capital that minimizes the firm’s cost. Sup- pose that the cost of employing a worker is W and the cost of using a unit of capital is R. Then the firm’s total cost is TC = 1W * L2 + 1R * K2. Formally, the firm’s managers face this problem:

Min TC = 1W * L2 + 1R * K2 subject to Q = f1L, K2 This constrained minimization problem can be solved using calculus and a Lagrange

multiplier. Alternatively, we can also solve the problem using a figure. To use a figure, let’s start by determining the different combinations of labor and capital that produce Q—that is, the different combinations of L and K such that f1L, K2 = Q. For production to stay at Q, an increase in one input must be offset by a decrease in the other. For example, using the Cobb– Douglas production function with the parameters featured in Figure A4.1, when L = 2 work- ers and K = 4 units, output is 123.1 Then if labor increases to 3 workers, to keep output equal to 123 capital must decrease to 1.55 units. Economists call the curve showing the combinations of inputs, labor and capital, that keep output at a fixed amount an isoquant.

Labor, L (workers) MPL, for K = 4 MPL, for K = 6

1 53 60

2 43 49

3 38 43

4 35 40

5 33 37

Figure A4.1 The Marginal Product of Labor for a Cobb–Douglas Production Function

The marginal products of labor are from the Cobb–Douglas production function, Q = 50L0.7K 0.3. The first column of marginal products has K = 4, and the second has K = 6. As labor increases, the marginal product of labor decreases. And as capital increases, the MPL curve shifts upward.

Marginal product of labor (units per worker)

Labor (number of workers) 6531 42

$30

$40

$50

$60

$70

$80

0

MPL (K 5 6)

MPL (K 5 4)

1 The output rounds to 123; more precisely, it is 123.11.

180  CHAPTER 4 APPENDIX The Calculus of Cost

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Figure A4.2 illustrates an isoquant for a general production function, not necessarily Cobb–Douglas. This isoquant shows the combinations of labor, L, and capital, K, that produce 20 units of output, f1L, K2 = 20. Though the figure shows only the isoquant for producing 20 units of output, there are isoquants for each possible level of production.

We can calculate the slope of an isoquant, dK>dL, by taking the total differential of f1L, K2 = 20:

a 0f 0L

* dLb + a 0f 0K

* dKb = 0 A4.3

In Equation A4.3, 0f 0L

is the marginal product of labor, MPL, and 0f 0K

is the marginal product of

capital, MPK. Using these definitions in Equation A4.3 gives

1MPL * dL2 + 1MPK * dK2 = 0 A4.4 We can rearrange Equation A4.4 to give

dK dL

= - MPL MPK

A4.5

Equation A4.5 shows that the magnitude of the slope of the isoquant equals the marginal product of labor divided by the marginal product of capital. This result explains the convex shape of the isoquant in Figure A4.2. Moving down the isoquant, the quantity of labor increases and the quantity of capital decreases, so that the marginal product of labor decreases and the marginal product of capital increases. Equation A4.5 shows that these changes in the marginal products decrease the magnitude of the isoquant’s slope, so that the isoquant becomes flatter as labor increases and capital decreases.

The isoquant in Figure A4.2 shows the combinations of labor and capital that produce 20 units of output. To find the least costly combination, we need to introduce the cost function, TC = 1W * L2 + 1R * K2. Economists call the line showing the combinations of labor and capital that keep the cost at a fixed amount an isocost. For example, if W = $30, R = $20, and TC = $90, then L = 1 worker and K = 3 units and also L = 2 workers and K = 1.5 units both have a total cost of $90. Consequently, these two combinations of labor and capital fall on the isocost line for W = $30, R = $20, and TC = $90. Figure A4.3 illustrates this isocost line and two others for the same labor and capital cost but total costs of $120 and $150.

Capital (units)

Labor (number of workers) 6531 42

1

2

3

4

5

6

7

8

0

Q 5 20

Figure A4.2 An Isoquant

The isoquant in the figure shows the different combinations of capital and labor that produce 20 units of output. The magnitude of the slope of the isoquant equals the marginal product of labor divided by the marginal product of capital, or MPL /MPK.

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The isocosts in the figure are straight lines. We can check this result by calculating the slope of an isocost, dK/dL. Take the total differential of TC = 1W * L2 + 1R * K2:

dTC = 1W * dL2 + 1R * dK2 Because the total cost is constant, dTC = 0. So, solving for the slope of the isocost, dK>dL, gives

dK dL

= - W R

This equation shows that the magnitude of the slope of an isocost line is equal to the wage rate divided by the cost of a unit of capital. Because the slope equals -W>R, it is the same at every point on the isocost line, which means that the isocost is a straight line. This value for the slope also shows that the isocost line will rotate and change its slope if the wage rate or cost of capital changes. If the total cost rises—say, from $90 to $120 to $150—then, as illustrated in Figure A4.3, the isocost line shifts outward, and its slope does not change.

Suppose that the managers’ goal is to produce 20 units of output using the minimum-cost combination of labor and capital. Further assume that the isoquant in Figure A4.2 is the rele- vant isoquant and that W = $30 and R = $20, so the isocost lines in Figure A4.3 are relevant. Then Figure A4.4 shows that the cost-minimizing combination of labor and capital is 2 work- ers and 3 units of capital. This combination of labor and capital is on the isoquant for 20 units of output and is on the lowest isocost line that touches the isoquant. Isocost lines with lower total costs, such as Isocost$90, do not touch the isoquant because they do not buy enough inputs to produce the 20 units of output. Isocost lines with higher total costs, such as Isocost$120, cross the isoquant at two points and so buy enough inputs to produce 20 units of output, but because the goal is to minimize total costs, they are not optimal.

Figure A4.4 shows that at the cost-minimizing combination of inputs, the isoquant is tan- gent to the isocost, so their slopes are equal. In terms of an equation, this result means that at the cost-minimizing combination of inputs

- MPL MPK

= - W R

A4.6

Capital (units)

Labor (number of workers)

6531 42

1

2

3

4

5

6

7

8

0

Isocost$120

Isocost$150

Isocost$90

Figure A4.3 Isocost Lines

Isocost$90 shows the different combinations of capital and labor that have a total cost of $90 when the wage rate is $30 and the cost of a unit of capital is $20. Isocost$120 shows the different combinations of capital and labor that have a total cost of $120 with the same costs per unit as before for labor and capital. The magnitude of the slope of the isocost equals the wage rate divided by the cost of capital, or W/R.

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In Equation 4.6, multiply both sides by −1 (to remove the annoying negative sign from the equality), and then divide both sides by W and multiply by MPK. So doing gives the cost- minimizing condition as

MPL W

= MPK

R

which is exactly the same result as the cost-minimization rule presented in the chapter. More generally, just as demonstrated in Equation 4.1 in the chapter, to minimize the cost of produc- tion managers must employ the quantity of inputs such that

MP1 P1

= MP2 P2

= MP3 P3

= … MPn Pn

where MP1 is the marginal product of the first input and P1 is the price of the first input, MP2 is the marginal product of the second input and P2 is the price of the second input, and so on.

Because the cost-minimization conditions are the same in the chapter and here, so, too, are the implications. For example, as the price of an input rises, to minimize costs managers should decrease their use of the higher-cost input and use more of the relatively lower-cost input(s).

C. Marginal Cost and the Marginal/Average Relationship Chapter 4 has one last, very important marginal concept: marginal cost. Once managers have selected the cost-minimizing combination of inputs, the firm’s total cost then becomes a func- tion of the quantity produced–that is, TC(Q). The firm’s marginal cost then equals the deriva- tive with respect to the quantity, or

MC = dTC dQ

A4.7

We can use the definition of the marginal cost to demonstrate that when the average total cost is at its minimum, the marginal cost equals the average total cost. Start with the definition

ATC = TCQ . Then average total cost is at its minimum when dATC

dQ equals zero. Accordingly,

applying the quotient rule for differentiation,

Capital (units)

Labor (number of workers)

6531 42

1

2

3

4

5

6

7

8

0

Isocost$120

Isocost$150

Isocost$90 Q 5 20

Figure A4.4 Cost-Minimizing Combination of Inputs

To produce 20 units of output, the cost-minimizing combination of labor and capital is 2 workers and 3 units of capital because this combination is on the lowest isocost that touches the isoquant for 20 units of output.

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dATC

dQ =

daTC Q

b dQ

= aQ * dTC

dQ b - 1TC2

Q2 = 0 A4.8

The term after the second equal sign follows by taking the derivative of the fraction TCQ . When taking this derivative, recall that total cost is a function of the quantity, TC1Q2.

For Equation A4.8 to equal zero, the numerator of the fraction, 1Q * dTCdQ 2 - 1TC2, must equal zero, which means

aQ * dTC dQ

b - 1TC2 = 0 A4.9

In Equation A4.9, divide both terms by Q and recall that dTCdQ = MC to obtain

MC - aTC Q

b = 0 A4.10

Finally, use the definition of ATC as TC>Q to get MC - ATC = 0 1 MC = ATC

This last equation shows the desired result: When the derivative of the average total cost equals zero, so that the average total cost is at its minimum, the marginal cost equals the aver- age total cost; that is, MC = ATC.

Calculus Questions and Problems A4.1 Suppose that blueberries are produced using land

and labor according to the following production function:

Q = L1 + 0.5L 0.52

where Q is the number of tons of blueberries har- vested, L1 is the number of acres of blueberry fields, and L2 is the number of labor-hours hired. a. What is the marginal product of land, MP1?

What is the marginal product of labor, MP2? b. What is the slope of the isoquant curve,

dL2>dL1? c. Suppose that the price of using an acre of land

is W1 = $144 and the price of an hour of labor is W2 = $9. What is the slope of the isocost line, dL2>dL1?

d. If the price of using an acre of land is W1 = $144 and the price of an hour of labor is W2 = $9, what is the cheapest combination of land and labor that a firm could employ to produce 5 tons of blueberries?

e. Suppose that the price of land changes so that the price of using an acre of land is W1 = $216 and the price of an hour of labor is W2 = $9. What is the slope of the isocost line?

f. If the new price of land is W1 = $216 and the price of an hour of labor is W2 = $9, what is the cheapest combination of land and labor that a firm could employ to produce 5 tons of blueberries?

A4.2 Suppose that the total cost of producing a business law handbook is

TC1Q2 = 10,000 + 25Q2 - 10Q where Q is the total number of handbooks

produced. a. What is the equation for the average total cost

of producing handbooks as a function of the quantity of handbooks produced?

b. At what quantity, Q*, is the average total cost of producing a handbook minimized? What is the value of the average total cost at Q*?

c. At the quantity Q* that you identified in part b, what is the marginal cost of an additional handbook?

A4.3 Train locomotives are produced using labor and capi- tal. The quantities of these inputs that a firm employs determine the number of locomotives that the firm can produce. Thomas’s Trains produces locomotives according to the following production function:

Q = ln1L2 + 2ln1K2 where ln is the natural logarithm, Q is the quantity

of locomotives produced, and L and K are the quan- tities of labor and capital employed, respectively. The price of one unit of labor is wL = $10, and the price of one unit of capital is rK = $60. a. Using the production function given above,

what is the slope of the isoquant curve, dK>dL?

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b. What is the slope of the isocost line, dK>dL? c. The specific production function above means

that Thomas’s Trains will always use a specific capital-to-labor ratio, K>L. Based on your answers to parts a and b, what is the value of this capital-to-labor ratio?

A4.4 Rose’s Roses is a local flower shop specializing in rose bouquets for weddings. Rose can produce her magnificent bouquets using roses imported from Colombia or roses imported from Ecuador. Due to altitude and Ecuador’s location on the equator, the Ecuadorean roses are slightly larger, meaning Rose needs fewer of them to produce each bouquet. Rose produces her bouquets according to the following production function:

Q = 0.1RC + 0.125RE

where Q is the quantity of bouquets produced and RC and RE are the quantities of Colombian roses and Ecuadorian roses used, respectively. The price of a Colombian rose is PC = $0.45, and the price of an Ecuadorian rose is PE = $0.45. a. Referring to the production function given

above, what is the slope of the isoquant line, dRE>dRC?

b. What is the slope of the isocost line, dRE>dRC? c. Based on your answers to parts a and b, how

many Colombian roses and how many Ecua- dorian roses will Rose use in each of her mag- nificent bouquets?

A4.5 Victoria Vineyards is an American wine producer, specializing in premium red blends (red wines that use multiple different varieties of grapes). Victoria Vineyards’ total cost of producing its famous red blend is

TC1Q2 = 200,000 + 5Q2 − 100Q where Q is the quantity of cases Victoria Vineyards

produces. a. What is Victoria Vineyards’ marginal cost equa-

tion, MC, of producing one case of its premium red blend?

b. What is Victoria Vineyards’ average total cost equation, ATC, of producing one case of its pre- mium red blend?

c. Identify the range of quantities over which MC 6 ATC.

d. Identify the quantity range over which the slope of ATC is negative; that is, dATCdQ 6 0.

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5

186  

Burger King Managers Decide to Let Chickens Have It Their Way

Executives at the nation’s major restaurants realize that American consumers are clamoring for more natural food, such as cage-free eggs. Caged chickens live in small spaces that prevent them from standing or stretching their wings. Cage-free chickens, on the other hand, are free to roam the barn and engage in roosting, foraging, and nest- ing. However, only about 10 percent of hens raised in the United States are cage-free.

Farmers who raise cage-free chickens are part of a per- fectly competitive industry. One farmer’s cage-free egg is a perfect substitute for any other farmer’s cage-free egg, and entry into the industry is cheap. The increased consumer demand for cage-free eggs, however, is a relatively recent change. Consequently, the farms producing cage-free eggs are small compared to the farms producing eggs from

caged hens. Eggs produced by cage-free chickens are more expensive than eggs produced by caged chickens due to differences in costs. For example, raising cage-free chickens requires farmers to employ more labor, and the mortality of cage-free chickens is approximately twice that of caged birds.

The executives at Restaurant Brands International’s Burger King division have been paying attention to con- sumers’ changing preferences. In 2016, these executives announced that Burger King would immediately start using some cage-free eggs and would switch to 100 percent cage- free by 2025. Why did Burger King’s managers decide to give themselves nine years to make this switch? Why didn’t they announce a more rapid changeover? This chapter explains how the adjustments that occur in perfectly competitive mar- kets shaped the decision made by Burger King’s managers.

Sources: Gregory Barber, “Are Cage-Free Eggs All They’re Cracked Up to Be?” Mother Jones, February 10, 2016, http://www.motherjones.com/blue-marble/2016/02/corporations-are-going-cage-free-whats-next-hens; Jennifer Chaussee, “The Insanely Complicated Logistics of Cage-Free Eggs for All,” Wired, January 25, 2016, http://www .wired.com/2016/01/the-insanely-complicated-logistics-of-cage-free-eggs-for-all/.

Perfect Competition

Learning Objectives After studying this chapter, you will be able to:

5.1 Summarize the conditions that make a market perfectly competitive. 5.2 Use marginal analysis to determine the profit-maximizing quantity that a perfectly

competitive firm produces in the short run. 5.3 Describe the long-run adjustments that managers in perfectly competitive markets make

to maximize profit. 5.4 Apply the theory of perfectly competitive firms and markets to help make better

managerial decisions.

C H

A P

T E

R

Introduction In Chapter 4, you learned how managers minimize costs when producing the desired quantity of output. The profit-maximizing quantity of a good or service depends on the extent of competition the firm faces. The amount of competition varies in different markets. Happy Jack’s Maple Syrup is one of several thousand maple syrup producers in North America. In contrast, PepsiCo is one of only two dominant soda producers in the world. This chapter and the next three describe five market structures that differ in the extent of competition. Table 5.1 outlines defining characteristics of each.

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5.1 Characteristics of Competitive Markets  187

This chapter tackles perfect competition by extending the analysis of competitive markets (first introduced in Chapter 2) to study the profit-maximizing decisions of managers of individual firms in this market. Managers of firms in competitive markets make fewer pricing decisions than managers of firms that face few or no competitors. Nonetheless, the decisions they do make affect their firms’ profitability.

The amount of competition a firm faces and the specific product it produces influence managerial decisions. Common threads will emerge, however, that can help you manage any firm producing any product. To assist your optimal decision making, Chapter 5 includes four sections:

• Section 5.1 explains the conditions that define perfectly competitive markets. • Section 5.2 examines how managers of a perfectly competitive firm can use marginal

analysis to determine the quantity that maximizes profit. The section also examines deci- sions about when to close a company and how to respond to a change in price.

• Section 5.3 discusses long-run adjustments to the scale of production. • Section 5.4 applies the concepts of the chapter to managerial decisions in a perfectly

competitive market and includes a cautionary tale for managers of competitive firms.

5.1 Characteristics of Competitive Markets Learning Objective 5.1 Summarize the conditions that make a market perfectly competitive.

In economics, the term competition refers to a market structure and the behavior of buyers and sellers in that market. Popular usage of the word generally conjures up images of intense personal rivalry, such as that among players on the football field,

Table 5.1 Different Market Structures

Level of Competition High Low

Perfect Competition (Chapter 5)

Monopolistic Competition (Chapter 6)

Oligopoly (Chapters 7

and 8)

Dominant Firm (Chapter 6)

Monopoly (Chapter 6)

Number of firms in the industry Many Many A few Few or many One

Barriers to entry by new firms None None

High to medium Medium High

Type of product Identical Differentiated Identical or differentiated Identical Unique

Control over price None; price taker Some; price

setter Some; price

setter Some; price

setter Price setter

Long-run economic profit Zero Zero Possible Possible Possible

Strategic behavior No No Yes No No

Example Maple syrup producer Apple PepsiCo Frito-Lay Roche Holding’s

drug Avastin

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188  CHAPTER 5 Perfect Competition

opponents on the tennis court, or contestants on reality television shows. In contrast, economic competition is highly impersonal. There is no active rivalry among indi- vidual market participants. In fact, competitors might even be friends: Two neigh- boring dairy farmers might be best friends and help each other out even as they are competing in the dairy market.

Defining Characteristics of Perfect Competition Five characteristics define a perfectly competitive market:

1. There are many buyers and sellers 2. There are no barriers to entry. 3. Products are homogeneous. 4. Buyers and sellers have perfect information about the price and product

characteristics. 5. There are no transaction costs.

Let’s examine each of these characteristics in turn.

Many Buyers and Sellers There are many buyers and many sellers in a competitive market. How many? The number of buyers must be large enough that no one buyer can influence the price. Similarly, the number of sellers must be large enough that no single seller can influ- ence the price. In most markets, the number of buyers is so large that an individual consumer’s purchases are minuscule relative to the total market sales. For example, no matter how many soft drinks, tomatoes, shares of Microsoft, or legal pads you buy, you know that your purchases are a minute fraction of the total number pur- chased and have no impact on the price. Similarly, if a firm accounts for a very small share of the total market output, its managers know they cannot affect the price of the product. Each seller has no market power—that is, no control over the price that is set. More formally, the sellers are price takers, with no ability to change the price of the good or service being bought and sold. Firms in an industry with a large num- ber of sellers of similar size are more likely to be price takers than firms in an indus- try with only a few sellers.

No Barriers to Entry Why are there many firms in the market? There are many firms because a perfectly competitive market has no barriers to entry. A barrier to entry is any factor that makes it difficult for new firms to enter a market. Some barriers to entry are legal barriers, such as a patent or copyright. Others are cost based, as when an existing firm has a substantial cost advantage over a new entrant into the market.

Perfectly competitive markets have free entry, which means that new firms are free to enter the market. Free entry is the reason that a perfectly competitive market includes many firms. Free entry, however, does not mean that entry is costless. For example, to enter the restaurant business, an entrepreneur needs enough capital to buy or rent a building as well as the necessary equipment, which might cost several hundred thousand or even millions of dollars. Entry into this market is still said to be free because there are no artificial barriers to surmount: The entrepreneur is not legally prevented from opening, and once the business has opened, it is not at a cost disadvantage relative to the previously existing restaurants.

Perfectly competitive market A market with the following five characteristics: many buyers and sellers, no barriers to entry, a homogeneous product, perfect information, and no transaction costs.

Price takers Market participants (buyers and sellers) who individually have no ability to change the price of the good or service being bought and sold.

Barrier to entry Any factor that makes it difficult for new firms to enter a market.

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5.1 Characteristics of Competitive Markets  189

Homogeneous Products The products sold in perfectly competitive markets are homogeneous, or essentially identical. For example, all Yukon gold potatoes are virtually the same, so potato buy- ers do not care from which farmer they buy. Similarly, manufacturers who want sheet metal of a particular specification are indifferent to its source because all pro- ducers provide the same product. One seller’s product is a perfect substitute for any other seller’s product.

Perfect Information The economic model of perfect competition assumes that all buyers and sellers have perfect information about all prices and product characteristics. In reality, no one can have perfect information. But frequently buyers and sellers have enough information that their market functions as if it were perfectly competitive. For example, even if the managers of an egg producer in Georgia do not know the price of eggs in Oregon, they will still operate their company as if it was in a perfectly competitive market because they know the prices of all relevant competitors.

No Transaction Costs Transaction costs are the costs of using a market, not the price of the good or service itself. For example, the cost of driving to the local farmers’ market and then the time and effort you spend examining the produce before you buy it are examples of transaction costs. If transaction costs are too high, then goods that otherwise would be identical are not: Egg consumers in Georgia don’t think eggs in Oregon are iden- tical to eggs in Georgia. For simplicity, the theoretical model of perfect competition assumes that there are no transaction costs. Reality, of course, is different. But as long as transaction costs are not so large as to create many small, separate markets for the product, transaction costs are low enough for the market to be perfectly competitive.

Perfectly Competitive Markets When all of the conditions just described are satisfied, the market is perfectly com- petitive, and the firms within the market are perfectly competitive firms. Many mar- kets approximate the theoretical model closely enough that it is fair to analyze them as perfectly competitive. For example:

• There are over 2,500 textile mills in the United States, and one mill’s product is very close to being a perfect substitute for any other mill’s product.

• Lumber (and sawdust!) produced by any one of the 2,729 sawmills in the United States is a virtually perfect substitute for that produced by any of the others.

• Financial markets, such as stock markets, are often close to perfectly competi- tive, as is the market for banking services.

The classic examples of perfectly competitive markets, however, are agricultural, such as the markets for eggs, wheat, cotton, and maple syrup. Consider the market for maple syrup. The product is homogeneous because one company’s Grade A, light amber maple syrup is identical to any other company’s similarly graded syrup. Clearly, there are a large number of buyers and, with 8,000 producers in the United States, a large number of sellers. There are no barriers to entry—if entrepreneurs want to enter the market, all they must do is buy a stand of sugar maple trees.

Transaction costs The costs of using a market.

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190  CHAPTER 5 Perfect Competition

Information is close to perfect because it is easy to learn the prices different firms charge. Transaction costs are low—discovering different producers is simple, and it is not difficult to buy or sell maple syrup.

Buyers and sellers in the maple syrup market are price takers. A buyer’s pur- chase of an additional bottle or even a case of maple syrup does not change its price, which demonstrates the effect of competition on the buying side: The price per unit is unaffected by the quantity purchased. There is also competition on the selling side: The managers of a single producer—say, once again, Happy Jack’s Maple Syrup—know that producing an extra 100 gallons has no discernible effect on the price of maple syrup.

As you learned in Chapter 2, market demand and supply determine the price in perfectly competitive markets. Although managers within such firms cannot control the price of their products, they must accomplish many other tasks. As a manager, you must pay close attention to details such as productive efficiency and mainte- nance of product and service quality. More importantly, however, you must deter- mine the amount to produce that will maximize the firm’s profit. We turn to this decision in the next section.

The Markets for Fencing and Cell Phones

The Affordable Fence Company is one of approximately 50 fencing companies in Pittsburgh, Pennsylvania. U.S. Cellular is one of four cell phone companies in Bangor, Maine.

a. Is the Affordable Fence Company competing in a perfectly competitive market? Is it a price taker? Explain your answers.

b. Is U.S. Cellular competing in a perfectly competitive market? Is it a price taker? Explain your answers.

Answer To determine if these companies compete in perfectly competitive markets, you need to decide how closely the market meets the five criteria of a perfectly competitive market.

a. A fence built by the Affordable Fence Company is virtually identical to a fence of the same style built by any other company, so the products are close to homoge- neous. There are a large number of buyers and sellers. Because any entrepreneur can open a fencing company and not face a cost disadvantage compared to the existing companies, there are no barriers to entry into this market. Buyers and sellers can easily determine the prices different fencing companies charge, so infor- mation is nearly perfect. Additionally, the transaction costs of buying a fence are not large, so there is effectively only one market for fences in Pittsburgh. Consequently, the Affordable Fence Company operates in a market that is very close to perfectly competitive. Because the company competes in a perfectly competitive market, it is a price taker.

b. U.S. Cellular does not compete in a perfectly competitive market. One of the charac- teristics of perfectly competitive markets is a large number of buyers and sellers. While there are a large number of buyers in this market, with only four sellers the market is not perfectly competitive. So U.S. Cellular is not a price taker.

SOLVED PROBLEM

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5.2 Short-Run Profit Maximization in Competitive Markets

Learning Objective 5.2 Use marginal analysis to determine the profit-maximizing quantity that a perfectly competitive firm produces in the short run.

Continue to assume that the objective of all managers, including managers of per- fectly competitive firms, is profit maximization. Total profit is equal to the difference between the total revenue (TR) and the total opportunity cost (TC) of producing and selling the product:

Total profit = TR - TC

To maximize profit, a manager must select the quantity of output that maxi- mizes the difference between total revenue and total cost.

Marginal Analysis As you learned in Chapter 1, marginal analysis compares the marginal benefit of an action to its marginal cost (see Section 1.4). In this and other chapters, you will see more specifically how managers can use marginal analysis as an extremely import- ant decision-making tool in many different circumstances. In this chapter, it helps determine the profit-maximizing quantity to produce.

How does the marginal analysis rule help you determine how much output to pro- duce? First, recall that the word marginal means “additional.” Marginal analysis focuses on the additional benefit and additional cost from an action, not the total benefit or total cost from all of the actions. In this case, the action is to produce another unit of output. The marginal benefit is the change in total revenue from selling the additional unit because that is the additional benefit. The change in the total revenue from selling an additional unit is the marginal revenue. The marginal cost is the change in total cost from producing the additional unit because that is the additional cost of the unit. The first step in applying marginal analysis to profit maximization is to determine the demand for the firm’s prod- uct because demand dictates the change in total revenue from an additional unit.

Market Demand and Firm Demand in a Competitive Market When analyzing a perfectly competitive market, you must distinguish between mar- ket demand and an individual firm’s demand. Figure 5.1 illustrates the difference between the market demand curve and an individual firm’s demand curve in the competitive market for maple syrup. Figure 5.1(a) shows the market demand curve (D) and the market supply curve (S) for maple syrup. Figure 5.1(b) shows the demand curve (d) for one individual firm—say, Happy Tree Maple Syrup, which is one of thousands of firms producing maple syrup. The equilibrium price and the equilibrium quantity are determined in the market as a whole from the intersection of the market supply curve and the market demand curve, so in Figure 5.1(a) the equilibrium price and quantity are $30 per gallon and 12 million gallons. As the arrow extending from Figure 5.1(a) to Figure 5.1(b) indicates, Happy Tree has no control over the price and takes the equilibrium price as given. It can sell whatever quantity of maple syrup it produces at the equilibrium price. Its demand is perfectly elastic at the equilibrium price, as demonstrated by the horizontal demand curve (d) at the price of $30 per gallon, because all other firms’ maple syrup is a perfect substi- tute for Happy Tree’s syrup. With perfectly elastic demand, Happy Tree’s managers effectively have no control over the price they set. If they set a price above the equi- librium price, their sales collapse to zero—no one will buy from them because there

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192  CHAPTER 5 Perfect Competition

are other, perfect substitutes available at a lower price. There is no need for them to set a price lower than the equilibrium price because they can sell whatever quantity they want at the (higher) equilibrium price.

Marginal Revenue To use marginal analysis, the managers at Happy Tree Maple Syrup must understand how changes in output change the firm’s total revenue. The first two columns of Table 5.2 show details of part of Happy Tree’s demand curve shown in Figure 5.1(b). In the table, the quantity ranges from 1,494 gallons to 1,505 gallons of maple syrup. (Because the firm is a small part of the market, we use “q” to indicate a firm’s quan- tity and “Q” to indicate the market’s quantity.) Of course, Happy Tree can sell any quantity it produces, from 1 gallon to whatever quantity its trees can produce, for $30 per gallon. Happy Tree’s total revenue (TR), price (P) multiplied by quantity (q), is included in the third column of Table 5.2.

To make their production decision, the managers at Happy Tree need to know the marginal revenue. Marginal revenue shows how total revenue changes when the firm sells another unit, so, more formally, marginal revenue (MR) is the change in total revenue (TR) divided by the change in quantity (q): MR = ∆TR∆q . where the delta symbol 1∆2 means “change in.” Typically, marginal revenue is calculated using a small change in output—say, one unit.

Using this definition, the marginal revenue from increasing production of Happy Tree’s maple syrup by one unit, from 1,494 gallons to 1,495 gallons, equals $44,850 - $44,820

1,495 - 1,494 = $30.

Marginal revenue The change in the total revenue divided by the change in quantity: MR = ∆TR∆q .

Figure 5.1 Market Demand Curve and Individual Firm Demand Curve in a Competitive Market

(a) Market Demand Curve (b) Individual Firm Demand Curve The market demand curve for maple syrup (D) and the market supply curve for maple syrup (S) determine the equilibrium price of maple syrup, $30 per gallon.

Happy Tree Maple Syrup is one of thousands of firms producing maple syrup. As the arrow extending between parts (a) and (b) indicates, Happy Tree takes the equilibrium price of $30 as given. At this price, Happy Tree is able to sell as much maple syrup as it produces, so its demand curve (d) is horizontal.

Price (dollars per gallon of maple syrup)

Quantity (millions of gallons of maple syrup per year)

$60

$70

$10

20 2412 164 8

$20

$30

$40

$50

0

S

D

Price (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

d

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Column 4 of Table 5.2 shows the marginal revenue for the rest of the quantities in the range, and Figure 5.2 illustrates the results. Notice anything striking? The marginal reve- nue (MR) is always the same ($30) and is always equal to the price (P). As an equation,

P = MR 5.1

This equality is true for all perfectly competitive firms. Because the price equals the marginal revenue for all quantities, the marginal revenue curve (MR) is horizontal and is identical to the firm’s demand curve (d) shown in Figure 5.2.

Table 5.2 Demand, Total Revenue, and Marginal Revenue for Happy Tree Maple Syrup

The first two columns show part of the demand facing Happy Tree Maple Syrup. Total revenue (TR) equals P * q. Marginal revenue (MR) is the change in total revenue caused by a change in sales. For a perfectly competitive firm, marginal revenue equals the price: MR = P .

Price, P Quantity Demanded, q Total Revenue, TR Marginal Revenue, MR

$30.00 1,494 $44,820 $30.00

30.00

30.00

30.00 30.00

30.00

30.00

30.00

30.00

30.00

30.00

30.00 1,495 44,850

30.00 1,496 44,880

30.00 1,497 44,910

30.00 1,498 44,940

30.00 1,499 44,970

30.00 1,500 45,000

30.00 1,501 45,030

30.00 1,502 45,060

30.00 1,503 45,090

30.00 1,504 45,120

30.00 1,505 45,150

Price (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

d 5 MR

Figure 5.2 A Perfectly Competitive Firm’s Demand and Marginal Revenue Curves

For a perfectly competitive firm, the marginal revenue curve (MR) is identical to the firm’s demand curve (d). Both are horizontal at the market’s equilibrium price.

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194  CHAPTER 5 Perfect Competition

Cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

MC

Figure 5.3 Marginal Cost Curve

The marginal cost curve (MC) is a U-shaped curve that reaches a minimum at 750 gallons and then rises.

Marginal Cost To use marginal analysis, managers need not only the marginal revenue but also the other half of the comparison, the marginal cost. As you learned in Chapter 4, marginal cost (MC) is the change in total cost (TC) divided by the change in output (q):

MC = ∆TC ∆q

Figure 5.3 shows Happy Tree’s marginal cost curve (MC). This U-shaped curve should be familiar because it is similar to those you saw in Chapter 4. As the quan- tity produced increases, the marginal cost curve in Figure 5.3 falls to its minimum (at 750 gallons) and then rises.

Using Marginal Analysis to Maximize Profit Figure 5.4 combines the marginal revenue curve in Figure 5.2 and the marginal cost curve in Figure 5.3. Marginal analysis shows that Happy Tree Maple Syrup maximizes its profit by producing the quantity (q) at which marginal revenue equals marginal cost 1MR = MC2, 2,000 gallons of maple syrup per year. You can use Figure 5.4 to illustrate how marginal analysis leads to this conclusion. Consider two quantity ranges:

• Quantity less than 2,000 gallons. Take a quantity less than 2,000 gallons—say, 1,000 gallons. Producing the 1,000th gallon increases total revenue by $30 (the MR) but increases total cost by only $10 (the MC). If this gallon is produced, profit increases by $20 1$30 - $102, which is equal to the length of the dou- ble-headed arrow at this quantity. Because the 1,000th gallon increases Happy Tree’s profit, it should be produced. This conclusion is confirmed by application of the marginal analysis rule: If the marginal benefit of producing the unit—in

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this case, the marginal revenue (MR)—exceeds the marginal cost (MC) of producing the unit, the unit should be produced. Applying this reasoning to Figure 5.4, you will see that all of the gallons of maple syrup up to 2,000 gallons should be produced because for each gallon in this range MR 7 MC, so each gallon is profitable.

• Quantity greater than 2,000 gallons. Now take a quantity greater than 2,000 gallons—say, 2,500 gallons. At this quantity, the revenue from the 2,500th gallon is $30 (the MR), and the cost of producing it is $60 (the MC). Producing this gal- lon imposes a loss of $30 1$60 - $302, which is equal to the length of the dou- ble-headed arrow at this quantity. So Happy Tree’s profit increases if it does not produce the 2,500th gallon. Again, the marginal analysis rule confirms this con- clusion: If the marginal benefit of producing the unit—the marginal revenue (MR)—is less than the marginal cost (MC) of producing the unit, the unit should not be produced. None of the gallons of maple syrup beyond 2,000 gallons should be produced. Each gallon in this range has MR 6 MC, so each gallon imposes a loss on Happy Tree.

By producing where MR = MC, the managers maximize Happy Tree’s profit because the firm is producing all of the profitable units and none of the unprofit- able units.1 Now that the managers know the profit-maximizing quantity, what price should they set for Happy Tree’s maple syrup? As you have already learned, the managers have no choice: In a competitive market, the price of a gallon of maple syrup is the equilibrium price of $30. From a managerial standpoint, how- ever, it is useful to ask “What is the highest price at which every unit produced

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

MC

d 5 MR

MR . MC MR , MC

Figure 5.4 Profit Maximization

The firm maximizes its profit by producing the quantity where MR = MC , which occurs at 2,000 gallons. If the firm produces less, it loses profit because it is not producing some profitable units. If the firm produces more, it loses profit because it is producing some unprofitable units.

1 Section 5.B of the Appendix at the end of this chapter demonstrates how to use calculus to solve for the profit-maximizing quantity.

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196  CHAPTER 5 Perfect Competition

can be sold?” because that price will maximize the firm’s profit. The firm’s demand curve answers this question. The demand curve shows that when Happy Tree pro- duces 2,000 gallons of syrup, the highest price consumers are willing to pay for this quantity is $30 per gallon. If the managers set a higher price—say, $31 per gallon—then consumers buy 0 gallons from Happy Tree because in a competitive market they can buy maple syrup elsewhere for $30. In this unhappy case, Happy Tree earns no revenue and incurs a loss. The managers could instead set a lower price and sell all 2,000 gallons produced, but setting a lower price lowers profit. The profit-maximizing price is $30.

This analysis can be summarized with the profit-maximization rule: Produce the quantity for which MR = MC, and then set the highest price that sells the quantity produced.

Say that you are a manager at the American Cancer Society, a nonprofit organiza- tion, and are considering a mass mailing to ask people for donations. You know that each letter will cost $1.00 + $0.00001Q, where Q is the number of letters mailed. You also estimate that each recipient will donate $21. How many letters should you mail?

Answer Although the goal of the American Cancer Society is to raise funds to fight cancer rather than to maximize profit, you still need to use marginal analysis to determine how many letters to mail. You want to mail all the letters for which the donation exceeds the cost, so the optimal number is the one at which MR = MC, where MR is the donation from the recipient, $21, and MC is the cost of mailing the letter, $1.00 + $0.00001Q. You will therefore use the equation $21 = $1.00 + 0.00001Q to determine the number of letters to mail. Solving this equation shows that Q = 2 million letters. By mailing 2 million, you will mail all the letters that result in a dona- tion above the cost of the letter and none of the letters with a cost exceeding the amount of the resulting donation.

DECISION SNAPSHOT

Marginal Analysis at the American Cancer Society

• Produce the quantity for which MR = MC .

• Set the highest price for which every unit produced can be sold.

PROFIT-MAXIMIZATION RULE

Changes in Costs If the marginal cost of production changes, you must change the quantity pro- duced to maximize profit. Suppose that the price of one of the variable inputs needed to produce Happy Tree’s maple syrup rises, perhaps the price of the fuel

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used to boil the tree sap to produce the maple syrup. You learned in Section 4.3 that an increase in variable cost increases the marginal cost. Figure 5.5 shows that when a variable input rises in price, the marginal cost curve shifts upward from MC0 to MC1. The increase in the marginal cost changes the profit-maximizing quantity. Assuming that the price of maple syrup does not change, Figure 5.5 demonstrates that the profit-maximizing quantity of syrup decreases from 2,000 to 1,500 gallons per year. The increase in marginal cost means that the gallons between 1,500 and 2,000 are no longer profitable—their marginal revenue is less than their marginal cost. If you apply marginal analysis, you see that Happy Tree should not produce these gallons of syrup because they would decrease profit.

As a perfectly competitive firm, there is nothing Happy Tree can do to offset the higher costs. Happy Tree’s managers are at the mercy of the market. As long as the firm stays open, the best the managers can do is respond to the increase in their cost by decreasing the quantity they produce.

Amount of Profit Once you have discovered the profit-maximizing quantity, your work is done, right? Wrong—in addition to monitoring production to continue to minimize costs and/or take account of changes in costs, you must be vigilant about changes in the price. In contrast to the simplified maple syrup example, in some markets prices change fre- quently—from day to day or even minute to minute. As a manager, in most indus- tries you will not be able to respond to minute-by-minute price changes. But when a price change lasts long enough, you will want to respond by changing your produc- tion. Indeed, the price may even fall low enough that you want to close the firm, either temporarily or permanently. To understand when this decision is necessary, you must first determine the firm’s profit.

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

MC0 MC1

d 5 MR

Initial quantity

Final quantity

Figure 5.5 A Change in Marginal Cost

An increase in Happy Tree’s variable cost increases its marginal cost, shifting the marginal cost curve upward from MC0 to MC1. Profit- maximizing managers respond to the increase in marginal cost by decreasing the firm’s production from 2,000 to 1,500 gallons.

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Economic Profit You know that producing the quantity at which marginal revenue equals marginal cost 1MR = MC2 maximizes profit, but to this point, the discussion has not included the amount of that profit. Economists measure the firm’s total profit as its total revenue minus its total opportunity cost. Recall from Chapter 1 (Section 1.4) and Chapter 4 (Section 4.3) that the owners’ competitive return (the return the owners could have made by using their funds in another endeavor) is one part of the firm’s opportunity cost.

Figure 5.6, which shows the average total cost curve (ATC), the marginal cost curve (MC), and marginal revenue curve (MR), can help you calculate total profit. The total revenue is the price of the product (P) multiplied by the quantity (q), or P * q, and the total cost is the average total cost (ATC) multiplied by the quantity (q), or ATC * q.2 Therefore, the total profit is equal to

1P * q2 - 1ATC * q2 5.3 Note that both terms in Equation 5.3 have the same factor, q. Taking that factor out and rewriting the equation, total profit is equal to

1P - ATC2 * q 5.4 Equation 5.4 has an immediate intuitive interpretation: The price minus the aver-

age total cost 1P - ATC2 is the profit per unit. Equation 5.4 shows that the total profit equals the profit per unit multiplied by the previously determined profit-maximizing number of units, q.

In Figure 5.6, this profit is equal to the area of the green rectangle. The area of a rectangle equals the height multiplied by the base. The height of the

2 The result stems from the definition of average total cost, ATC = Total cost

q . Multiplying both sides of this equality by Q gives ATC * q = Total cost.

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

MC

A

B

ATC

d 5 MR

Economic profit $20,000

Figure 5.6 Economic Profit for a Perfectly Competitive Firm

The firm’s economic profit equals its total revenue, P * q, minus its total cost, ATC * q. The area of the green rectangle equals the firm’s economic profit, $20,000. A firm makes an economic profit if P 7 ATC .

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rectangle in Figure 5.6 is the distance between points A and B. Point A is the price ($30), and point B is the average total cost of producing 2,000 gallons of syrup ($20), so the height is P - ATC, the profit per unit, or $30 - $20 = $10. The base of the rectangle in the figure equals 2,000 gallons, the profit-maximizing quantity (q). So the area of the rectangle is equal to the total profit, or 1$30 - $202 * 2,000 gallons = $20,000.

The profit just calculated is the firm’s total revenue minus its total opportunity cost. Because the owners’ competitive return is already part of the opportunity cost, the $20,000 profit calculated using Equation 5.4 and illustrated in Figure 5.6 is a profit over and above the normal competitive return. This profit is an economic profit, the firm’s profit over and above the competitive return. Figure 5.6 and Equa- tion 5.4 show that a business makes an economic profit whenever the price per unit is greater than the average total cost: P 7 ATC.

Competitive Return Although managers (and owners) definitely prefer making an economic profit, sometimes the best they can achieve is a competitive return. Figure 5.7 illustrates a situation in which the market price of maple syrup has fallen to $15 per gallon. The managers at Happy Tree continue to maximize profit by producing the quantity for which MR = MC. Figure 5.7 shows that the best managers can do is produce 1,500 gallons of syrup because this quantity is the profit-maximizing amount when the price is $15 per gallon.

Figure 5.7 also shows that when Happy Tree produces 1,500 gallons of maple syrup, the average total cost equals the price ($15 per gallon). Total revenue and total cost both equal $15 * 1,500 gallons, or $22,500. Because the total revenue and

Economic profit A firm’s profit over and above the competitive return.

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

MC

ATC

d 5 MR

Figure 5.7 Competitive Return for a Perfectly Competitive Firm

The firm’s economic profit equals its total revenue, P * q, minus its total cost, ATC * q. If P = ATC , the firm makes zero economic profit; that is, its owners make a competitive return on the funds they have invested in the business.

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the total cost are equal, the owners of Happy Tree make no economic profit. You can calculate this same result using Equation 5.4: Economic profit is 1P - ATC2 * q, or 1$15 - $152 * 1,500 gallons = $0. Zero economic profit does not mean that Happy Tree is making no profit at all. Instead, the owners are making a competitive return, the same profit they expect they would make if they used their resources in some other competitive venture. A firm makes zero economic profit whenever P = ATC because at that point the total revenue equals the total opportunity cost, which includes the owners’ competitive return.

Economic Loss Despite managers’ best efforts, a firm sometimes cannot make even a competitive return. In this case, the best the managers can do is to minimize the firm’s loss. Figure 5.8 illustrates this outcome for Happy Tree. Note that the equilibrium price in the market has fallen still lower, to $13 per gallon. The managers continue to maxi- mize profit, which in this case means minimizing loss, by producing the quantity that sets MR = MC, 1,300 gallons of syrup at $13 per gallon.

When Happy Tree produces 1,300 gallons of syrup, average total cost is $16 per gallon. Total revenue is $13 * 1,300 gallons, or $16,900, and total cost is $16 * 1,300 gallons, or $20,800. The “profit” is $16,900 - $20,800, or a loss of $3,900. Happy Tree incurs an economic loss, the amount by which the firm’s total opportunity cost exceeds its total revenue. Happy Tree’s owners are not happy because they are mak- ing $3,900 less than a competitive return. A firm incurs an economic loss whenever P 6 ATC because the firm’s total opportunity cost is greater than its total revenue. The economic loss is equal to (P - ATC) * q, which is the area of the light red rect- angle in Figure 5.8.

Economic loss The amount by which the firm’s total opportunity cost exceeds its total revenue.

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

Economic loss, $3,900

MC

ATC

d 5 MR

Figure 5.8 Economic Loss for a Perfectly Competitive Firm

The firm’s economic profit equals its total revenue, P * q, minus its total cost, ATC * q. If the average total cost exceeds the price, P 6 ATC , the total cost exceeds the total revenue. The area of the light red rectangle, $3,900, equals the firm’s economic loss.

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• Economic profit: For any firm, if P 7 ATC , the firm makes an economic profit— that is, more than a competitive return.

• Competitive return: For any firm, if P = ATC , the firm makes a competitive return—that is, zero economic profit.

• Economic loss: For any firm, if P 6 ATC , the firm incurs an economic loss— that is, less than a competitive return.

RULES FOR DETERMINING THE AMOUNT OF PROFIT

Shutting Down The managers of a business that is incurring an economic loss face a very important decision: Should their firm stay open, or should it close? If they believe that condi- tions will improve in the future, so the economic loss will not persist, their initial response might be to keep the firm open. Indeed, that is a reasonable option. Another option is to close temporarily and then reopen. The managers must decide which option is more profitable.

Suppose, however, that the managers believe that conditions will not change in the future, so the economic loss will persist indefinitely. Even in this dismal situa- tion, they might decide to keep the firm open temporarily because the loss might be lower than if they close it. Managers should choose the option that minimizes the amount of loss. So, let’s take a closer look at the losses in these two situations:

• Firm closes. A closed firm has no sales, so its total revenue is zero. Because the closed firm does not employ any variable inputs, its variable cost (VC) is also zero. Fixed costs (FC), however, are unavoidable in the short run, so the firm must continue to pay them. Therefore, the closed firm’s loss is FC.

• Firm remains open. The firm’s loss is its total revenue minus its total cost, TR - TC. It is useful to separate the total cost into fixed cost and variable cost, in which case you can see that the loss when the firm remains open is TR - (FC + VC).

Now suppose that total revenue is greater than variable cost: TR 7 VC. In this case, if the firm remains open, its revenue pays all of its variable cost with some rev- enue left over to pay some of its fixed cost. The key observation is that if the business is open, the loss is less than the fixed cost. In this case, the firm should remain open.

Next, suppose that TR 6 VC. In this case, the revenue the firm collects if it is open cannot pay all of its variable cost. The total loss if open equals the fixed cost plus whatever part of the variable cost cannot be paid. In this unfortunate situation, the loss if the business is open is greater than the fixed cost, so to minimize the loss, the managers must close the firm.

Shut-Down Rule The analysis of the loss when open and closed shows that the decision to stay open or to close hinges on the comparison of total revenue and variable cost. The decision to keep a firm open if TR 7 VC and close if TR 6 VC is generally called the shut-down rule.

In summary, a perfectly competitive firm makes an economic profit if P 7 ATC, makes a competitive return if P = ATC, and incurs an economic loss if P 6 ATC. The following box summarizes these results.

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This rule can be transformed into an alternative formulation that is useful. To transform the rule, use price (P) multiplied by quantity (q) in place of total revenue 1because TR = P * q2 and average variable cost (AVC) multiplied by quantity (q) in place of variable cost 1because VC = AVC * q2.3 The shut-down rule can then be rewritten as “stay open if P * q 7 AVC * q and close if P * q 6 AVC * q.” There’s one more step: Divide both sides of the inequalities by q, so the rule finally becomes to “stay open if P 7 AVC and close if P 6 AVC.”

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

The firm closes if the price is less than the minimum average variable cost (AVC).

MC

ATC

AVC

Figure 5.9 Shutting Down

The minimum average variable cost is $10 per gallon of maple syrup. At any price less than $10, Happy Tree closes.

3 The second equality comes from the definition of AVC = Variable cost

q . Multiplying both sides of the equality by q yields AVC * q = Variable cost.

• Stay open: The firm stays open if TR 7 VC or, equivalently, if P 7 AVC . The firm’s loss is less if it stays open than if it closes.

• Close: The firm closes if TR 6 VC or, equivalently, if P 6 AVC . The firm’s loss is less if it closes than if it stays open.

SHUT-DOWN RULE

Figure 5.9 illustrates the modified version of the shut-down rule by adding the average variable cost curve (AVC) to the marginal cost and average total cost curves presented in Figure 5.8. As shown, the minimum average variable cost is $10 per gallon of maple syrup. Consequently, at any price less than $10 per gallon, the price is less than the average variable cost, so if you apply the shut-down rule, Happy Tree

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closes whenever the price is less than $10 per gallon. At any price higher than $10 per gallon, the firm remains open.

What should Happy Tree’s managers do if the price is exactly the minimum average variable cost, $10 per gallon? Unfortunately, there is no clear-cut answer to this question. At $10 per gallon, the loss will be the same whether Happy Tree remains open or closes its doors. If there is a cost associated with closing and then reopening, the firm might stay open. After taking into account all revenues and all costs, if the loss is the same in both cases, it just might be time for a coin flip.

Long-Run Exit In the short run, a firm that incurs an economic loss stays open as long as the total revenue exceeds the variable cost. But what happens in the long run? As you learned in Chapter 4, fixed costs become variable costs with the passage of time. For exam- ple, when a lease comes up for renewal, the rent changes from a fixed cost to a vari- able cost. Ultimately, as time passes, the variable cost increases enough that it

The market for rice is a perfectly competitive, worldwide market. Between 2013 and 2014, the price of rice fell approximately 18 percent, from $519 per ton to $426 per ton. Lundberg Family Farms is a large rice grower located in Richvale, California. This company has many different fields in which it can grow rice. Assume that when the price of rice was $519 per ton, the company was making zero economic profit, so that the owners were making a competitive return on the funds they had invested in the company. As a manager at Lundberg Family Farms, what decisions should you make in response to the fall in the price of rice?

Answer As a manager of a perfectly competitive firm, you must first decide how much rice to produce. By applying marginal analysis, you conclude that the fall in the price of rice (which is a fall in the marginal revenue) means that the profit-maximizing quantity of rice decreases. Selecting which fields you will plant determines how much rice Lundberg Family Farms will produce. You must determine which of your rice fields are still profitable: For which fields does the marginal revenue from the field exceed the marginal cost of using the field? Fields that are less fertile or require additional transportation after harvesting the rice might not be profitable with the lower price of rice and accordingly should be left fallow.

After determining which fields you will plant, you face an additional decision: Because the firm was making only a competitive return (zero economic profit) with the higher price of rice of $519 per ton, when the price falls to $426 per ton, the firm incurs an economic loss. You must determine whether the economic loss is less if Lundberg Family Farms remains open or if it closes. This decision requires you to compare the total revenue and the variable cost. Once you have determined which fields to plant, if the total revenue exceeds the variable cost, you minimize the loss by staying open. If the total revenue is less than the variable cost, however, you minimize the loss by closing.

DECISION SNAPSHOT

Lundberg Family Farms Responds to a Fall in the Price of Rice

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204  CHAPTER 5 Perfect Competition

ultimately becomes greater than the total revenue 1TR 6 VC2. When this happens, the managers’ decision switches from keeping the business open to closing it. If the loss will recur when the business reopens, the business stays closed permanently, or as an economist would put it, the business exits the market.

The managerial lesson is straightforward: A business incurring a persistent eco- nomic loss might continue to operate for a while, but eventually it closes and exits the market. In other words, no business will sustain a long-run economic loss. As a manager, your responsibility is clear: When the passage of time converts fixed costs to variable costs, you must determine whether the loss incurred by remaining open is less than the loss incurred by exiting.

The Firm’s Short-Run Supply Curve Suppose that the price of maple syrup is above the minimum average variable cost, so that the firm is open. As a Happy Tree manager, how do you respond to a change in the price? How much should you produce at different prices? Figure 5.10 helps answer both of these questions.

Figure 5.10 shows the demand curves (d) for three prices: $15 per gallon, $30 per gallon, and $45 per gallon. Managers maximize profit by producing the quantity for which MR = MC, so when the price is $15 per gallon, Happy Tree produces 1,500 gallons; when it is $30 per gallon, Happy Tree produces 2,000 gallons; and when it is $45 per gallon, Happy Tree produces 2,250 gallons.

These three price/quantity combinations are three points on Happy Tree’s supply curve, the curve that shows the quantity the firm produces at different prices. All three points fall on the marginal cost curve. In general, a short-run firm supply curve shows the quantity the firm produces at different prices; it is the portion of the mar- ginal cost curve above the minimum of the average variable cost. In Figure 5.10, Happy Tree’s short-run supply curve is the wide blue part of the marginal cost curve.

Short-run firm supply curve The curve that shows the quantity the firm produces at different prices; the short-run firm supply curve is the portion of the marginal cost curve above the minimum average variable cost.

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$70

$10

2,500 3,0001,500 2,000500 1,000

$20

$30

$40

$50

0

MC

ATC

AVCd$45 5 MR$45

d$30 5 MR$30

d$15 5 MR$15

Figure 5.10 The Firm’s Short-Run Supply Curve

At a price of $15 per gallon of syrup, Happy Tree maximizes its profit by producing 1,500 gallons. If the price is $30 per gallon, Happy Tree’s profit-maximizing quantity increases to 2,000 gallons. And if the price is $45 per gallon, Happy Tree produces 2,250 gallons. Because Happy Tree maximizes its profit by producing the quantity for which MR = MC , Happy Tree’s supply curve is the wide blue portion of the marginal cost curve above the minimum point on the average variable cost curve.

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If the price is lower than the minimum average variable cost, the managers close the firm, so that the quantity produced is zero.

The fact that the firm’s short-run supply curve is the same as its marginal cost curve is no accident: Managers are producing the quantity that sets the price (which equals the marginal revenue) equal to the marginal cost. At any price for which Happy Tree remains open (at any price above the minimum average variable cost), the quantity produced is a point on its marginal cost curve. In other words, a firm’s short-run supply curve is equal to its marginal cost curve at all points above its aver- age variable cost curve. For all prices below the minimum point on the average vari- able cost curve, the managers maximize the firm’s profit (minimize its loss) by producing zero output and just closing its doors.

Particleboard is made, in part, from sawdust. The market for particleboard is worldwide and is perfectly competitive. Suppose that you are a manager of a firm like Collins Products, located in Klamath Falls, Oregon, when the price of sawdust falls from $75 per ton to $50 per ton. In the short run, how will you respond to this fall in price? What do you expect will happen to the price of particleboard? In the short run, what do you expect will happen to your company’s profit? Draw a graph to support your answer.

Answer Sawdust is a variable input because the more particleboard you produce, the more sawdust you use. The fall in the price of sawdust means that your marginal cost of producing particleboard falls, shifting the marginal cost curve down- ward. For example, in the figure, the marginal cost curve shifts downward, from MC0 to MC1. At the original quan- tity you produced—30 million square feet, as shown in the figure—the marginal revenue now exceeds the marginal cost. To maximize your profit, you should apply marginal analysis and respond to the fall in cost by increasing the quantity of particle- board that you produce to 40 million square feet. Because all particle- board suppliers will be increasing the quantity they produce, the market supply curve shifts to the right, so the price of particleboard falls. In the short run, however, you can expect to make an eco- nomic profit.

DECISION SNAPSHOT

A Particleboard Firm Responds to a Fall in the Price of an Input

Price and cost (dollars per square foot of particleboard)

Quantity (millions of square feet of particleboard per year)

$0.50

5030 4010 20

$1.00

$1.50

$2.00

$2.50

0

d 5 MR

MC0 MC1

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206  CHAPTER 5 Perfect Competition

The Short-Run Market Supply Curve As you have already learned, in a perfectly competitive market the production deci- sion of any single firm does not affect the equilibrium price. Instead, market demand and the collective supply produced by all firms in the market determine the equilib- rium price. The short-run market supply curve represents the quantity supplied by all of the firms in the market at various prices in the short run.

To construct the short-run market supply curve, add the quantities produced by the individual firms at any given price. For simplicity, assume that the market has only two firms in it. Of course, a perfectly competitive market contains many more than sim- ply two firms, but once you understand how the market supply curve is created for two firms, understanding its creation for any number of firms is immediate. Figure 5.11 illustrates the quantities of maple syrup produced by the two firms. Firm 1’s supply curve is s1, and firm 2’s supply curve is s2. At a price of $20 per gallon, firm 1 supplies 1,000 gallons, and firm 2 supplies 2,000 gallons. The quantity supplied in the market is 1,000 gallons plus 2,000 gallons, for a total market quantity of 3,000 gallons, at point A on the short-run market supply curve (S). When the price is $30 per gallon, firm 1 sup- plies 1,500 gallons, and firm 2 supplies 2,500 gallons, for a total market supply of 4,000 gallons (point B). At a price of $60 per gallon, the quantity supplied in the market is 2,000 gallons plus 3,000 gallons, or 5,000 gallons (point C). These are three points on the short-run market supply curve. All the other points are calculated similarly: At any price, add the quantity produced by firm 1 to that produced by firm 2.

Recall from Chapter 2 that an increase in the number of firms in the market shifts the market supply curve to the right (see Section 2.2). Now you can see why in more detail: At each price, the market quantity supplied equals the quantities supplied by the firms already in the market plus the quantities supplied by the new entrants. So, for example, if a third firm entered the market illustrated in Figure 5.11, to create the market supply curve you would add the quantity supplied by the third firm at the price of $20, at the price of $30, at the price of $60, and at all other prices to the quantities supplied by the first two firms already in the market. Conversely, a decrease in the number of firms in the market shifts the supply curve to the left: At each price, the market quantity supplied is less because the quantities supplied by the firms that exit are no longer included.

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$60

$10

5,000 6,0003,000 4,0001,000 2,000

$20

$30

$40

$50

0

SMC2 5 s2MC1 5 s1

B

C

A

Figure 5.11 The Short-Run Market Supply Curve

At a price of $20 per gallon, firm 1 produces 1,000 gallons and firm 2 produces 2,000 gallons, for a total market supply of 3,000 gallons (point A). At a price of $30 per gallon, firm 1 produces 1,500 gallons and firm 2 produces 2,500 gallons so the market supply is 4,000 gallons (point B). At any price, the market supply equals the sum of the quantities supplied by all of the firms in the market.

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Amount of Profit and Shutting Down at a Plywood Producer

Suppose that you are a manager at a perfectly competitive producer of plywood similar to Nashville Plywood, a plywood producer located in Nashville, Tennessee. The following figure shows your marginal cost curve (MC), average total cost curve (ATC), and average variable cost curve (AVC).

a. At what price or prices do you make an economic profit?

b. At what price or prices do you make a competitive return?

c. At what price or prices do you incur an economic loss?

d. Below what price do you shut down the company?

Answer

a. At any price greater than $3,000 per thousand square feet of plywood, you make an economic profit because P 7 ATC .

b. At the price of $3,000 per thousand square feet of plywood, you make a competitive return because P = ATC .

c. At any price less than $3,000 per thousand square feet of plywood, you incur an economic loss because P 6 ATC .

d. At any price less than $2,000 per thousand square feet of plywood, you shut down the company because P 6 AVC .

SOLVED PROBLEM

Price and cost (dollars per thousand square feet of plywood)

Quantity (thousands of square feet of plywood per day)

$6,000

$7,000

$1,000

50 6030 4010 20

$2,000

$3,000

$4,000

$5,000

0

MC ATC

AVC

5.2 Short-Run Profit Maximization in Competitive Markets  207

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208  CHAPTER 5 Perfect Competition

5.3 Long-Run Profit Maximization in Competitive Markets

Learning Objective 5.3 Describe the long-run adjustments that managers in perfectly competitive markets make to maximize profit.

In the short run, managers maximize their firm’s profit, but they are limited because at least one input is fixed. In the long run, however, all of a firm’s inputs are variable, which provides managers with additional options. Even managers who have maxi- mized short-run profit might have an incentive to alter the quantity they use of a newly variable input to further increase their firm’s profit.

Long-Run Effects of an Increase in Market Demand The market as a whole and the managers of the individual firms within it all respond to a change in market demand. As you will see, the long-run market adjustments following a change in demand force individual managers to make further responses in order to continue to maximize profit.

The Firm’s Adjustment to an Increase in Market Demand Figure 5.12 helps illustrate the adjustments managers make in response to an increase in market demand. Initially, the market demand curve is D0, and the market supply curve is S; Happy Tree’s short-run marginal cost curve is MC0, its short-run average total cost curve is ATC0, its long-run marginal cost curve is LMC, and its long-run average cost curve is LAC. Recall from Chapter 4 that these long-run curves reflect the marginal cost and average cost in the long run after the managers have made adjustments to all inputs (see Section 4.4). For clar- ity in illustrating the long-run marginal cost curve, assume that the LAC is U-shaped, with a single minimum point. The LMC intersects the minimum point on the LAC.

With demand curve D0, the price of maple syrup is $15 per gallon. This price means Happy Tree’s demand and marginal revenue curve is d0 = MR0, so Happy Tree’s managers maximize profit by producing 1,500 gallons of maple syrup. For reasons that will become clear shortly, assume that Happy Tree is initially producing at the minimum point on the LAC.

Suppose that the market demand for maple syrup permanently increases to D1, so that the price of maple syrup rises to $30 per gallon. Happy Tree’s demand and marginal revenue curve shifts upward to d1 = MR1. The managers’ short-run response is to boost production to 2,000 gallons by employing more variable inputs and moving upward along the short-run marginal cost curve. At 2,000 gallons, the short-run marginal cost (MC0) is $30, which equals the new marginal revenue (MR1). Because the short-run marginal cost equals the marginal revenue, marginal analysis shows that Happy Tree’s managers have maximized their short-run profit. Indeed, Happy Tree is now making an economic profit.

In the short run, the managers cannot change the quantity of fixed inputs they use, so the short-run marginal cost curve remains MC0, and the short-run profit- maximizing quantity is 2,000. The profit-maximizing long-run quantity is the amount at which the long-run marginal cost equals the marginal revenue. Figure 5.13 shows that Happy Tree’s LMC equals marginal revenue when it produces 2,500 gallons,

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5.3 Long-Run Profit Maximization in Competitive Markets  209

which means that if Happy Tree’s managers expect the price to remain at $30 per gallon for a sufficient period of time, they can increase the firm’s profit by increasing the scale of its operations. In the long run, the managers can buy more of the inputs that are fixed in the short run, perhaps by buying more sugar maple trees and increasing the size of the sugar house (the plant in which the sap is boiled) to move along the LAC and minimize the average cost of producing its 2,500 gallons. With the increase in the scale of operations, Figure 5.13 shows that the new short-run average total cost curve (ATC1) allows production of 2,500 gallons at the minimum long-run average cost for this quantity, $21 per gallon. Corresponding to the new average total cost curve is the new short-run marginal cost curve (MC1). By produc- ing 2,500 gallons, as long as the price remains equal to $30, the newly expanded Happy Tree maximizes its short-run profit (because MR1 = MC1) and its long-run profit (because MR1 = LMC). In other words, Happy Tree is not only making an economic profit (because P 7 ATC) but also making the largest possible economic profit when the price is $30 per gallon.

Price (dollars per gallon of maple syrup)

Quantity (millions of gallons of maple syrup per year)

$30

$35

$5

3.02.0 2.51.0 1.5

$10

$15

$20

$25

0

S

D1D0

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$30

$35

$5

2,5001,500 2,000500 1,000

$10

$15

$20

$25

0

MC0 ATC0 LMC

LAC

d0 5 MR0

d1 5 MR1

Figure 5.12 A Firm’s Short-Run Adjustment to an Increase in Demand

Initially, the demand curve is D0, and the equilibrium price is $15 per gallon. At this price, in part (b) Happy Tree’s demand and marginal revenue curve is d0 = MR0, and Happy Tree produces 1,500 gallons. The firm’s owners make a competitive return because P = ATC .

When the demand increases to D1, part (a) shows that the price rises to $30 per gallon. Happy Tree’s demand and marginal revenue curve shifts upward to d1 = MR1. The managers maximize profit by producing 2,000 gallons, where the short-run marginal cost curve, MC0, intersects the new marginal revenue curve, MR1. Happy Tree now makes an economic profit because P 7 ATC .

(a) Before the Increase in Market Demand (b) A Firm’s Short-Run Response to an Increase in Market Demand

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210  CHAPTER 5 Perfect Competition

The Market’s Adjustment to an Increase in Market Demand After Happy Tree Maple Syrup has adjusted the scale of operations so its average total cost curve is ATC1, its managers are satisfied. The firm is maximizing its profit, and unless something else changes, the managers foresee making no further changes. Unfortunately for them, in a competitive market further change outside their control can and does occur.

In Figure 5.13, Happy Tree is making an economic profit. Presumably all other firms in the market are making an economic profit as well. The economic profit in the market for maple syrup attracts entrepreneurs who are always seeking new markets with the potential for an economic profit. As you learned in Section 5.1, a perfectly competitive market has no barriers to entry, so entrepreneurs flock to the syrup market. As new firms enter, the market supply curve shifts to the right, lower- ing the price. How low the price goes depends on whether the entry of the new firms affects the other firms’ costs.

Entry That Does Not Affect Firms’ Costs To start, assume that the entry of new firms has no effect on other firms’ costs and that the firms have identical costs. The question remains: How low will the price go? As long as there is an economic profit

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$30

$45

$40

$35

$5

3,0002,5001,500 2,000500 1,000

$10

$15

$20

$25

0

MC1

ATC1LMC

LAC

d1 5 MR1

Figure 5.13 A Firm’s Long-Run Adjustments

If the managers believe the price will remain $30 for an extended period of time, they increase the scale of production to reduce costs. The short-run average total cost curve and short-run marginal cost curve become ATC1 and MC1, respectively. The firm now maximizes its profit by producing 2,500 gallons, where its new MC1 curve crosses the MR1 curve. The firm has maximized its short-run and long-run economic profit because it is producing 2,500 gallons, the quantity that sets its short-run marginal cost, MC1, and its long-run marginal cost, LMC, equal to its marginal revenue MR1. It is producing this quantity at the lowest possible average cost since it is producing at a point on the long-run average cost curve.

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5.3 Long-Run Profit Maximization in Competitive Markets  211

to be made, new firms continue to enter the market. Entry stops when the economic profit is eliminated, which occurs when the firms in the market are making zero economic profit. Figure 5.14 shows that this outcome occurs only when the price of maple syrup is forced all the way back down to the initial price, $15 per gallon. At this price, and after the firms have again adjusted the scale of their operations, you see that the price equals the average total cost, which is the condition required for zero economic profit.

Other than again changing the scale of their production, the existing firms, such as Happy Tree, play no active role in this series of adjustments. Instead, profit-seeking entrepreneurs cause these changes. Because there are no barriers to entry, the man- agers of the firms already in the market are, as always, at the mercy of the market and can do nothing but sit back and watch both their price and their profit fall.

Entry That Does Affect Firms’ Costs Suppose that as entrepreneurs start up new maple syrup enterprises, the demand for land with sugar maple trees increases, thereby increasing its price and hence its cost for maple syrup firms. In this case, entry raises the costs for all firms. What is the long-run outcome in this case?

If the entry of new firms raises the costs for all firms, the path leading to the long-run outcome is similar to what you just learned: Firms continue to enter until

Price (dollars per gallon of maple syrup)

Quantity (millions of gallons of maple syrup per year)

$30

$35

$5

3.02.0 2.51.0 1.5

$10

$15

$20

$25

0

S0

S1

D1

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$30

$35

$5

2,5001,500 2,000500 1,000

$10

$15

$20

$25

0

MC0 ATC0 LMC

LAC

d0 5 MR0

Figure 5.14 The Long-Run Outcome

(a) Increase in Market Supply

In the long run, entry of new firms increases the supply and lowers the price. If entry by new firms does not affect the existing firms’ costs, new firms continue to enter the market until the price equals the initial price, $15 per gallon, which occurs when the supply curve is S1.

In the long run the price is the same as the initial price, so the “new” demand and marginal revenue curve is d0 = MR0, exactly the same as the initial demand and marginal revenue curve. Happy Tree again adjusts the scale of production, so its average total cost curve is ATC0 and its marginal cost curve is MC0. The company maximizes profit by producing 1,500 gallons, the quantity at which MC0 intersects MR0. The firm is making a competitive return because P = ATC . Once Happy Tree and the other firms in the market make only a competitive return, entry of new firms into the market stops.

(b) A Firm’s Response to an Increase in Market Supply

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212  CHAPTER 5 Perfect Competition

the economic profit is gone, at which point entry ceases. The difference is this: In addition to lowering the price, entry raises all the firms’ average costs. The lower price and the higher cost both squeeze the economic profit. Because of the rise in average total cost, the price will not fall all the way back to the original level. It will fall only until it equals the new, higher average total cost. Once the price equals the higher average total cost, the economic profit is eliminated, which stops entry by new firms.

Decrease in Market Demand If the market demand for maple syrup decreases, the reverse scenario plays out. In the short run, the equilibrium price falls, each firm’s demand and marginal reve- nue curve shifts downward, and the managers decrease production as their firms incur economic losses. As time passes, the economic loss causes some managers to close their businesses. As firms close, the market supply decreases, which raises the price. The higher price decreases the surviving firms’ economic losses. How- ever, as long as firms incur an economic loss, from time to time some exit the industry by closing. As those firms close, they further decrease the supply, raising the price still higher. Ultimately, the price rises enough to eliminate the economic losses. In the long run, there are fewer firms in the market, but each firm makes at least a competitive return. The market equilibrium quantity decreases, but the effect on the price depends on how the costs of the surviving firms are affected by the exit of the firms that close. If the costs of the remaining firms are unaffected, then in the long run the price will return to its original level, the price before the decrease in market demand.

Change in Technology In many industries, technological change is practically a day-to-day occurrence. But even in industries in which it is less frequent, technological change can be critical to managers. For example, managers and owners of strawberry farms are paying attention to entrepreneurs who are developing robots (such as the Agrobot with 14 arms) to harvest the fruit. Many maple syrup producers have switched from the traditional method of collecting sap (hanging a bucket on the tree under the tap and then sending workers out to the trees to collect the buckets) to using long blue tubes extending from the tree’s tap to a vacuum pump that extracts a larger amount of sap from the tree and delivers it to a central collection station. These sorts of techno- logical changes affect the market as a whole as well as the managerial decisions at individual firms.

The costs of a sap-sucking vacuum pump and a strawberry picking robot are fixed costs. Both technologies decrease the use of workers, which decreases the producers’ variable cost. The increase in fixed cost raises a firm’s short-run average total cost (ATC) at low levels of production, but the decrease in variable cost lowers the short-run aver- age total cost and long-run average cost (LAC) at larger levels of production. The larger levels of production are more relevant because managers will adopt new technology if it lowers the cost of producing their equilibrium output. Accordingly, Figure 5.15 shows that when the managers at Happy Tree adopt the new sap extraction technology, the firm’s cost curves shift downward from the initial cost curves labeled with a “0” to the cost curves labeled with a “1.”

Before the advance in technology, Happy Tree’s demand and marginal revenue curve, d0 = MR0, was horizontal at the market equilibrium price of $25 per gallon of syrup. Happy Tree was maximizing profit at point A, where MR0 = MC0,

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5.3 Long-Run Profit Maximization in Competitive Markets  213

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$30

$35

$5

2,5001,500 2,000500 1,000

$10

$15

$20

$25

0

MC1

MC0

ATC1 LAC1

LAC0ATC0

d1 5 MR1

d0 5 MR0 A B

C

Figure 5.15 The Effect of New Technology

Initially, Happy Tree’s cost curves are those labeled with a “0” (MC0, ATC0, and LAC0), and its demand and marginal revenue curve is d0 = MR0. Happy Tree maximizes its profit at point A, producing 1,500 gallons of syrup at a price of $25 per gallon. Happy Tree makes zero economic profit. The new technology shifts the cost curves downward to those labeled with a “1” (MC1, ATC1, and LAC1). If Happy Tree is one of the early adopters of the new technology, so that the price has not yet changed from $25 per gallon, Happy Tree initially maximizes its profit at point B, producing 2,250 gallons of syrup. Happy Tree makes an economic profit. As more firms adopt the new technology and as new firms enter the market, the market supply of syrup increases, driving the equilibrium price lower. Eventually, the price falls to $10 per gallon. At this price, Happy Tree’s demand and marginal revenue curve is d1 = MR1. Happy Tree’s managers now maximize profit at point C, producing 2,000 gallons of syrup at a price of $10 per gallon. Happy Tree makes zero economic profit. Those firms that did not adopt the new technology have cost curves that remain MC0, ATC0, and LAC0, incur an economic loss, and eventually close.

producing 1,500 gallons of syrup at a price of $25 per gallon and making zero economic profit. After Happy Tree’s managers adopt the new technology, they initially maximize profit at point B, where MR0 = MC1, producing 2,250 gallons of syrup at a price of $25 per gallon and make an economic profit.

But the good times won’t last! As more syrup producers use the new technology, the market supply of maple syrup increases, which drives the price down. Eventu- ally, enough incumbent firms have adopted the technology and new firms, also using the new technology, have entered so that the market supply increases, lower- ing the price to $10 per gallon. In the long run, Happy Tree’s demand and marginal revenue curve becomes d1 = MR1, and the managers maximize profit by producing at point C, where MR1 = MC1. The long-run outcome is sadly familiar for managers of competitive firms: In the long run, the firms make zero economic profit, so the owners make only a competitive return. But firms that opt not to adopt the new tech- nology face an even bleaker fate. Because they do not gain the advantage of lower costs, they incur economic losses and eventually close.

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214  CHAPTER 5 Perfect Competition

The Long Run at a Plywood Producer

You are still a manager at a firm similar to Nashville Plywood. The following figure illustrates your marginal cost, average total cost, long-run marginal cost, and long-run average cost curves.

a. In the short run, if the price of ply- wood is $6,000 per thousand square feet of plywood, what quantity of plywood will your firm produce? Does your firm make an economic profit at this quantity?

b. If all other plywood producers have the same cost curves as yours, what will be the price of a thousand square feet of plywood in the long run? If you stay open, will you increase or decrease the scale of operations?

c. What quantity of plywood will you produce in the long run? Does your firm make an economic profit at this price?

Answer

a. As a manager, to maximize your profit you will produce the quantity of plywood that sets the marginal revenue equal to the marginal cost. For a perfectly competi- tive firm, the price equals the marginal revenue, so your marginal revenue equals $6,000 per thousand square feet. Using the figure, the profit-maximizing quantity is 70,000 square feet of plywood because at this quantity the marginal cost, MC, equals the marginal revenue. Since at this quantity P 7 ATC , your firm makes an economic profit.

b. In a perfectly competitive market, in the long run the price equals the minimum of the long-run average cost curve, $3,000 per thousand square feet of plywood. Your firm’s current scale of production has the average total cost curve (ATC) shown in the figure. You will increase the scale of production and move to a new short-run ATC with its minimum equal to $3,000 per thousand square feet of plywood.

c. In the long run, in a perfectly competitive market the price equals the minimum of the long-run average cost (LAC), and the firms’ owners make only a competitive return. Accordingly, in the long run, your company will produce 60,000 square feet of plywood and will make zero economic profit.

SOLVED PROBLEM

Price and cost (dollars per thousand square feet of plywood)

Quantity (thousands of square feet of plywood per day)

$6,000

$7,000

$8,000

$1,000

50 1101009070 806030 4010 20

$2,000

$3,000

$4,000

$5,000

0

MC ATC LMC LAC

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5.4 Perfect Competition Learning Objective 5.4 Apply the theory of perfectly competitive firms and markets to help make better managerial decisions.

Managers can use marginal analysis—which involves comparing the additional ben- efit of an action to its additional cost—to determine the profit-maximizing quantity to produce. Marginal analysis is an important tool in the arsenal of managers of firms in perfectly competitive markets because they can use it to make a wide vari- ety of decisions.

Applying Marginal Analysis To maximize profit, a firm produces the quantity that sets MR = MC. Unfortunately, as a manager, no one will give you graphs or equations showing the marginal reve- nue and marginal cost. Instead, your discovery of the profit-maximizing amount of output is often a trial-and-error process, in which you use your judgment and are guided by marginal analysis. Apply the lessons you have learned: If you believe that the marginal revenue from an additional unit exceeds its marginal cost, marginal analysis indicates that you want to produce that unit because it will increase your firm’s total profit. Conversely, if you estimate that the marginal revenue from the unit is less than its marginal cost, you do not want to produce that unit because doing so will decrease the total profit.

The profit-maximization rule, MR = MC, can be rewritten as MR - MC = 0. Although the change is small, the managerial interpretation of this modified ver- sion can be large when it comes to using your judgment about whether to pro- duce additional units. The amount MR - MC is the additional profit or loss on each unit of production. The profit-maximization rule means that you, as a man- ager, should continue to produce additional units of output as long as they are profitable, which will be the case as long as MR - MC is positive. You should stop producing additional units when you hit the unit for which MR - MC = 0. If you continue beyond that point, you will produce units for which MR - MC is negative, which creates losses for your firm. Consequently, reworking the profit- maximization rule in the form of MR - MC = 0 causes you to ask whether pro- ducing a unit is profitable—in which case it should be produced—or unprofitable— in which case it should not be produced. Sometimes simply deciding whether a unit will be profitable is significantly easier than separately estimating the unit’s marginal revenue and marginal cost.

Optimal Long-Run Adjustments You can learn a critical managerial lesson from the analysis of long-run profit maxi- mization: Use caution. If you are managing a competitive firm and economic times are good (demand, price, and profit are all high), do not expect the good times to last forever. Even if an increase in demand is permanent, the initial increase in price and resulting economic profit are temporary. With no barriers to entry, new firms will enter your market, force the price lower, and compete away your economic profit.

It is extremely easy for managers to believe that the price of their product will remain high for much longer than it actually does. Optimistic managers who make this mistake and elect to expand the scale of their firm may certainly later regret their decision. For example, if the managers at Happy Tree think the price of maple syrup will be $30 per gallon indefinitely, they might expand the firm’s scale of production, shifting the average cost curve to ATC in Figure 5.16. With this

MANAGERIAL APPLICATION

5.4 Managerial Application: Perfect Competition  215

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216  CHAPTER 5 Perfect Competition

Price and cost (dollars per gallon of maple syrup)

Quantity (gallons of maple syrup per year)

$30

$35

$5

2,5001,500 2,000500 1,000

$10

$15

$20

$25

0

MC

ATC

LAC

d0 5 MR0

d1 5 MR1

Figure 5.16 Overexpansion

If the managers believe the price will remain $30 for an extended period of time, they increase the scale of production so that their (short-run) average total cost curve is ATC, with short-run marginal cost curve MC. As long as the price remains equal to $30, the firm produces 2,500 gallons and makes an economic profit because P 7 ATC . But if the price rapidly falls to $15 per gallon and if the firm cannot quickly decrease the scale of its production, the firm incurs an economic loss. It produces 2,000 gallons, the quantity where MC is equal to the lower MR of $15. But the firm incurs an economic loss because P 6 ATC . To eliminate the firm’s economic loss, the managers must decrease the scale of production, thereby moving down the long-run average cost curve. Eventually, with the revised, smaller scale of production, the firm eliminates its loss and makes zero economic profit, so the owners make a competitive return.

expansion, when the price is $30 per gallon Happy Tree produces 2,500 gallons and makes an economic profit because P 7 ATC. Once the entry of new firms drives the price down to $15 per gallon, Happy Tree’s managers are in a less happy place. In that case, the firm produces 2,000 gallons (the quantity where MC equals the lower MR of $15 per gallon) and incurs an economic loss because P 6 ATC. Indeed, Happy Tree will incur economic losses until it can decrease the scale of its operations and move down its long-run average cost curve. If the firm cannot make this change quickly enough, it faces the decision of whether to remain open or close its doors.

This cautionary tale is not a mere theoretical curiosity. You have probably seen industries and firms that expanded like rapidly growing weeds, only to regret the expansion shortly thereafter. For example, in the face of high demand for ethanol, in the mid-2000s ethanol producers expanded rapidly to take advantage of what they expected would be a long-lasting high price. Additionally, there are virtually no barriers to entry into this market, so new producers streamed in. By the time the price collapsed in 2008, scores of producers had overexpanded and ultimately about half of them declared bankruptcy. The same cycle—increased demand, expanded scale and entry, and then a fall in price and numerous bankruptcies— occurred again in 2012.

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Revisiting How Burger King Managers Decided to Let Chickens Have It Their Way

As you learned at the beginning of the chapter, in 2016 Burger King execu- tives announced that the company would switch to 100 percent cage-free eggs by 2025. The executives made the announce- ment nine years in advance because they wanted to give time for the market for cage-free eggs to adjust and evolve. In particular, they want enough time (1) to enable more farmers to enter the cage-free egg market, (2) to give farmers already producing cage-free eggs time to increase their scale of operation, and (3) to allow technological innovations to occur. All of these changes will lower the price of cage-free eggs.

Figure 5.17 shows the effect of these changes by illustrating the situa- tion at a (hypothetical) typical cage-free egg producer. Suppose that in 2016 the price was $3.50 for a dozen cage-free eggs. In this case, the demand and mar- ginal revenue curve was d2016 = MR2016. Farmers maximized their profit by pro- ducing at point A. These farmers made an economic profit because the price exceeded the average total cost. Now let’s consider each change that Burger King’s managers anticipate:

• Entry. Economic profit attracts entry by new producers. As time passes, entry increases the supply, decreasing the price. Assuming that the farmers do not change the scale of their production, eventually the price falls to $3.00 per dozen, so that the farmers wind up producing at point B, where the price equals the minimum average total cost.

• Increase in scale. From point B, however, with the passing of more time the farmers make fur- ther adjustments by increasing the scale of their production and moving down the long-run average cost curve (LAC2016) to point C. Once farmers are producing at point C, competition forces the price of a dozen eggs to $2.50.

• New technology. Perhaps the largest change Burger King’s managers are anticipating is new technology to produce cage-free eggs. This tech- nology—perhaps the discovery of ways to reduce hen mortality or the development of robots to mon- itor the chickens—will change the farmers’ long-run average cost, shifting the LAC curve downward, as shown in Figure 5.17, to LAC2025. In this case, com- petition pushes the farmers to produce at point D, the minimum point on LAC2025, and the price of a dozen cage-free eggs is only $1.00.

Price and cost (dollars per dozen eggs)

Quantity (eggs per year)

$3.00

$3.50

$4.00

$4.50

$5.00

$0.50

600,000300,000 500,000400,000100,000 200,000

$1.00

$1.50

$2.00

$2.50

0

MC2016

A

B

C

D

ATC2016

LAC2025

LAC2016

d2016 5 MR2016

Figure 5.17 Costs at a Cage-Free Egg Producer

When Burger King’s executives announced they would switch to cage-free eggs, the price of cage-free eggs was $3.50 per dozen, and farmers were producing at point A. Because the farmers were making an economic profit, entry occurs, lowering the price to $3.00 per dozen and leading the farmers to produce at point B. From point B, as more time passes the farmers increase the scale of their production, moving down the LAC curve to point C and lowering the price still more to $2.50 per dozen. Burger King’s managers also hope that over the period of time during which they are switching to cage-free eggs, technological progress occurs, so that the long-run average cost curve shifts downward to LAC2025. In this happy state of affairs, the farmers eventually produce at point D on the new LAC curve, at which the price of a dozen cage-free eggs will be only $1.00.

Revisiting How Burger King Managers Decided to Let Chickens Have It Their Way  217

(Continues)

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218  CHAPTER 5 Perfect Competition

Summary: The Bottom Line

5.1 Characteristics of Competitive Markets • Perfectly competitive markets have five characteristics:

(1) The market includes a large number of buyers and sellers, (2) the market has no barriers to entry, (3) each firm produces a homogeneous product, (4) buyers and sellers have perfect information about the price and prod- uct characteristics, and (5) there are no transaction costs.

• Firms in perfectly competitive markets are price takers.

5.2 Short-Run Profit Maximization in Competitive Markets

• A perfectly competitive firm’s demand is perfectly elastic at the market price, so its demand curve is hori- zontal at that price. Marginal revenue is the change in total revenue divided by the change in quantity. A per- fectly competitive firm’s marginal revenue equals the market price, so the marginal revenue curve is hori- zontal and is the same as the firm’s demand curve.

• A firm maximizes profit by producing the quantity that sets marginal revenue equal to marginal cost 1MR = MC2. If MR 7 MC, managers can increase their firm’s profit by increasing production. If MR 6 MC, managers can increase profit by decreasing production. The profit-maximizing price is the highest price the firm can set and sell the quantity it produces. For a firm in a perfectly competitive market, the profit- maximizing price equals the market price.

• The firm (1) makes an economic profit if the price exceeds the average total cost 1P 7 ATC2, (2) makes zero economic profit (its owners make a competitive return) if the price equals the average total cost 1P = ATC2, and (3) incurs an economic loss if the price is less than the average total cost 1P 6 ATC2.

• Managers will keep their firm open—even if it is incurring an economic loss—if the price exceeds the average variable cost 1P 7 AVC2, but they will close it if the price is less than the average variable cost 1P 6 AVC2.

• The firm’s short-run supply curve is the portion of its marginal cost curve above the shut-down point, the minimum of the average variable cost.

5.3 Long-Run Profit Maximization in Competitive Markets

• In the long run, managers can adjust all inputs. • If a firm in a perfectly competitive market is making an

economic profit, new firms enter the market, increase the supply, lower the price, and compete away the eco- nomic profit. In the long run, firms in a perfectly com- petitive market are limited to making a competitive return—that is, zero economic profit.

5.4 Managerial Application: Perfect Competition

• Marginal analysis shows that you, as the manager of a perfectly competitive firm, maximize profit by produc- ing the units of output for which MR - MC is positive and stopping when you reach the unit for which MR - MC equals zero.

• If a price change is expected to last for a more extended period, you might adjust the scale of your firm’s production by changing your fixed inputs. Any change in price will not be permanent, however, so your scale of production should not be changed so much that your firm incurs large economic losses after the entry of firms moderates the price change.

Using insights from the analysis of perfectly competitive markets, Burger King’s managers decided that rather than switch immediately to cage-free eggs, they would slowly switch over nine years. Burger King’s managers know that

during this extended period of time, changes in the com- petitive market will lower the price of cage-free eggs. The decision made by these executives increased Burger King’s profit.

Key Terms and Concepts Barrier to entry

Economic loss

Economic profit

Marginal revenue

Perfectly competitive market

Price takers

Short-run firm supply curve

Transaction costs

Revisiting How Burger King Managers Decided to Let Chickens Have It Their Way (continued)

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Questions and Problems

2.6 You are managing a perfectly competitive landscaping firm. You have carefully calcu- lated that the cost of mowing and tending one additional yard is $25 and the price of that work is $40. To increase your profit, what decision should you make? Explain your answer.

2.7 In the figure, if the price is $500 per unit, what is the firm’s profit-maximizing price and quantity? What is the amount of the firm’s economic profit or loss?

2.8 Suppose that you are a manager of a firm like Sproule Farms, a perfectly competitive grower of sugar beets. The market price of sugar beets is $50 per ton. The table has your total cost. What is the profit-maximizing quantity of sugar beets? What is the amount of your economic profit or loss?

Questions and Problems  219

Price and cost (dollars per unit)

Quantity (units per month)

$600

$100

2,500 3,0001,500 2,000500 1,000

$200

$300

$400

$500

0

ATC

AVC

MC

Quantity (tons) Total Cost (dollars)

5,000 $235,510

5,001 235,550

5,002 235,600

5,003 235,651

5,004 235,703

5,005 235,756

5.1 Characteristics of Competitive Markets Learning Objective 5.1 Summarize the conditions that make a market perfectly competitive.

1.1 Which of the following firms compete in a per- fectly competitive market or a market that closely approximates perfect competition? a. Verizon Wireless b. Swaz Potato Farms c. Alcoa Aluminum d. Gucci Perfumes

1.2 Why does it make no sense for the managers of a perfectly competitive firm to spend money on advertising?

1.3 No matter how many soft drinks you buy, you have no effect on the price of soft drinks. The soft drink industry includes two very large pro- ducers and several smaller ones. Is this industry perfectly competitive? Explain your answer.

1.4 Give three examples of products or firms pro- tected by barriers to entry. Describe the barrier to entry for each example.

1.5 In a perfectly competitive market, no individual producer can affect the price of the product. How, then, is the price of the product determined?

5.2 Short-Run Profit Maximization in Competitive Markets Learning Objective 5.2 Use marginal analysis to determine the profit-maximizing quantity that a perfectly competitive firm produces in the short run.

2.1 In your own words, explain the concept of mar- ginal analysis, making sure to include the marginal aspect of this rule.

2.2 What is the difference between a market demand curve and a perfectly competitive firm’s demand curve?

2.3 How does a perfectly competitive firm’s price com- pare to its marginal revenue? How does its demand curve compare to its marginal revenue curve?

2.4 What is the relationship between marginal cost and total cost?

2.5 A perfectly competitive firm is producing the quantity that sets its marginal revenue equal to its marginal cost. Explain to this firm’s manag- ers why producing more output or less output would decrease the firm’s profit.

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220  CHAPTER 5 Perfect Competition

2.14 You are managing a perfectly competitive dairy farm, and sadly you have determined that your firm is incurring an economic loss. You do not fore- see any future changes in your costs or the price of milk. Discuss all factors that influence your deci- sion about whether to close or remain open.

2.15 “A manager of any firm that is paying out more in costs than it is making in revenue should shut down operations at once.” Is this advice sound? Explain your answer.

2.16 You are the manager of a large, perfectly competi- tive wheat farm. The price of wheat is $6 per bushel. The table gives your total costs for different quantities. What is the profit-maximizing quantity of wheat? Carefully explain your answer.

Price and cost (dollars per unit)

Quantity (units per day)

$100

100 12060 8020 40

$200

$300

$400

$500

0

ATC

AVC

MC

2.10 In a perfectly competitive market, the equilib- rium market price for a good is $60 per unit, and a firm has a marginal cost curve given by

MC = 10 + 0.25q

What is the firm’s profit-maximizing quantity and price?

2.11 Your company just spent $5.0 million on a state- of-the-art production facility. As a result, the marginal cost of producing the product is

MC = 10 + 0.0001q

If the market is perfectly competitive and the price is $50 per unit, how many units will you produce? If the price falls to $25, how many units will you produce?

2.12 A perfectly competitive firm’s marginal cost curve is upward sloping but not vertical. If the price of the product increases, in the short run is it possible for the firm’s economic profit to decrease (or for its economic loss to increase)? Explain your answer.

2.13 In the figure, in the short run what is the lowest price at which the firm will remain open? At this price, what does the firm’s economic loss per day equal?

5.3 Long-Run Profit Maximization in Competitive Markets Learning Objective 5.3 Describe the long-run adjustments that managers in perfectly com- petitive markets make to maximize profit.

3.1 In the long run, why does a firm in a perfectly competitive market produce the quantity that minimizes its long-run average cost?

3.2 What sort of profit does a perfectly competitive firm make in the long run?

Price and cost (dollars per ton of pellets)

Quantity (thousands of tons of pellets per year)

$40

50 6030 4010 20

$80

$120

$160

0

ATCMC

Quantity (bushels of wheat) Total Cost (dollars)

100,000 $555,000 100,001 555,002 100,002 555,005 100,003 555,009 100,004 555,014 100,005 555,020

2.9 Suppose that you are a manager at a firm like Yulong Machine Company, a perfectly competi- tive producer of pellets used in biomass plants to generate electricity. The price of a ton of pellets is $120. In the figure, producing 30,000 tons of pel- lets per year minimizes the average total cost of producing the pellets. Does producing 30,000 tons maximize your firm’s profit? Explain your answer.

M05_BLAI8235_01_SE_C05_pp186-226.indd 220 25/08/17 12:35 PM

a. If the price is $20 per bushel and the firm stays open, in the short run what is the firm’s profit-maximizing price and quan- tity? Explain whether the firm makes an eco- nomic profit or loss.

b. Will firms enter or exit the market? In the long run, will the price rise, fall, or not change? If there are no technological changes, what will be the price in the long run? Explain your answers.

3.4 The market for paper is perfectly competitive. Draw a demand and supply figure showing the entire paper market and another figure for a typical paper manufacturing firm with the long- run average cost (LAC), average total cost (ATC), marginal cost (MC), demand (d), and marginal revenue (MR) curves showing the long-run out- come. Presuming that an increase in the number of firms does not affect the firms’ cost curves, describe the short-run and long-run effects of an increase in the market demand for paper.

3.5 The plywood market is perfectly competitive. The demand for home construction increases, increasing the demand for plywood. If the increase in demand for plywood is permanent, should the managers of a plywood firm increase their firm’s capacity? Why or why not?

3.6 You are the manager of a bagel producer that is in a perfectly competitive industry comprised of iden- tical firms. The cost of flour used to produce bagels decreases from $25 to $20 per hundred pounds.

Price and cost (dollars per bushel of peaches)

Quantity (bushels of peaches per year)

$10

10,0006,000 8,0002,000 4,000

$20

$30

$40

$50

0

LACATC MC

a. In the short run, how do you respond to the fall in the price of flour?

b. Describe the long-run adjustments that take place in the market.

c. What long-run decisions will you make as the manager of your firm?

3.7 Describe the long-run outcome for a competitive wild rice producer and the competitive wild rice industry. Now suppose that the demand for wild rice increases. a. Discuss the adjustments by the firm and the

industry. b. What happens to the firm’s long-run eco-

nomic profit? Now suppose that demand increases again but

that the government forbids entry by new wild rice producers. c. Discuss the adjustments by the firm and the

industry. d. What happens to the firm’s long-run eco-

nomic profit? e. Is the firm’s long-run economic profit higher

when entry is forbidden or when entry is allowed?

f. What is the managerial lesson illustrated in your answer to part e?

5.4 Managerial Application: Perfect Competition Learning Objective 5.4 Apply the theory of perfectly competitive firms and markets to help make better managerial decisions.

4.1 As a manager of a house painting firm like the Queen Anne Painting Company, a perfectly com- petitive firm in Seattle, Washington, you are maxi- mizing your profit and are currently making an economic profit. For simplicity, assume that you use only capital and labor. You determine that at your current production, your long-run average cost curve is downward sloping; that is, if you increased both your capital and your labor by the same pro- portion, your long-run average cost would fall. a. Draw a figure to illustrate your situation. In

your figure include short-run average total cost (ATC) and marginal cost (MC) curves, a long- run average cost (LAC) curve, and a demand and marginal revenue 1d = MR2 curve.

b. Using your figure, do you want to increase the scale of your production? Explain your answer.

4.2 Managers of perfectly competitive firms must be cautious when deciding to permanently expand (or contract) the scale of production. What fac- tors should go into the decision to expand the scale of production? Which factors make it neces- sary to proceed with caution?

Questions and Problems  221

3.3 Peach growing is perfectly competitive. For sim- plicity, suppose that all peach growers have the same cost curves. In the figure, each grower’s initial average total cost curve is ATC, its initial marginal cost curve is MC, and its long-run average cost curve is LAC.

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222  CHAPTER 5 Perfect Competition

MyLab Economics Auto-Graded Excel Projects 5.1 The Weinandt Family Farm in Wynot, NE raises

livestock and grows crops. Commonly grown crops in Nebraska are corn and soybeans. Sup- pose you are helping a farm similar to the Wein- andt Farm make decisions about how much corn to grow this year. As an agricultural prod- uct, the market for corn meets the requirements of a perfectly competitive market. a. Using the market data provided, create a

market supply and demand graph. b. What are the market equilibrium price and

quantity? c. Using the firm cost and quantity data, find

FC, VC, ATC, AFC, AVC, and MC. Graph ATC, AFC, AVC, and MC.

d. Based on your answers in part c, between which quantities is ATC minimized?

e. Based on your answers in part c, between which quantities should the farm aim to produce?

f. Using the lower of these two quantities, cac- ulate TR, TC, and the firm’s economic profit or loss.

g. Will the farm decide to grow corn or leave the fields bare? Explain your answer.

h. Will farms enter this market, leave the mar- ket, or remain constant? Explain your answer.

5.2 The Weinandt Family Farm in Wynot, NE raises livestock and grows crops. Commonly grown crops in Nebraska are corn and soybeans. Sup- pose you are helping a farm similar to the Wein- andt Farm make decisions about how much corn to grow this year. As an agricultural prod- uct, the market for corn meets the requirements of a perfectly competitive market. The original market demand (Qd1) and mar- ket supply (Qs) are given. Suppose the market demand shifts to Qd2 because, in addition to being used as a food product, corn is now used for ethanol production. a. Using the market data provided, create a

market supply and demand graph which includes both Qd1 and Qd2.

b. What are the market equilibrium price and quantity before and after the demand shift?

Accompanies problem 5.1.

M05_BLAI8235_01_SE_C05_pp186-226.indd 222 25/08/17 12:35 PM

c. Using the firm cost and quantity data, find FC, VC, ATC, AFC, AVC, and MC.

d. Based on your answers in part c and b, between which quantities should the farm aim to produce before and after the demand shift?

e. Using the lower of these two quantities, calcu- late TR, TC, and the firm’s economic profit or loss before and after the change in demand.

f. Will farms enter this market, leave the mar- ket, or remain constant after the demand shift? Explain your answer.

MyLab Economics Auto-Graded Excel Projects  223

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224

The most important result in Chapter 5 is the profit-maximization rule, MR = MC. Deriving this rule using calculus is straightforward. We can start with the definition of marginal revenue.

A. Marginal Revenue Marginal revenue is the change in total revenue (TR) that results from a change in quantity (q), or using calculus, marginal revenue (MR) is defined as

MR = dTR dq

A5.1

Total revenue equals price multiplied by quantity, P * q. For a perfectly competitive firm, the price is the same no matter the quantity the firm produces. Consequently, for a perfectly competitive firm,

dTR dq

= d1P * q2

dq = P A5.2

Combining Equations A5.1 and A5.2 shows that for a perfectly competitive firm MR = P.

B. Maximizing Profit Managers want to determine the amount of output that maximizes the firm’s profit. The profit equals total revenue minus total cost, or

Profit1q2 = TR1q2 - TC1q2 To maximize profit, take the derivative of Profit(q) with respect to q, and set it equal to zero:

dProfit

dq =

dTR dq

- dTC dq

= 0 A5.3

Recall from Chapter 4 that the marginal cost (MC) equals the derivative of total cost (TC) with respect to quantity, or MC = dTC>dq. Accordingly, in Equation A5.3, dTR>dq is MR and dTC>dq is MC, so the equation can be rewritten as

MR - MC = 0 1 MR = MC

which is precisely the same result presented in the profit-maximization rule in Section 5.2 of the chapter.

C. Maximizing Profit: Example Suppose that you are a manager of a company like B.W. Recycling, a perfectly competitive gold scrap recycler near Fort Lauderdale, Florida. Your company has daily fixed cost of $18,000 and variable cost given by VC = 0.05q3 - 4.5q2 + 600q. The total cost is equal to the sum of the variable cost plus the fixed cost, or TC = 0.05q3 - 4.5q2 + 600q + 18,000. Using the power rule to differentiate the total cost with respect to q gives your marginal cost function:

MC = 0.15q2 - 9.0q + 600 A5.4

CHAPTER 5 APPENDIX

The Calculus of Profit Maximization for Perfectly Competitive Firms

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The average total cost (ATC) equals TC>q, so the average total cost function is

ATC = 0.05q2 - 4.5q + 600 + 18,000

q A5.5

If the market price for the recycled gold is $1,005 per ounce, then P = MR = $1,005. To maximize profit, you must produce the quantity at which MR = MC, or using Equation A5.4

1,005 = 0.15q2 - 9.0q + 600 1 0 = 0.15q2 - 9.0q - 405 A5.6

Using the quadratic formula to solve the second part of Equation A5.6, the profit-maximizing quantity is 90 ounces of gold.1 Of course, the profit-maximizing price equals the market price, $1,005 per ounce. To determine the economic profit or loss, using Equation A5.5 and the price we can first calculate the economic profit per ounce as P - ATC, or

1,005 - c 10.05 * 9022 - 14.5 * 902 + 600 + 18,000 90

d = 1,005 - 800 = 205

The total economic profit equals the profit per ounce multiplied by the quantity of ounces, or

$205 * 90 = $18,450

Figure A5.1 illustrates these calculations. The MC curve is based on Equation A5.4, and the ATC curve is based on Equation A5.5. The demand and marginal revenue curve is horizontal at $1,005 per ounce. The profit-maximizing quantity is 90 ounces per day because this is the quantity at which MR = MC. The price is $1,005 per ounce. Figure A5.1 shows that at the profit-maximizing quantity, the firm’s average total cost is $800 per ounce. The firm’s eco- nomic profit is therefore the area of the green rectangle, which is equal to $18,450.

1 The other root of Equation A5.6 is −30, which is meaningless because the quantity must be positive.

Price and cost (dollars per ounce of gold)

Quantity (ounces of gold per day)

$1,200

$1,400

$200

150 18090 12030 60

$400

$600

$800

$1,000

0

MC ATC

d 5 MR

Economic profit $18,450

Figure A5.1 Profit-Maximizing Quantity, Price, and Economic Profit

The profit-maximizing quantity is the quantity at which MR = MC , which is 90 ounces of gold per day. The profit-maximizing price is equal to the market price, $1,005 per ounce. The economic profit per ounce equals the price per ounce minus the average total cost of producing an ounce, or P - ATC . At the profit-maximizing quantity, the average total cost is $800 per ounce, so the firm’s economic profit per ounce is $1,005 - $800, or $205 per ounce. The firm’s total economic profit equals the economic profit per ounce multiplied by the number of ounces, $205 per ounce * 90 ounces, which equals the area of the green rectangle in the figure, $18,450.

CHAPTER 5 APPENDIX The Calculus of Profit Maximization for Perfectly Competitive Firms  225

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Calculus Questions and Problems A5.1 Suppose that Nuñez Consulting offers management

consulting services in a perfectly competitive mar- ket and that the total cost the firm incurs when pro- viding consulting services is

TC1q2 = 4,500 + 5q2

where q is the number of hours of consulting ser- vices provided by Nuñez Consulting. a. What is the average total cost of providing con-

sulting services as a function of the number of hours of consulting services provided?

b. The price of consulting services is $500 per hour. At what quantity is Nuñez Consulting’s profit maximized? What is the maximum amount of economic profit that Nuñez Consult- ing can earn in this market?

c. Suppose that the price of a consulting services rises to $600 per hour. At what quantity is Nuñez Consulting’s profit maximized after this price change? What is the maximum amount of eco- nomic profit that Nuñez Consulting can earn?

A5.2 Suppose that Laylita sells empanadas at a perfectly competitive local farmers’ market and that her total cost of producing an empanada is

TC1q2 = 40 + 0.1q2 - 0.2q where q is the total number of empanadas that she

produces. a. What is the average total cost of producing

empanadas as a function of the quantity of empanadas produced?

b. At what quantity, q*, is the average total cost of producing an empanada minimized? What is the value of the average total cost at q*?

c. The price of an empanada is $4.20. What quan- tity of empanadas should Laylita produce to maximize her profit? If she remains open, what is her economic profit or loss?

d. Suppose that the price of an empanada falls to $3. What quantity of empanadas should Laylita produce to maximize her profit? If she remains open, what is her economic profit or loss?

A5.3 Gerardo’s Geraniums is a flower farm, specializing in the production of cut geraniums. The cut gera- nium market is a perfectly competitive market. Gerardo has hired an economist to determine his total cost function, which the economist reports as

TC1q2 = 30,000 + 0.0025q2

where q is the number of cut flowers Gerardo’s Geraniums produces.

a. What is Gerardo’s Geraniums’ marginal cost of supplying an additional cut geranium?

b. Suppose that the price of a cut geranium is $2.50. How many cut geraniums will Gerardo’s Geraniums supply?

c. Suppose that the price of a cut geranium rises to $3.00. How many cut geraniums will Gerar- do’s Geraniums supply?

A5.4 Jessica is a 10-year-old entrepreneur. She produces lemonade in her family’s kitchen and sells that lem- onade at a stand that she sets up in front of her family’s house each Saturday afternoon. Jessica lives in a neighborhood with many other entrepre- neurial children, all selling identical lemonade. Therefore, along Jessica’s street, the lemonade mar- ket is perfectly competitive. The price of a cup of lemonade on Jessica’s street is $2. Jessica’s total cost of setting up her lemonade stand and producing lemonade is

TC1q2 = 10 + 0.025q2

where q is the number of cups of lemonade Jessica produces. a. What is Jessica’s marginal cost of producing an

additional cup of lemonade? b. What is Jessica’s marginal revenue of produc-

ing an additional cup of lemonade? c. What is the profit-maximizing number of cups

of lemonade? What is Jessica’s economic profit at this quantity?

A5.5 Larry’s Lasers is a laser hair-removal firm that oper- ates in the perfectly competitive laser hair-removal market. Dr. Larry specializes in removing women’s facial hair, and his total cost of performing these procedures is

TC1q2 = 200,000 + 5q2 - 100q where q is the number of facial hair removal proce-

dures he performs. a. What is Larry’s Lasers’ marginal cost of per-

forming an additional facial hair removal procedure?

b. Suppose that the price of a facial hair removal procedure is $2,300. How many facial hair removal procedures does Larry perform?

c. If the price of a facial hair removal procedure is $2,300, does Larry make an economic profit? If so, how much?

d. What is the long-run price of a facial hair removal procedure?

226  CHAPTER 5 APPENDIX The Calculus of Profit Maximization for Perfectly Competitive Firms

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 227

Premature Rejoicing by the Managers at KV Pharmaceutical

A pharmaceutical company typically spends approx-imately 10 years and over $1 billion to research, develop, and test a potential drug in order to prove its safety and effectiveness to the federal Food and Drug Administra- tion (FDA). The company can apply for a government pat- ent for exclusive rights to sell the drug for 20 years from the date of filing, though sometimes the company can gain extra time if the FDA is slow to approve the drug.

An exception to this general policy is the orphan drug policy. Orphan drugs are legally defined as drugs devel- oped for diseases that affect 200,000 or fewer individuals in the United States. Under this policy, a pharmaceutical company that receives FDA approval has a seven-year period of marketing exclusivity even if the company does not have a patent on the drug.

In 1956, the FDA approved hydroxyprogesterone caproate to treat various issues during pregnancy, including premature birth. After the patent expired, the market evolved. From 2000 until 2011, a number of different compounding pharmacies (smaller companies that manufacture drugs for specific individuals) made the drug under the name 17P. In this competitive market, the price for a shot of 17P was approxi- mately $15. To prevent premature birth, typically doctors pre- scribe weekly shots for the last 20 weeks of the pregnancy.

Studies conducted after 2000 indicated that 17P helped prevent subsequent premature births in women with a history of premature births. KV Pharmaceutical used these studies to gain orphan drug designation and then conducted its own test with 463 women, which con- firmed the findings. KV Pharmaceutical submitted these studies to the FDA. The March of Dimes, a charity group concerned with preventing premature births, lobbied the FDA for quick approval of KV’s submission. Based on KV’s study, the FDA granted the firm the standard seven-year period of orphan-drug marketing exclusivity for its drug, which the firm called Makena. The FDA’s decision effec- tively made the firm a monopoly. Believing that the FDA ruling gave KV Pharmaceutical a seven-year monopoly, its managers celebrated, and its stock price doubled. Manag- ers set the price at $1,500 per dose, up approximately 100 times from the $15 competitive price for 17P.

How did the managers at KV Pharmaceutical determine the price of their drug? How can they ensure that it is the profit-maximizing price? This chapter will show you how to answer these key questions about KV Pharmaceutical and other monopolies. At the end of the chapter, we revisit the situation faced by KV Pharmaceutical’s managers and show how they made a fundamental error in their pricing process.

Sources: Courtney Hutchison and ABC News Medical Unit, “KV Pharma Cuts Price of Costly Premature Birth Prevention Drug,” ABC News. April 1, 2011; Yesha Patel and Martha M. Rumore, “Hydroxprogesterone Caproate Injection (Makena) One Year Later,” Pharmacy and Therapeutics, July 2012, pp. 404–411; Tom Schoenberg, “K-V Pharmaceutical Loses FDA Lawsuit over Makena Drug,” Bloomberg, September 6, 2012.

Monopoly and Monopolistic Competition Learning Objectives After studying this chapter, you will be able to:

6.1 Explain the relationship between a monopoly’s demand curve and its marginal revenue curve. 6.2 Discuss how managers of a monopoly can determine the quantity and price that

maximize profit and how they compare to those of a perfectly competitive firm. 6.3 Describe how managers of a dominant firm determine the quantity and price that

maximize profit. 6.4 Explain how managers of a monopolistically competitive firm determine the quantity and

price that maximize profit. 6.5 Apply what you have learned about monopolies, dominant firms, and monopolistically

competitive firms to make better managerial decisions.

6CHAPTE R

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228  CHAPTER 6 Monopoly and Monopolistic Competition

Introduction In Chapter 5, you learned that the price-taking behavior of a firm in a perfectly compet- itive market severely limited its managers’ pricing responsibilities. In this chapter, you will see that a manager’s pricing responsibilities increase when a firm has market power, the ability to determine the price of its good or service. Later chapters will examine different pricing schemes that managers of firms with market power can use. First, however, you need to understand the economic fundamentals of managerial decisions in these firms. To explain these fundamentals, Chapter 6 includes five sections:

• Section 6.1 explains the conditions that define a monopoly market and compares a monop- oly’s demand curve and marginal revenue curve to those of a perfectly competitive firm.

• Section 6.2 explains how managers of monopolies can use marginal analysis to determine the profit-maximizing quantity and price and compares these results to those in a perfectly competitive market.

• Section 6.3 explains why managers of dominant firms face the same decisions as those of monopolies—but with an added wrinkle: They must take into account the actions of all of the competitive firms in the market.

• Section 6.4 examines how monopolistically competitive firms compete with a large number of other firms, all producing similar but somewhat differentiated products. Because of a limited degree of market power, managers of these firms make profit-maximizing decisions similar to those of monopolies, but the amount of economic profit differs.

• Section 6.5 applies what you have learned about monopolies, dominant firms, and monop- olistically competitive firms to help you make better managerial decisions.

6.1 A Monopoly Market Learning Objective 6.1 Explain the relationship between a monopoly’s demand curve and its marginal revenue curve.

Chapter 5 covered perfectly competitive markets and perfectly competitive firms. Now it is time to turn your attention to monopoly markets and monopoly firms to explain how they determine their profit-maximizing price and quantity. The first step is understanding the definition of a monopoly. Then you will learn how a firm’s monopoly position affects its demand and marginal revenue.

Defining Characteristics of a Monopoly Market It is tempting to define a monopoly market as a market with a single seller. Although this aspect is the most prominent characteristic, it is not the only one. A more com- plete definition of a monopoly market includes three parts:

1. Single seller. There is only one firm in the market, which gives it immense market power. As noted in the introduction, market power is the ability of a firm to determine the price of its good or service. By definition, perfectly com- petitive firms have no market power, but monopoly firms do—they are free to decide the price of their product. Essentially, the managers of a monopoly firm set the price in a monopoly market, while the market sets the price in a perfectly competitive market.

2. No close substitute. The good or service a monopoly produces has no close sub- stitutes. This characteristic is necessary to adequately define the market. For

Market power The ability of a firm to determine the price of its good or service.

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6.1 A Monopoly Market  229

instance, you cannot assert that McDonald’s is a monopoly at a particular inter- section if there is a Burger King one block away. Both McDonald’s and Burger King sell their own unique versions of a hamburger, but most consumers find them very close substitutes. McDonald’s and Burger King are examples of firms in monopolistic competition, a market structure you will learn more about in Section 6.4. On the other hand, Roche Holdings’ drug Herceptin is a monoclonal antibody used to treat certain breast and gastric cancers, and there is no other drug that has a similar genetic target. The market for Herceptin meets this part of the definition of a monopoly market.

3. Insurmountable barriers to entry. As you learned in Chapter 5, a barrier to entry is any factor that makes it difficult for new firms to enter a market. In a monopoly, the barriers to entry are insurmountable, which is why there is only one firm in the market. Patents, trademarks, copyrights, and significant cost advantages for a firm already in the market can serve as barriers to entry. For example, the market for Herceptin is a monopoly because Roche Holdings has a patent that prevents other pharmaceutical or biotech companies from producing the drug. As long as the patent remains in force, it is an insurmountable barrier to entry. Barriers to entry ensure there is only one firm in the market. They play a crucial role in the firm’s long-run outcome. You will learn more about their long-run role in Section 6.2.

So a complete definition of a monopoly market is a market with only a single seller, which is producing a product that has no close substitute and is protected by an insurmountable barrier to entry.

Demand and Marginal Revenue for a Monopoly Although a monopoly and a perfectly competitive firm differ in important character- istics, the managers’ ultimate goal in both firms is the same: to maximize profit. Man- agers of a perfectly competitive firm control only the quantity they produce because the price is determined by the market. As you learned in Chapter 5, marginal analysis helps guide these managers to the profit-maximizing quantity. Managers of a monop- oly might appear to have a more difficult task because they must determine both the

Monopoly market A market with only a single seller, which is producing a product that has no close substitute and is protected by an insurmountable barrier to entry.

You are a government official responsible for monitoring the behavior of monop- olies to discover violations of antitrust laws. For a small fee, airlines can fly in and out of the airport in Rochester, New York. Say that Delta Airlines is the only carrier flying from Rochester to LaGuardia Airport in New York City, but JetBlue Airways flies from Rochester to JFK International, also in New York City. Do you decide that Delta Airlines is a monopoly? Explain your answer.

Answer Delta Airlines is not a monopoly for two reasons. First, flying to JFK International Airport is a close substitute for flying to LaGuardia Airport. Second, there is no insurmountable barrier to entry: If another airline wants to fly from Rochester to LaGuardia Airport, it can do so at only a small expense.

DECISION SNAPSHOT Is Delta Airlines a Monopoly?

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230  CHAPTER 6 Monopoly and Monopolistic Competition

quantity to produce and the price to charge. It turns out, however, that marginal anal- ysis is a powerful tool for monopoly managers as well. Of course, to use marginal analysis, the monopoly’s managers must know the firm’s marginal revenue and marginal cost. Let’s begin by examining marginal revenue.

Monopoly’s Demand and Marginal Revenue Curves In your study of a perfectly competitive firm, you had to distinguish between the firm’s demand curve and the market demand curve (see Section 5.2). You do not need to make this distinction for a monopoly. Because the monopoly is the only firm in the market, the monopoly’s demand curve is the same as the market demand curve. For example, Roche Holdings’ patent on Herceptin makes it the only com- pany allowed to sell Herceptin, so the market demand curve for Herceptin is also Roche Holdings’ demand curve for it.

Suppose that you are a manager for a pharmaceutical company that also has a patent on a drug. Similar to Roche Holdings, your company is the only one allowed to sell that drug. Figure 6.1 shows the (hypothetical) market demand curve for this drug. Because you are the only seller, the market demand curve is also your firm’s demand curve.

Even with the difference in demand, marginal revenue is calculated for a monop- oly firm in the same way as for a perfectly competitive firm: the change in total reve- nue resulting from a change in quantity sold, or

MR = ∆TR ∆Q

Although the definition of marginal revenue is the same for a perfectly competitive firm and a monopoly, a monopoly’s marginal revenue curve differs from that of a per- fectly competitive firm because of the differences in their demand curves. Table 6.1 shows some data from points on the demand curve for your drug from Figure 6.1.

D

Price (thousands of dollars per treatment)

Quantity (thousands of treatments per year)

$90

$0

$10

$20

35030025020015010050

$30

$40

$50

$60

$70

$80

2$20

2$10

Figure 6.1 The Market Demand Curve and Monopoly Firm Demand Curve

Because your firm is the only company allowed to sell your drug, the market demand curve, D, is also your demand curve for the drug.

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6.1 A Monopoly Market  231

Figure 6.2 illustrates your demand curve and the resulting marginal revenue curve. Both curves show that for any quantity, the price, measured from the demand curve, is greater than the marginal revenue, measured from the marginal revenue curve. Why is P 7 MR? In Table 6.1, you can see that your pharmaceutical company can sell 199,999 units at a price of $50,000.20 for each unit. Because the demand curve is downward sloping, the managers can sell an additional unit, the 200,000th unit, only if they lower the price for all the units. Table 6.1 shows that the price of a treatment must fall to $50,000.00 in order to sell the 200,000th unit. The extra unit directly adds $50,000.00 to your firm’s total revenue, but to sell that unit, you had to lower the price of a treatment from $50,000.20 to $50,000.00, a loss of $0.20 in revenue on each of the initial 199,999 treatments you had been selling at the higher price. The price reduction means that your firm loses a total of $0.20 * 199,999 or $39,999.80 in reve- nue on the quantity that it had been selling. So the total change in revenue from sell- ing the 200,000th unit equals $50,000.00 - $39,999.80 or $10,000.20, making the marginal revenue from the 200,000th unit $10,000.20.

D

MR

Price (thousands of dollars per treatment)

Quantity (thousands of treatments per year)

$90

$0

$10

$20

35030025020015010050

$30

$40

$50

$60

$70

$80

2$20

2$10

Figure 6.2 A Monopoly’s Demand and Marginal Revenue Curves

The graph shows the market demand curve (D) and the resulting marginal revenue curve (MR) for your drug. For any quantity, P 7 MR. Because the demand curve is linear, the marginal revenue is also linear, with the same intercept on the price axis and a slope that is twice the slope of the demand curve.

Table 6.1 Demand, Total Revenue, and Marginal Revenue

The first two columns are (part of) the demand facing your firm. Total revenue equals P * Q. Marginal revenue is the change in total revenue caused by a change in quantity, or ∆TR∆Q . For a monopoly, price is greater than marginal revenue, P 7 MR.

Price, P

Quantity Demanded, Q

Total Revenue, TR

Marginal Revenue, MR

50,000.40 199,998 $9,999,979,999.20 $10,000.60

10,000.20

9,999.80

9,999.40

50,000.20 199,999 9,999,989,999.80

50,000.00 200,000 10,000,000,000.00

49,999.80 200,001 10,000,009,999.80

49,999.60 200,002 10,000,019,999.20

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232  CHAPTER 6 Monopoly and Monopolistic Competition

This reasoning applies to all units produced and makes clear why P 7 MR for a monopoly: To sell an additional unit, you must lower the price, thereby losing some revenue on the initial units already sold. Recall that for a perfectly competi- tive firm, P = MR because the competitive firm’s demand curve is horizontal—the managers do not need to lower the price to sell additional units. When a perfectly competitive firm sells another unit, there is no need to subtract a loss in revenue from the initial units because the constant price means there is no loss in revenue.

Figure 6.2 shows that there are quantities where the marginal revenue (MR) is negative. This occurs when there are so many units sold before the price change that the revenue lost on these initial units is larger than the revenue gained on the newly sold unit. In this case, the change in total revenue is negative, which makes the mar- ginal revenue negative.

Marginal Revenue Curve for a Linear Demand Curve Figure 6.2 also shows that when the demand curve is linear, the marginal revenue curve also is linear. In addition, while both curves have the same intercept on the price axis, the marginal revenue curve is twice as steep as the demand curve.1 This mathemat- ical result is correct only for linear demand curves. For these sorts of curves, it is a very handy result because it allows you to quickly determine the marginal revenue curve. The result that for a monopoly P 7 MR is more general. Indeed, as long as the demand curve is downward sloping, P 7 MR no matter if the demand curve is linear or not.

Elasticity, Price, and Marginal Revenue Closer analysis of the definition of marginal revenue reveals an important relation- ship among the elasticity of demand, the price, and the marginal revenue. Some mathematics relegated to a footnote2 shows that the marginal revenue from a one- unit change in Q is equal to

MR = a ∆P ∆Q

* Qb + P 6.1

Equation 6.1 reflects the two effects of a change in the quantity on the total revenue: (1) the effect of the change in the price on the initial quantity, the first term (in parentheses), and (2) the effect of the change in quantity itself. With an increase in the quantity, Equation 6.1 divides the marginal revenue from the increase in Q into the following:

1. 1 �P�Q : Q 2 term. An increase in the quantity sold requires a decrease in price. In other words, there must be a downward movement along the demand curve.

The amount of the decrease in price depends on the slope of the demand curve, ∆P∆Q. Because the slope of the demand curve is negative, the term 1 ∆P∆Q * Q2 is negative. This term captures the effect of the lower price decreasing the reve-

nue collected from all the initial units previously sold—that is, from Q units. 2. P term. An increase in the quantity directly increases the total revenue. This

increase in the total revenue equals P * ΔQ, so a one-unit increase in the quantity raises the total revenue by P. The second term, P, captures this effect.

1 We prove this result in Section 6.A of the Appendix at the end of this chapter.

2 Using the definition of total revenue 1P * Q2 in the equation for marginal revenue gives MR = ∆TR∆Q = ∆ 1P * Q2

∆Q = 1∆P * Q2 + 1P * ∆Q2

∆Q = 1 ∆P∆Q * Q2 + P.

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6.1 A Monopoly Market  233

You can rearrange Equation 6.1 into a form that is more valuable for managers and managerial decision making3:

MR = P * a1 - 1 e b = P * a e - 1

e b 6.2

Equation 6.2 shows important relationships among the firm’s marginal revenue, price, and price elasticity of demand for its product that hold for any demand curve4. As a manager, you can use these relationships to help make decisions. For example, if you know or have an estimate of your firm’s price elasticity of demand (recall that this can change at different points on a demand curve), you can use it along with the price of the product to calculate the marginal revenue of a unit. In addition to its managerial use, Equation 6.2 has two significant implications for your study of monopoly:

1. The equality MR = P * 11 - 1e2 shows that unless 1e equals zero, marginal revenue is less than the price, in which case the marginal revenue curve lies below the

demand curve. The amount by which the marginal revenue is less than the price depends on e, the price elasticity of demand—the larger e, the larger 11 - 1e2 and therefore the closer MR to P.

2. The equality MR = P * 1e - 1e 2 demonstrates that the marginal revenue is

• Positive when the price elasticity of demand exceeds 1 because 1e - 1e 2 is positive. • Zero when the price elasticity of demand equals 1 because 1e - 1e 2 is zero. • Negative when the price elasticity of demand is less than 1 because 1e - 1e 2 is

negative.

Using the definitions of elastic, unit-elastic, and inelastic demand from Chapter 3 (see Section 3.4), these results mean that for any demand curve, the marginal revenue is positive when demand is elastic, zero when demand is unit elastic, and negative when demand is inelastic.

3 In Section 6.B in the Appendix at the end of this chapter, we prove Equation 6.2 using calculus. 4 The price elasticity of demand equals the percentage change in the quantity demanded caused by a one- percentage-point change in the price. The more substitutes for a product, the stronger the response to a change in the price, which means the larger the elasticity. Chapter 3 defines and discusses elasticity in more detail.

The Relationship Among the Price Elasticity of Demand, Marginal Revenue, and Price

Use the relationship among the price elasticity of demand, marginal revenue, and price to answer the following questions.

a. If the price elasticity of demand is 3 and the price is $100, what is the marginal revenue?

b. If the price elasticity of demand is 1 and the price is $100, what is the marginal revenue?

c. If the price elasticity of demand is 0.4 and the price is $100, what is the marginal revenue?

d. If the price elasticity of demand is 1.1 and the marginal revenue is $100, what is the price?

SOLVED PROBLEM

(Continues)

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234  CHAPTER 6 Monopoly and Monopolistic Competition

6.2 Monopoly Profit Maximization Learning Objective 6.2 Discuss how managers of a monopoly can determine the quantity and price that maximize profit and how they compare to those of a perfectly competitive firm.

Now that you understand the basics of a monopoly market, you are ready to investi- gate how managers of a monopoly can maximize their profit. Then you will learn how the profit-maximizing price and quantity compare for monopoly markets and perfectly competitive markets.

Profit Maximization for a Monopoly In Chapter 5, marginal analysis demonstrated that managers of a perfectly competitive firm maximize profit by producing the amount of output that sets the marginal revenue (MR) equal to the marginal cost (MC). Marginal analysis and the profit-maximization rule can help managers of a monopoly maximize their firm’s profit as well.

Profit Maximization for a Monopoly: Marginal Analysis The key to maximizing profit in any firm, whether it is a monopoly or one of thve many firms in a perfectly competitive market, is to produce all of the profitable units and none of the unprofitable units. Using this fundamental insight, in Chapter 5 you learned that marginal analysis led to the profit-maximization rule: Produce the quantity for which MR = MC, and then set the highest price that sells the quantity produced. Managers of monopolies can use the same profit-maximization rule to maximize their firm’s profit.

To use marginal analysis and the profit-maximization rule, you compare the mar- ginal revenue of a unit to its marginal cost. Continuing the example with you as a manager of a pharmaceutical company, Figure 6.3 includes the marginal cost curve for your firm’s drug along with the demand and marginal revenue curves that appear in Figure 6.2. As Figure 6.3 shows, the marginal revenue of all quantities up to 150,000 exceeds their marginal cost. Following the profit-maximization rule, you produce all of these units. The figure also shows that the marginal revenue of all quantities beyond 150,000 is less than their marginal cost. So you produce none of these units. The conclusion from this analysis is identical to that for a perfectly competitive firm: To maximize profit, your firm produces the quantity of output for which the marginal revenue equals the marginal cost 1MR = MC or MR - MC = 02.

You must now set a price. Monopolies, and other firms with market power, have control over the price they set. In this chapter, assume that the same price is set for all units sold and for all buyers. In Chapter 10, you will learn about other pricing strategies that can lead to increased profit.

Answer All of the answers require using the equation MR = P * 1e - 1e 2 to quantify the relationship among the marginal revenue, price, and price elasticity of demand.

a. MR = $100 * 13 - 13 2 = $66.67. When e 7 1, the marginal revenue is positive. b. MR = $100 * 11 - 11 2 = $0. When e = 1, the marginal revenue equals zero. c. MR = $100 * 10.4 - 10.4 2 = -$150. When e 6 1, the marginal revenue is negative. d. Rearrange the equation MR = P * 1e - 1e 2 to MR * 1 ee - 12 = P , so P = $100 * 1 1.11.1 - 12 = $1,100.

SOLVED PROBLEM (continued )

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6.2 Monopoly Profit Maximization  235

According to the profit-maximization rule, the price is determined from the demand curve as the highest price that sells the quantity produced. In Figure 6.3, the demand curve shows that the highest price buyers are willing to pay for 150,000 treatments is $60,000 per treatment, so $60,000 is the profit-maximizing price.

Markup Equation In Figure 6.3, the price of a treatment, $60,000, is twice the marginal cost of $30,000. The factor by which the price is higher than the marginal cost, PMC, or 2.0 in this case, is the markup. You can use the relationship among the price elasticity of demand, price, and marginal revenue shown in Equation 6.2, MR = P * 1 e - 1e 2 , to determine the role the price elasticity of demand plays in determining the profit-maximizing price and markup. When the managers maximize profit, MR = MC. Accordingly, substi- tuting MC for MR, Equation 6.2 becomes

MC = P * a e - 1 e

b 6.3

Rearranging Equation 6.3 illustrates two key results. First, dividing both sides of Equation 6.3 by e - 1e shows the role the price elasticity of demand plays in setting the profit-maximizing price:

P = MC * a e e - 1

b 6.4

Second, dividing both sides of Equation 6.4 by MC gives the markup equation, the equation showing the markup of the price over marginal cost:

P

MC = a e

e - 1 b = 1 + a 1

e - 1 b 6.5

Markup equation The equation showing the markup of the price over marginal cost: PMC =

e e - 1.

D

MR

MC

Price and cost (thousands of dollars per treatment)

Quantity (thousands of treatments per year)

$90

$0

$10

$20

35030025020015010050

$30

$40

$50

$60

$70

$80

2$20

2$10

Profit-maximizing price

Profit- maximizing quantity

MR . MC MR , MC

Figure 6.3 Profit Maximization for a Monopoly

The quantity that sets MR = MC (150,000 treatments) maximizes your company’s profit. This quantity produces all of the profitable units (those for which MR 7 MC ) and none of the unprofitable units (those for which MR 6 MC ). The demand curve shows that the profit-maximizing price is $60,000 per treatment, the highest price demanders will pay for 150,000 treatments.

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236  CHAPTER 6 Monopoly and Monopolistic Competition

Equation 6.4 shows how to use your estimates of the marginal cost and price elasticity of demand to set the profit-maximizing price, and Equation 6.5 shows how the markup depends on the price elasticity of demand. The equations also show a key qualitative result: The smaller the price elasticity of demand, the higher the price and the larger the markup. Figure 6.4 illustrates these general results. In Figure 6.4(a), at the profit-maximizing quantity on the demand curve (point A), the price elasticity of demand is 3.0.5 When the price elasticity of demand equals 3, the markup is 33 - 1, or 1.5, so the price is 1.5 times the marginal cost, $30. In Figure 6.4(b), however, the price elasticity of demand at the profit-maximizing point (point B) is smaller, 1.67. Consequently, the markup, 1.671.67 - 1, or 2.5, is larger, so that the price, $50, is higher.

The intuition that a smaller price elasticity of demand leads to a higher price is as important as the actual formula. Recall from Chapter 3 that the fewer substitutes for a good, the smaller its price elasticity of demand. That observation combined with the markup equation means that the fewer the substitutes for a good, the higher the price a monopoly can charge. This intuition (and the quantitative result in Equation 6.4) explains why pharmaceutical companies that produce unique, lifesav- ing drugs are free to set sky-high prices for those drugs.

5 From Chapter 3, the price elasticity of demand along a linear demand curve is e = � b * 1P>Qd2 � , where b is the change in the quantity demanded from a $1 change in price. In Figure 6.4(a), b equals 40 units per dollar, so at point A the price elasticity of demand is � 40 * 1$30>4002 � = 3.0. In Figure 6.4(b), b equals 13.33 units per dollar, so at point B the price elasticity of demand is � 13.33 * 1$50>4002 � = 1.67.

Price and cost (dollars per unit)

Quantity (units per day)

$60

$10

1,000 1,200600 800200 400

$20

$30

$40

$50

0

D

MR

MC

A

Profit-maximizing price

Price and cost (dollars per unit)

Quantity (units per day)

$60

$10

1,000 1,200600 800200 400

$20

$30

$40

$50

0

DMR

MC

B

Profit-maximizing price

Figure 6.4 Markup and Elasticity

(a) Markup with Larger Elasticity (b) Markup with Smaller Elasticity To maximize profit, managers produce 400 units per day. The profit-maximizing markup of price over marginal cost is ee - 1. At point A on the demand curve, the price elasticity of demand 1e2 is 3.0, so the markup is 33 - 1 = 1.5. Consequently, the profit-maximizing price equals $20 * 1.5 = $30 per unit.

To maximize profit, managers produce 400 units per day. The profit-maximizing markup of price over marginal cost is ee - 1. At point B on the demand curve, the price elasticity of demand 1e2 is 1.67, so the markup is 1.671.67 - 1 = 2.5. Consequently, the profit- maximizing price equals $20 * 2.5 = $50 per unit.

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6.2 Monopoly Profit Maximization  237

Suppose that you are a manager in the pricing department of a tire-producing company like Michelin US. Your research department reports that the best esti- mate of the price elasticity of demand for your tires is 1.6 but that the elasticity might be as large as 1.8 or as small as 1.4. Your marginal cost is $100 per tire. What is the range of the profit-maximizing price for your product? What might you ask your research department to do next?

Answer Equation 6.4 shows that the profit-maximizing price equals MC * ee - 1. If the price

elasticity of demand is 1.8, then the price equals $100 * 1.81.8 - 1, or $225 per tire. If

the price elasticity of demand is 1.4, then the price equals $100 * 1.41.4 - 1, or $350 per tire. Consequently, your profit-maximizing price per tire ranges from $350 to only $225, a rather wide range. You might return to your research department and ask the analysts to try to tighten the range for the price elasticity of demand.

DECISION SNAPSHOT

Profit-Maximizing Range of Prices for Tires

Amount of Profit In Chapter 5, you learned that a perfectly competitive firm makes an economic profit if P 7 ATC, makes a competitive return if P = ATC, and incurs an economic loss if P 6 ATC. Thankfully, you do not need to memorize yet another rule because the same set of results holds true for monopoly firms. In fact, these relationships apply to any firm.

Figure 6.5 includes the average total cost curve (ATC) for your firm’s drug, assum- ing that it makes an economic profit. In the figure, the price ($60,000 per treatment) exceeds the average total cost ($40,000), which shows that your company is making an economic profit. The area of the green rectangle in Figure 6.5 is 1P - ATC2 * Q. As you learned in Chapter 5, this area equals the amount of the firm’s economic profit because it is the economic profit per unit 1P - ATC2 multiplied by the quantity sold (Q). In Figure 6.5, the economic profit is 1$60,000 - $40,0002 * 150,000 treat- ments, which comes out to $3 billion.

Figure 6.5 shows the monopoly is making an economic profit, so it would be easy to suppose that all monopolies make an economic profit. However, the fact that there is only one firm in the industry is no guarantee that a monopoly will make an economic profit, much less an exorbitant one. If production costs are high relative to demand, profits will be low, and economic losses may even occur. For instance, take the classic online failure, Pets.com. This pet-food delivery company was founded in 1998 and used a sock puppet dog in its advertising. Pets.com faced no competition in the market for home delivery of pet supplies, so it was effectively a monopoly. The company had both high costs—it offered free shipping for heavy products, such as dog food and cat litter, which were expensive to ship—and low demand—consumers tend to buy pet food and litter when they run out and therefore did not want to wait for delivery from Pets.com. Observers suggested that P 6 ATC for each item Pets.com shipped; that is, each bag of dog food and cat litter shipped increased Pets.com’s loss. Pets.com incurred a large economic loss and survived for approximately two years before it declared bankruptcy. What happened to the sock puppet dog remains a mystery.

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Shut-Down Rule for a Monopoly Pets.com ultimately closed. In Chapter 5, you learned the shut-down rule for a firm in a perfectly competitive market: The firm closes if total revenue is less than total variable cost and remains open if total revenue is greater than total variable cost. Equivalently, the firm closes if price is less than average variable cost 1P 6 AVC2 and remains open if price is greater than average variable cost 1P 7 AVC2. When does a monopoly close? It turns out that the same shut-down rule applies. If any firm cannot make enough revenue to cover its variable costs, which means P 6 AVC, the firm minimizes its loss by closing.

Long-Run Profit Maximization for a Monopoly Because there is only one firm in a monopoly market, when the firm is in long-run equilibrium, the market is also in long-run equilibrium. Recall from Chapter 5 that when firms in a perfectly competitive market are making an economic profit, entry occurs, and in the long run, the entry drives the firms’ economic profit to zero. In a monopoly, however, the presence of insurmountable barriers to entry prevents entry by new firms, so the firm can continue to make an economic profit. Even so, the managers may still need to adjust the scale of production to minimize the firm’s long-run average cost and increase its economic profit even more.

Figure 6.6 shows the long-run outcome for your pharmaceutical firm after you have changed the scale of production of your firm’s drug by adjusting the firm’s inputs. The managers are maximizing long-run profit by producing so that marginal revenue equals long-run marginal cost, or MR = LMC. In the figure, the firm maxi- mizes its long-run profit by producing 175,000 treatments and setting a price of $55,000 per treatment. The company is producing its profit-maximizing quantity, 175,000, at the lowest possible average cost, $15,000, and is making the largest possi- ble economic profit, $7 billion. As long as no other firm can enter the market, the economic profit can persist.

D

MR

MC ATC

Price and cost (thousands of dollars per treatment)

Quantity (thousands of treatments per year)

$90

$0

$10

$20

35030025020015010050

$30

$40

$50

$60

$70

$80

2$20

2$10

Economic profit, $3 billion

Figure 6.5 Economic Profit for a Monopoly

Your firm is making an economic profit because its price, $60,000 per treatment, exceeds its average total cost, $40,000 per treatment. The amount of the economic profit equals the area of the green rectangle.

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6.2 Monopoly Profit Maximization  239

Comparing Perfect Competition and Monopoly You have learned that the profit-maximization rule and the shut-down rule apply to both monopoly firms and firms in perfectly competitive markets. How does the equilib- rium in a perfectly competitive market compare to the equilibrium in a monopoly market? Understanding the differences is essential for the formulation of public policy, such as antitrust policy (presented in Chapter 9).

Comparing a Perfectly Competitive Market and a Monopoly Market Although the goal of managers of both monopolies and firms in perfectly competi- tive markets is to maximize profit, their impact on society differs dramatically. As you learned in Section 2.4, perfectly competitive markets maximize society’s total surplus of benefit over cost. Figure 6.7(a) illustrates the maple syrup market first presented in Chapter 5. In a perfectly competitive market for maple syrup, the equi- librium quantity is 12 million gallons, and the price is $30 per gallon. In this perfectly competitive market, the total surplus of benefit over cost to society is equal to the area of the green triangle.6 The area equals the largest possible amount of total sur- plus, which is why economists generally favor perfectly competitive markets.

Suppose that one firm becomes a monopoly by buying all of the others and somehow manages to create a barrier to entry that keeps any other firm from enter- ing the market. Instead of having many separate firms under independent owner- ship and control, there is now a single firm with many separate plants or production

D

MR

LMC LAC

Price and cost (thousands of dollars per treatment)

Quantity (thousands of treatments per year)

$90

$0

$10

$20

35030025020015010050

$30

$40

$50

$60

$70

$80

2$20

2$10

Economic profit, $7 billion

Figure 6.6 Long-Run Profit Maximization

Your firm is maximizing its long-run economic profit because its marginal revenue equals its long- run marginal cost, MR = LMC . You are producing the profit- maximizing quantity, 175,000 treatments, at the lowest average cost for this quantity, $15,000 per treatment. The price is $55,000 per treatment so the economic profit equals the area of the green rectangle, $7 billion.

6 Applied to the maple syrup market, Chapter 2 explained that for any gallon of maple syrup, the maxi- mum price a consumer is willing to pay, measured by the demand curve, is the marginal benefit from that gallon. The supply curve measures the marginal cost of any gallon. So the difference between the demand curve and the supply curve equals society’s surplus of marginal benefit over marginal cost for each gallon of syrup. The total surplus is the sum of the surpluses of all gallons produced, 12 million gallons in Figure 6.7(a).

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240  CHAPTER 6 Monopoly and Monopolistic Competition

facilities. Figure 6.7(b) shows this situation in the monopoly market. The market demand curve (D) is the monopoly firm’s demand curve. Associated with this demand curve is the monopoly’s marginal revenue curve (MR). This marginal reve- nue curve was present when the market was competitive, but because it was irrele- vant, it was omitted from Figure 6.7(a). Now, however, the MR curve matters. Because the monopolist’s managers equate marginal revenue and marginal cost to determine the profit-maximizing output, you also need the marginal cost curve. As you learned in Chapter 5, the competitive supply curve is the sum of the individual competitive firms’ supply curves, and each individual firm’s supply curve is that firm’s marginal cost curve. Once these firms are brought under single ownership as a monopoly, the sum of the individual firms’ marginal cost curves becomes the monopoly’s marginal cost curve, MC in Figure 6.7(b). The monopoly’s managers now use marginal analysis to maximize their profit by producing 8 million gallons and setting a price of $40 per gallon.

You can see that, when compared to a perfectly competitive market, the monopoly sets a higher price—$40 per gallon versus $30—and produces a smaller quantity— 8 million gallons versus 12 million. The higher price means that the firm’s owners are better off at the expense of the consumers. Economists have traditionally had lit- tle to say about such reallocations between groups because both producers and con- sumers are members of society and everyone counts. Rather, economists’ main objection to monopoly stems from the resulting misallocation of resources, which can be seen by considering the total surplus to society. In Figure 6.7(b), all of the 8 million gallons of syrup the monopoly produces have a surplus to society because

Price (dollars per gallon of maple syrup)

Quantity (millions of gallons of maple syrup per year)

$60

$10

20 2412 164 8

$20

$30

$40

$50

0

D

SEquilibrium price

Equilibrium quantity

Total surplus

Price (dollars per gallon of maple syrup)

Quantity (millions of gallons of maple syrup per year)

$60

$10

20 2412 164 8

$20

$30

$40

$50

0

D

MC

MR

Profit-maximizing price

Profit-maximizing quantity

Total surplus Deadweight

loss

Figure 6.7 Comparing the Total Surplus to Society in a Competitive Market and a Monopoly Market

(a) Total Surplus in a Competitive Market (b) Total Surplus in a Monopoly Market The equilibrium quantity is 12 million gallons, and the equilibrium price is $30 per gallon. Society’s total surplus of benefit over cost is equal to the area between the demand and supply curves (the area of the green triangle). This is the maximum possible amount of surplus.

The managers of the monopoly maximize profit by producing the quantity that sets MR equal to MC, 8 million gallons, and setting a price of $40 per gallon. With this price and quantity, society’s total surplus equals the area of the green trapezoid. This surplus is less than that shown in Figure 6.7(a) for a competitive market because of the deadweight loss, which is equal to the area of the red triangle.

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6.2 Monopoly Profit Maximization  241

their marginal benefit exceeds their marginal cost. The total surplus for these 8 million gallons is the sum of all the individual surpluses, which equals the area of the green trapezoid in Figure 6.7(b).

Comparing the green triangle in Figure 6.7(a) to the green trapezoid in Figure 6.7(b), you can see that society’s total surplus is less with the monopoly. The difference in total surplus to society is the deadweight loss. The deadweight loss is society’s loss of total surplus from producing less than or more than the efficient quantity, 12 million gallons. In Figure 6.7(b), where the monopoly produces less than the efficient quantity, the deadweight loss from the monopoly is equal to the area of the red triangle, $40 million per year. The deadweight loss is the funda- mental economic social harm created by monopoly. The damage a monopoly causes is the production of too little output and the decrease in the number of employees and other resources involved in producing the product. Neither the economic profit nor the high monopoly price is the social problem. Instead, these are symp- toms of the real problem, which from the social perspective is the misallocation of resources and the resulting deadweight loss. The deadweight loss from monopoly is the basis for the nation’s antitrust laws, but aside from this rationale, it has no direct relevance to managers.

Comparing a Perfectly Competitive Firm and a Monopoly Firm You know that managers of both perfectly competitive firms and monopoly firms follow the same profit-maximization rule: Produce the quantity that sets marginal revenue equal to marginal cost 1MR = MC2, and charge the highest price possible that still allows the firm to sell the quantity produced. This similarity, however, masks the differ- ences between monopolies and perfectly competitive firms summarized in Table 6.2.

Barriers to entry are significant to a firm and its managers because they enable a monopoly to make a long-run economic profit. Let’s turn to a more detailed exam- ination of this important concept.

Barriers to Entry As you learned in Chapter 5, a barrier to entry is any factor that makes it difficult for new firms to enter a market. Examples include legal barriers (such as patents, trade secrets, copyrights, and trademarks), control of an essential raw material, the exis- tence of overwhelming economies of scale, government control of entry, sunk costs, and—possibly—advertising.

Deadweight loss The loss in total surplus from producing less than or more than the efficient quantity.

Table 6.2 Comparing a Perfectly Competitive Firm to a Monopoly

Perfectly Competitive Firm Monopoly

Amount of markup? Zero; the price equals marginal cost

Positive; the amount of the markup of the price over marginal cost depends on the price elasticity of demand

Can make a short-run economic profit? Yes Yes

Can make a long-run economic profit? No

Yes; some type of barrier to entry protects the economic profit from entry by new firms

Always produces at the minimum average total cost in the long run? Yes

No; the firm might produce at the minimum average total cost but does not necessarily do so

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242  CHAPTER 6 Monopoly and Monopolistic Competition

Patents, Trade Secrets, Copyrights, and Trademarks Chapter 15 presents a more complete discussion of patents, trade secrets, copyrights, and trademarks. This chapter focuses on how they serve as legal barriers to entry, how they provide their owners some legal protection from infringement, and the different types of products they protect.

• Patents. Patents protect products or specific production processes by giving the owner the exclusive right to produce a certain commodity or to use a spe- cific production process for a 20-year period that begins at the time the pat- ent application is filed. Granting a patent ensures that no competitor can legally copy the inventor’s creation during the life of the patent. Although it affords legal protection against blatant copying, a patent does not provide absolute protection. The market power from a patent is limited because pat- ents are often narrowly defined, which may allow other firms to approximate closely the process or product without infringing. For example, Merck pat- ented the first statin (a cholesterol-lowering drug), Mevacor, and began mar- keting it in the United States in 1987. Ultimately, however, other companies began selling six other, closely related statins. After Mevacor enjoyed a U.S. market share of 100 percent for the first three years, other companies started selling their statins, and its market share fell to less than 15 percent within seven years.

• Trade secrets. The fact that patents are often narrowly defined may leave man- agers concerned that a patent on a product or production process will not pre- vent competitors from selling or using a closely related product. For this reason, some managers opt to keep their production process a trade secret. KFC’s “secret recipe of eleven herbs and spices” is a trade secret. Less tasty examples include Google’s search algorithms and the ingredients of the WD-40 Company’s name- sake product, WD-40.

• Copyrights. Copyright law gives legal protection to works of authorship, such as movies, songs, and books. This book is copyrighted, as is the film Avatar, which to date has grossed $2.7 billion. The length of copyright protec- tion varies. For works produced after January 1, 1978, the copyright protec- tion lasts for the life of the creator plus an additional 70 years, but the copyright for a work-for-hire (such as a pamphlet) is typically 95 years from the first publication.

• Trademarks. Trademarks protect brand names, symbols, or designs that iden- tify the source of the product. For example, The Walt Disney Company has trademarked Mickey Mouse, and Nike, Inc., has trademarked its “Swoosh” logo. No one else can use Mickey Mouse or the “Swoosh” design without per- mission from Disney or Nike, respectively. In the United States, trademark owners are protected for 10 years, but they can renew their trademarks indefinitely.

The economic value of patent, trade secret, copyright, or trademark protection depends on the value of the protected item in the marketplace. For example, a patent on a solar-powered mousetrap would not be worth much because few people want to buy them. Similarly, copyright protection on a film about famous economists that no one wants to see is worthless. In contrast, a patent on a cure for cancer would be worth a fortune. Patents, trade secrets, copyrights, and trademarks offer legal pro- tection to a monopoly and protect its economic profit by preventing the entry of copycat producers into the market.

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6.2 Monopoly Profit Maximization  243

Control of an Essential Raw Material It should be obvious that if one firm controls the supply of an essential input, other firms will be unable to compete. The classic example of this situation is the alleged control of bauxite reserves in the 1930s and 1940s by the Aluminum Company of America (Alcoa). Through purchases and long-term contracts, Alcoa was purported to have preempted control of the available supplies of bauxite ore, the ore used to produce aluminum. Through that control, Alcoa allegedly prevented the entry of other firms into the U.S. aluminum market. More recently, in 1987, De Beers had approximately a 90 percent share of the gem diamond market because it controlled virtually all of the world’s raw gem diamonds.

In some cases, it may be possible to restrict the availability of the raw material. For example, New York’s ban on hydraulic fracturing (fracking) has limited the sup- ply of natural gas from the Marcellus Shale. Although this ban does not create a monopoly producer of natural gas, it does protect natural gas firms from entry by competitors located in New York.

Ultimately, it is difficult for managers to preserve their grasp on an essential raw material. For example, Alcoa lost its alleged death grip on bauxite after the U.S. gov- ernment financed a vast expansion of U.S. aluminum capacity during World War II and then sold its interests to competing firms after the war. De Beers also failed to protect its positions and fell prey to competition from new sources of raw diamonds that were not under the firm’s control: Today, De Beers’ market share is under 40 percent.

Economies of Scale Sometimes new firms do not enter the industry because they would be at a sub- stantial cost disadvantage to the larger established firm. Natural monopolies, such as water, sewage, electricity, and natural gas utilities, are extreme examples. Natural monopolies have massive economies of scale, so that as their produc- tion increases, their long-run average cost constantly falls throughout the range of demand. Recall from Chapter 4 that economies of scale refers to the region of the long-run average cost curve where the long-run average cost falls as produc- tion increases; it is the downward-sloping segment of the curve. A natural monopoly’s economies of scale are so extensive that the firm’s minimum efficient scale—the quantity at which the long-run average cost first reaches its mini- mum—exceeds the quantity customers demand. Figure 6.8 illustrates this situa- tion. Suppose that a firm like Georgia Power, an electric utility operating out of Atlanta, reaches its minimum efficient scale of 60 billion kilowatt hours per year at a cost of 6¢, while at the price of 6¢, customers demand only 47 billion kilowatt hours per year.

The interaction between the demand for the product and the technological conditions that require large scale for efficient, low-cost production limits the number of firms in the market. For example, Figure 6.8 shows that this electric utility company’s managers maximize profit by producing 20 billion kilowatt hours per year—the quantity that sets the marginal revenue (MR) equal to the long-run marginal cost (LMC)—and setting a price of 14¢ per kilowatt hour—the highest price consumers will pay for 20 billion kilowatt hours per year. The firm’s average cost of producing 20 billion kilowatts is 10¢ per kilowatt hour. If another firm enters the market, it will be unable to immediately attain the economies of scale that this firm enjoys. Suppose that the new firm has the same long-run aver- age cost as this one but produces only one-half of the output, or 10 billion kilowatt hours. Even though the new firm’s scale of production is remarkably large, the

Natural monopoly A firm with economies of scale so large that as its production increases, its long-run average cost constantly falls throughout the range of demand.

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244  CHAPTER 6 Monopoly and Monopolistic Competition

new entrant still has higher costs. The new firm’s lowest possible average cost of producing 10 billion kilowatt hours is 15¢ per kilowatt hour, much higher than the existing firm’s average cost of 10¢ per kilowatt hour. Indeed, the 15¢-per-kilowatt- hour cost is above the existing firm’s monopoly price of 14¢ per kilowatt hour. If the new firm tried to match this price, it would incur a significant economic loss. The prospect of such an economic loss will deter many—likely all—other firms from entering the market. The profound economies of scale operate as a barrier to entry and create a natural monopoly.

As Figure 6.8 shows, because the minimum efficient scale is larger than the quantity demanded, the long-run average cost curve (LAC) continues to decrease even after it crosses the demand curve (D). This result poses a problem for society because it means that one firm can produce the quantity demanded in the market at a lower total cost than could two or more firms. For example, with one firm in the market, the electric utility can produce 20 billion kilowatt hours at an average cost of 10¢ per kilowatt hour, for a total cost of 10¢ * 20 billion or $2.0 billion. If two equal-sized firms produced the 20 billion kilowatt hours, each would produce 10 billion kilowatt hours at an average cost of 15¢ per kilowatt hour. Each firm’s total cost would be 15¢ * 10 billion = $1.5 billion. The total cost of producing 20 billion kilowatt hours in a market with two firms is $3.0 billion 1$1.5 billion + $1.5 billion2, higher than the total cost of the single firm. Why is the total cost lower with only one firm? With only one firm distributing electricity in a city, only one set of poles and wires must be erected, but if two (or more) companies distribute power, two (or more) sets of poles and wires are necessary which drastically increases the total cost of distributing power.

The lower total cost with one firm makes it socially desirable to have a single firm supply the entire market. As a monopoly, however, the firm produces less than a competitive market would, thereby creating a deadweight loss. Because of this

D MR

LMC

LAC

Price and cost (cents per kilowatt hour)

Quantity (billions of kilowatt hours per year)

18¢

20¢

0

2¢

4¢

70605040302010

6¢

8¢

10¢

12¢

14¢

16¢

Profit-maximizing price

Profit-maximizing quantity

Figure 6.8 A Natural Monopoly

This electric utility company has such extensive economies of scale that its minimum efficient scale of 60 billion kilowatt hours, with a long-run average cost of 6¢, exceeds the quantity demanded of 47 billion kilowatt hours at a price of 6¢. To maximize profit, managers produce 20 billion kilowatt hours because that is the quantity at which the marginal revenue equals the long-run marginal cost. The profit-maximizing price is 14¢ per kilowatt hour and its average cost is 10¢ per kilowatt hour. If another firm entered the market, the new firm’s scale of production would be less than 20 billion kilowatt hours. The smaller scale of production places the new firm at a severe competitive disadvantage because its average cost would be much higher than this firm’s average cost.

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6.2 Monopoly Profit Maximization  245

social tension—lower costs versus deadweight loss—state governments generally regulate natural monopolies. While all firms face some government regulation, the magnitude of the regulation imposed on natural monopolies, such as utilities, is con- siderably higher. In particular, the regulators (state public utility commissions) effec- tively determine what price the firm can charge and require production of the quantity consumers demand. In exchange, the government grants the firm a legal franchise that prevents other firms from entering the market. The regulatory goal is to preserve the social benefits of the lower costs while avoiding the social drawback of the deadweight loss. The type of regulation used and the question of whether the regulators achieve their admirable goals are best described in courses dealing exclu- sively with government regulation of business.

The overwhelming economies of scale relative to demand enjoyed by a natural monopoly make for a highly effective barrier to entry. To serve as a barrier to entry, however, economies of scale do not need to be so extreme. The presence of econo- mies of scale that are merely substantial also creates an entry barrier. In Figure 6.9, the managers of a monopoly producer of eyeglasses maximize profit by producing 300 million pairs of eyeglasses per year and setting a price of $250 per pair. The firm makes an economic profit because the price ($250) exceeds the long-run average cost ($150). If another firm enters the market and immediately also produces 300 million pairs of eyeglasses, the total quantity produced by the two firms is 600 million. The demand curve shows that in this case the price falls to $100 per pair. Both firms would incur an economic loss. More generally, an entrant that produces a substantial quantity in order to gain economies of scale so it can successfully com- pete causes a large decrease in price and creates the possibility of an economic loss. The risk of an economic loss deters entry into the market even though the firm already in the market is making an economic profit. On the other hand, an entrant that produces only a small quantity does not lower the price significantly but has

D MR

LMC

LAC

Price and cost (dollars per pair of eyeglasses)

Quantity (millions of pairs of eyeglasses per year)

$350

$400

0 700600500400300200100

$50

$100

$150

$200

$250

$300

Figure 6.9 Economies of Scale as a Barrier to Entry

The firm maximizes its profit by producing 300 million pairs of eyeglasses per year and setting a price of $250 per pair. If a new firm enters the market and, in order to gain economies of scale, also produces 300 million pairs, the total market quantity becomes 600 million pairs. The demand curve shows that at this quantity the price falls to $100 per pair so that both firms incur economic losses.

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246  CHAPTER 6 Monopoly and Monopolistic Competition

higher costs because it does not gain any economies of scale. So the new entrant (again) faces the possibility of an economic loss. Once again, the risk of an economic loss may be enough to prevent entry.

Government Control of Entry The government controls market entry in a variety of industries. The agency that exercises jurisdiction can confer market power on a firm, at least locally, simply by restricting or prohibiting the entry of competing firms, as in the electric utility exam- ple. Industries in which the government regulates entry include banking, television and radio broadcasting, and hospitals. In other markets, such as that for sugar, gov- ernment tariff and quota restrictions mean that firms need government approval to import sugar. None of these markets is strictly a monopoly because the firms in them face at least some competition, but the government limitations often create substan- tial barriers to entry.

In other circumstances, government regulations do not prohibit entry but instead impose requirements that must be met before entry is allowed. Certification and licensing are examples. At the individual level, physicians, nurses, and lawyers must pass qualifying exams before they are allowed to practice. So, too, must hair stylists, interior designers, and greenhouse managers. Many people will agree that requiring physicians, nurses, and lawyers to pass qualifying exams is reasonable but will doubt the validity of the similar requirements imposed on people who cut hair, design home interiors, and oversee plant greenhouses. Clearly, these professions are not monopolies, but the licensing requirements serve as barriers to entry and boost the salaries earned by those in these professions.

Sunk Costs Over the years, the economics literature has pointed to the existence of substantial sunk costs from entering a market as a barrier to entry. As you learned in Chapter 1, sunk costs are costs that cannot be recovered because they were paid or incurred in the past. Many of the costs necessary to enter a market become sunk because they cannot be recouped upon exit. For example, when the managers at Alamo Drafthouse Cinema open a new theater, they must purchase specialized digital projectors. Say that these cost $100,000 per screen, so opening an 8-plex theater requires spending $800,000 on projectors. In addition, the owners must spend a sizable amount on advertising to alert potential customers to the theater’s open- ing. If the theater fails, the resale price of the projectors is substantially less than $800,000, and all of the funds spent on advertising are irretrievable. Because sunk costs are lost if the entering firm later exits the industry, the presence of large sunk costs increases the financial risk of entering the market, thereby creating a barrier to entry. Clearly, the greater the sunk costs of entry, the higher the barrier to entry.

Advertising As noted above, advertising can increase the sunk cost of entering a market, but economists have debated its other effects on market entry. On the one hand, adver- tising by the incumbent producers can create brand loyalty that new entrants must overcome. On the other hand, advertising by the new entrant can make consumers aware of the new product’s attributes and price, facilitating profitable entry into the market. So, in addition to creating a sunk cost, advertising can both discourage and encourage market entry. Because its net effect varies from one industry to another, the status of advertising as a barrier to entry is unclear.

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6.3 Dominant Firm  247

Merck’s Profit-Maximizing Price, Quantity, and Economic Profit

The following figure shows hypothetical demand, marginal revenue, marginal cost, and average total cost curves for Januvia, a patented medicine made by Merck & Company to help treat diabetes. Januvia has a very large market share in its market (that for DPP-4 inhibitors) because of its safety profile, so for simplicity we assume it is a monopoly. Use the figure to answer the following questions.

a. What is the profit-maximizing quantity and price? What is the average total cost of the profit-maximizing quantity?

b. Is Merck & Company making an economic profit or incurring an economic loss? How much is the economic profit or loss?

Answer

a. The profit-maximizing quantity is the quantity that sets MR = MC , which is 200 million pills per month. The profit-maximizing price is the highest price the managers can set and sell 200 million pills, which from the demand curve in the figure is $5 per pill. The average total cost at the quantity of 200 million is $2 per pill.

b. Merck & Company is making an economic profit because P 7 ATC . The economic profit equals 1P - ATC2 * Q, or 1$5 - $22 * 200 million = $600 million.

SOLVED PROBLEM

D MR

MC

ATC

Price and cost (dollars per pill)

Quantity (millions of pills per month)

$7

$9

$8

0 400350300250200100 15050

$1

$2

$3

$4

$5

$6

6.3 Dominant Firm Learning Objective 6.3 Describe how managers of a dominant firm determine the quantity and price that maximize profit.

Outside the economics classroom, a single-firm monopoly is a relatively rare sight. There are, however, many markets containing multiple firms in which one firm is substantially larger than the others. Take the corn chip market. Frito-Lay, a division

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248  CHAPTER 6 Monopoly and Monopolistic Competition

of PepsiCo, controls about 76 percent of the corn chip market in the United States. General Mills is the next largest company. It produces Bugles, which has about a 12 percent market share. The market also includes a number of small, regional pro- ducers, each with market shares smaller than 3 percent. In this market structure, Frito-Lay is considered a dominant firm, and the other producers are the competi- tive fringe. A dominant firm, the one large firm in a market that includes many other, smaller competing firms, has the lion’s share of the market. The competitive fringe is a collective term for the many smaller firms in the market competing with the one large, dominant firm.

The dominant firm model assumes that the dominant firm acts as a monopoly, using its demand curve to maximize its profit, while the firms in the competitive fringe act as perfectly competitive firms, maximizing their profit by taking the mar- ket price—the dominant firm’s price—as given.

Dominant Firm’s Profit Maximization Figure 6.10 is a hypothetical depiction of the corn chip market. Start by supposing that Frito-Lay has a monopoly in this market. Using the profit-maximization rule, Frito-Lay’s managers produce 140,000 tons of corn chips and set a price of $2.05 per pound.

In reality, Frito-Lay is a dominant firm rather than a monopoly, so its managers face the challenge of taking the collective supply response of the competitive fringe into account when making their production and pricing decisions.

Dominant firm The one large firm in a market that includes many other, smaller competing firms.

Competitive fringe The many smaller firms in a market that includes a dominant firm.

D

MR

MC

Price and cost (dollars per pound of corn chips)

Quantity (thousands of tons of corn chips per year)

$2.25

$2.50

0

$0.25

$0.50

35030025020015010050

$0.75

$1.00

$1.25

$1.50

$1.75

$2.00

Monopoly profit- maximizing price

Monopoly profit- maximizing quantity

Figure 6.10 A Monopoly and the Market Demand Curve

The graph shows the hypothetical market demand curve (D), the marginal revenue curve (MR), and marginal cost curve (MC) for Frito-Lay. If Frito-Lay was a monopoly, its managers would maximize profit by producing 140,000 tons of corn chips and setting a price of $2.05 per pound.

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6.3 Dominant Firm  249

Residual Demand In the more realistic case of Frito-Lay as a dominant firm, the competitive fringe affects the demand for Frito-Lay’s corn chips. Figure 6.11 is a hypothetical depiction of this effect. The graph shows the market demand curve (D) and the supply curve of the competitive fringe (SCF). The demand that Frito-Lay faces does not equal the market demand. Instead, it is the market demand minus the quantity supplied by the competitive fringe, referred to as the residual demand. In Figure 6.11, the resid- ual demand is RD. To see how the residual demand is constructed, take the price of $2.00 per pound. At this price, the market demand curve (D) shows that the total quantity demanded is 150,000 tons of chips, and the competitive fringe supply curve (SCF) shows that the fringe firms produce 100,000 tons. Frito-Lay’s residual demand is the quantity left over for consumers to demand from Frito-Lay and equals 150,000 - 100,000, or 50,000 tons. Consequently, at a price of $2.00 per pound, Frito-Lay’s residual demand is 50,000 tons. The rest of the residual demand is deter- mined similarly. Therefore, the dominant firm’s demand curve (D) has two parts: It is the residual demand curve (RD) until it reaches the price at which it intersects the market demand curve (D). After it reaches this point, the dominant firm’s demand curve is identical to the market demand curve because after this point the com- petitive fringe’s supply curve shows that its production is zero. Figure 6.12 illus- trates the residual demand curve more clearly (without the irrelevant upper part of the market demand curve).

The marginal revenue curve for the dominant firm also has two separate parts. The top part is the marginal revenue curve that corresponds to the residual demand curve—the light green line labeled RMR in Figure 6.12. At the quantity where the

Residual demand The market demand minus the quantity produced by the competitive fringe.

D

RD

SCF

Price and cost (dollars per pound of corn chips)

Quantity (thousands of tons of corn chips per year)

$2.25

$2.50

0

$0.25

$0.50

35030025020015010050

$0.75

$1.00

$1.25

$1.50

$1.75

$2.00

Figure 6.11 Residual Demand Curve

The graph shows the hypothetical market demand curve (D) for corn chips. The dominant firm, Frito- Lay, faces the residual demand curve, which is the market demand minus the quantity supplied by the small, competitive fringe firms. For example, at the price of $1.75 per pound of corn chips, the supply curve of the competitive fringe (SCF) shows that these firms produce 50,000 tons of chips. At this price, the total quantity demanded is 200,000 tons of chips, so Frito-Lay’s residual demand is 200,000 minus 50,000, or 150,000 tons of chips. The remainder of Frito-Lay’s residual demand is derived similarly. Frito-Lay’s demand curve is the light blue residual demand curve (RD) until it intersects the market demand curve (D), after which Frito-Lay’s demand curve becomes the same as the dark blue market demand curve.

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250  CHAPTER 6 Monopoly and Monopolistic Competition

residual demand curve merges into the market demand curve, 250,000 tons, the dominant firm’s marginal revenue curve drops downward and becomes the same as the market marginal revenue curve, the dark green line labeled MR.

To maximize profit, Frito-Lay’s managers use the residual demand curve (RD) and residual marginal revenue curve (RMR) because they represent the demand and the marginal revenue for their chips, respectively. Frito-Lay produces the quantity that sets its residual marginal revenue equal to its marginal cost (RMR = MC), so Frito-Lay produces 150,000 tons of corn chips. The managers set the price using the residual demand, resulting in a price of $1.75 per pound. The competitive fringe firms are price takers, so they take the price of $1.75 as given and as their supply curve shows, produce a total of 50,000 tons of corn chips at this price. The total quantity of chips produced in the market is 200,000 tons—150,000 tons by the dominant firm and 50,000 tons by the competitive fringe firms. The price is $1.75 per pound. This price and total quantity reflect a point on the market demand curve (D) shown in Figure 6.11.

Effect on the Dominant Firm of the Competitive Fringe You can see the effect of competition on the choices the dominant firm’s managers make. Faced with competition from the fringe firms, the managers increase production from their monopoly amount of 140,000 tons of chips to 150,000 tons and lower the price from the monopoly price of $2.05 per pound to $1.75 per pound. You can under- stand why the managers lower the price by using the markup equation, Equation 6.5:

P MC

= a e e - 1

b

D

RD

RMR

MC

MR

SCF

Price and cost (dollars per pound of corn chips)

Quantity (thousands of tons of corn chips per year)

$2.25

$2.50

0

$0.25

$0.50

35030025020015010050

$0.75

$1.00

$1.25

$1.50

$1.75

$2.00

Dominant firm profit-maximizing price

Dominant firm profit-maximizing quantity

Figure 6.12 A Dominant Firm’s Profit Maximization

The dominant firm faces the light blue residual demand curve, RD, until it intersects the market demand curve at 250,000 tons of chips, after which its demand curve becomes the dark blue market demand curve, D. The marginal revenue curve for the residual demand curve is the light green residual marginal revenue curve, RMR, until the quantity at which the residual demand curve merges with the market demand curve, 250,000 tons of chips. After that, the marginal revenue curve drops down and becomes the dark green market marginal revenue curve, MR. The dominant firm produces the quantity that sets its marginal cost equal to its residual marginal revenue, MC = RMR, and sets the price using the residual demand curve. In the figure, the dominant firm produces 150,000 tons of corn chips and sets a price of $1.75 per pound. The competitive fringe supply curve, SCF, shows that at this price the fringe firms produce 50,000 tons of corn chips.

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6.3 Dominant Firm  251

The markup depends on the price elasticity of demand 1e2: The larger the price elasticity of demand, the smaller the markup. At any quantity, the price elasticity of demand is larger on the residual demand curve than on the market demand curve. Why? Because a given change in the price leads to a larger change in the quantity demanded along the residual demand curve than along the mar- ket demand curve. Suppose that the price falls. Then the quantity demanded along the market demand curve increases. The quantity demanded along the residual demand curve also increases, but for two reasons: (1) The quantity demanded in the market as a whole increases (the same effect just noted), and (2) the fringe firms decrease the amount they sell. Because the change in the quantity demanded is larger along the residual demand curve than the market demand curve, the elasticity of demand for Frito-Lay’s chips is larger when it faces competition. Consequently, the presence of the competitive fringe decreases Frito-Lay’s price markup. This result is analogous to that illustrated in Figure 6.4, in which a monopoly’s markup falls as the price elasticity of demand for its product increases.

A dominant firm’s profit is less with the presence of the competitive fringe than if it were a monopoly. As illustrated in Figure 6.12, even with an increase in produc- tion (which conceivably could increase profit), the price falls substantially (which substantially decreases the firm’s profit). From the perspective of Frito-Lay’s manag- ers, the presence of the other firms decreases Frito-Lay’s profit. Indeed, the larger the number of other firms, the greater the supply of the fringe firms, and the larger the decrease in Frito-Lay’s profit. The managerial lesson is easy to state but difficult to accomplish: Managers of dominant firms must strive to decrease the number of competitive fringe firms.

Data centers and local area networks use Ethernet switches to join computers together. Suppose that you are a manager at a firm like Cisco Systems, and yours is the dominant firm in this market. Your market share exceeds 60 percent. Suppose also that the next largest market shares are much smaller: Hewlett- Packard has 9 percent, Alcatel-Lucent has 3 percent, Dell has 2 percent, and a number of still smaller firms share the remaining 26 percent. Several of the competitive fringe firms close. How should you adjust your firm’s quantity and price in response to their exit from the market?

Answer When several fringe firms exit, the supply of the competitive fringe decreases, so your residual demand and marginal revenue increase. You should respond to the increase in demand and marginal revenue by raising the quantity and price of your Ethernet switches, increasing your firm’s economic profit.

DECISION SNAPSHOT

How a Technology Firm Responds to Changes in the Competitive Fringe

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252  CHAPTER 6 Monopoly and Monopolistic Competition

The Demand for Shoes at a Dominant Firm

The following table shows the hypothetical demand and competitive fringe supply for the market for athletic shoes. Your firm has a market share of approximately 45 percent and dominates this market. The next largest firm has a market share of less than 10 per- cent. The table shows the market demand and competitive supply at different prices. Use the table to solve the following problems.

a. Complete the table by calculating the residual demand at each price.

b. Use the formula from Chapter 3 for the price elasticity of demand, e = �b * 1P>Qd2 � , where b is the change in the quantity from a $1 change in price (calculated for any two points on the demand curve as the change in quantity divided by the change in price), to calculate the price elasticity of demand on the market demand curve and on the residual demand curve at prices of $90, $85, $80, and $75 per pair of shoes. How do the price elasticities of demand on the two demand curves compare?

Price (dollars per pair of shoes)

Market Demand (millions of shoes)

Competitive Supply (millions of

shoes)

Residual Demand (millions of shoes)

$90 100 40

85 120 30

80 140 20

75 160 10

70 180 0

65 200 0

Answer

a. The residual demand equals the market demand minus the competitive supply, so at the price of $90, the residual demand equals 100 million shoes - 40 million shoes = 60 million shoes. Moving down the column, in millions of shoes, the rest of the residual demands are 90, 120, 150, 180, and 200.

b. On the market demand curve, b = 4,000,000, and on the residual demand curve, b = 6,000,000. At the price of $90 on the market demand curve, the price elasticity of demand is 3.6, and on the residual demand curve, the price elasticity of demand is 9.0; at the price of $85, they are 2.8 and 5.7; at the price of $80, they are 2.3 and 4.0; and at the price of $75, they are 1.9 and 3.0. At each price, the price elasticity of demand is larger on the residual demand curve than on the market demand curve.

SOLVED PROBLEM

6.4 Monopolistic Competition Learning Objective 6.4 Explain how managers of a monopolistically competitive firm determine the quantity and price that maximize profit.

To this point in the chapter, you have learned about firms that are either alone in the market or large relative to the competition. Not all firms with market power are alone or dominant, however. For example, Apple has some control over the price it

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6.4 Monopolistic Competition  253

sets for its iPhone, but it faces numerous similar-sized competitors, including Sam- sung, Google, LG, Microsoft, Huawei, Xiaomi, and HTC. Although Apple has a large market share—about 15 percent worldwide—effectively it is only one firm among many selling smartphones. The smartphone market is a monopolistically competi- tive market, and Apple is a monopolistically competitive firm. Let’s begin our study of monopolistic competition by discussing the characteristics that define this market structure and the firms that compete within it.

Defining Characteristics of Monopolistic Competition As its name implies, monopolistic competition combines elements of perfect compe- tition and monopoly. Monopolistic competition is a market with many firms, with no barriers to entry, and in which each firm produces a differentiated product. Let’s begin with the two characteristics that monopolistic competition shares with perfect competition and conclude with the one it shares with monopoly:

1. Many sellers. Both monopolistically competitive markets and perfectly com- petitive markets include many firms, which limits each firm’s market power over its price. Unlike the situation in a perfectly competitive market, however, a monopolistically competitive firm’s market power is not totally eliminated (see item 3).

2. No barriers to entry. Both perfectly competitive and monopolistically competi- tive markets have many firms for the same reason: There are no barriers to entry. This characteristic is a key difference between monopolistically competitive firms and monopolies.

3. Differentiated products. Each product produced by a monopolistically competi- tive firm is slightly different from the ones produced by other firms. Smart- phones are an example of a differentiated product. All of the producers listed above produce smartphones, but each smartphone is different—differentiated— from the others. Although Apple’s smartphone is a substitute for those pro- duced by its competitors, it is not a perfect substitute, which gives Apple some market power to set its price.

Short-Run Profit Maximization for a Monopolistically Competitive Firm Assume that the managers of a monopolistically competitive firm want to maximize profit. Like the managers of the other types of firms presented, these managers can use marginal analysis and the profit-maximization rule to achieve their goal. They need to determine their firm’s marginal revenue and combine it with their marginal cost to determine the profit-maximizing quantity.

Demand, Marginal Revenue, and Marginal Cost for a Monopolistically Competitive Firm What does a monopolistically competitive firm’s demand curve look like? Con- sider Apple and the iPhone. Because Apple’s smartphone differs from those of its competitors, if Apple raises its price, some consumers will still buy it because they prefer the iPhone. Likewise, if Apple lowers its price, not all consumers will switch to an Apple smartphone because some still prefer their Android phones. So the demand curve for an Apple smartphone is downward sloping, illustrated in Figure 6.13 by hypothetical demand curve D. As you saw with the downward-sloping

Monopolistic competition A market with many firms, with no barriers to entry, and in which each firm produces a differentiated product.

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254  CHAPTER 6 Monopoly and Monopolistic Competition

monopoly and dominant firm demand curves, the downward-sloping monopolisti- cally competitive firm’s demand curve makes its marginal revenue curve (MR) lie beneath the demand curve so that P 7 MR. The marginal cost curve (MC) shown in Figure 6.13 is the same as the marginal cost curves used for monopolies and perfectly competitive firms.

Figure 6.13 looks very similar to Figure 6.3, which shows the same curves for a monopoly. This similarity, however, conceals a key difference: Figure 6.3 shows demand and marginal revenue curves for the market, while Figure 6.13 shows the demand and marginal revenue curves for the firm’s specific product.

Short-Run Profit Maximization for a Monopolistically Competitive Firm: Marginal Analysis The managers at a monopolistically competitive firm like Apple face the same profit- maximization problem as the managers at a monopoly or dominant firm: They must produce the quantity for which marginal revenue equals marginal cost and use the demand to set their price. Figure 6.14 shows that short-run profit maximization is the same for a monopolistically competitive firm as for a monopoly or dominant firm. The figure shows that managers produce 200 million smartphones per year, the quantity that sets the firm’s marginal revenue equal to its marginal cost, MR = MC, or, equivalently, MR - MC = 0. All of the phones up to 200 million are profitable because for each of them MR 7 MC. None of the phones beyond 200 million is prof- itable because for each of them MR 6 MC. The firm then uses the demand for its smartphones to set the highest price that consumers will pay for the 200 million smartphones produced, $500.

As Figure 6.14 shows, the firm is making an economic profit because its price exceeds its average total cost 1P 7 ATC2. The amount of the economic profit equals the area of the green rectangle, 1$500 per phone - $300 per phone2 * 200 million phones, or $40 billion. But can the firm’s economic profit last? Answering that important question is the topic of the next section.

Figure 6.13 Demand, Marginal Revenue, and Marginal Cost Curves for a Monopolistically Competitive Firm

The downward-sloping demand curve (D) for a monopolistically competitive firm makes the marginal revenue curve (MR) lie below the demand curve. The marginal cost curve (MC) is the same as the marginal cost curves for monopolies and perfectly competitive firms.

D

MR

MC

Price and cost (dollars per smartphone)

Quantity (millions of smartphones per year)

$900

$0

$100

$200

35030025020015010050

$300

$400

$500

$600

$700

$800

2$200

2$100

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6.4 Monopolistic Competition  255

Long-Run Equilibrium for a Monopolistically Competitive Firm To this point, the analysis of a monopolistically competitive firm has been identical to that of a monopoly. There is a key difference, however: A barrier to entry does not protect the economic profit. Other firms can produce differentiated products similar to those produced by the original firm. Once again, take Apple as an example. After Apple released the first iPhone, many companies started to produce similar smart- phones, such as the Samsung Galaxy and HTC One. As new products appear on the market, some consumers prefer them, so the initial firm’s demand decreases, and its demand and marginal revenue curves shift leftward. As long as the firms in the mar- ket make an economic profit, new firms continue to enter. Entry stops only when the firms are making zero economic profit, so that the owners are making only a com- petitive return.

Figure 6.15 illustrates the long-run equilibrium for a monopolistically com- petitive firm. As you can see, its managers maximize profit by producing 100 mil- lion smartphones, the quantity for which MR = MC. Because of the new competition it faces, the firm no longer makes an economic profit, since the price equals the average total cost, P = ATC. In Figure 6.15, the price and average total cost are $400 per smartphone. The long-run, zero economic profit result means that the firm produces where its ATC curve is tangent to (just touches at one point) its demand curve.

This conclusion reinforces what you learned in Chapter 5 about perfectly com- petitive firms. If a monopolistically competitive firm is making a short-run eco- nomic profit, the absence of a barrier to entry leads to increased competition in the long run, which in turn forces the firm to produce at a point where it makes no economic profit. This result clearly highlights the managerial importance of a bar- rier to entry!

Figure 6.14 Short-Run Profit Maximization for a Monopolistically Competitive Firm

The managers maximize profit by producing 200 million smartphones, the quantity that sets MR = MC . The price of $500 is set using the demand: It is the highest price that consumers will pay for the 200 million smartphones produced. The firm is making an economic profit because its price exceeds its average total cost. The amount of the economic profit equals the area of the green rectangle, $40 billion.

D

MR

MC

ATC

Price and cost (dollars per smartphone)

Quantity (millions of smartphones per year)

$900

$0

$100

$200

35030025020015010050

$300

$400

$500

$600

$700

$800

2$200

2$100

Profit-maximizing price

Profit- maximizing quantity

MR . MC MR , MC

Economic profit, $40 billion

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256  CHAPTER 6 Monopoly and Monopolistic Competition

J-Phone’s Camera Phone

In 2000, the Japanese cell phone company J-Phone introduced the first widely successful cell phone camera. It caught on quickly because it had a new feature not included in any of the competitors’ phones: Customers were able to snap pictures and then immediately share them with friends. J-Phone was a monopolistically competitive firm because it competed with several other cell phone producers, each producing their own unique cell phone.

a. As a manager of J-Phone, how would you expect the price of your phone to change over the next five years? How would you expect your sales to change over the same period of time?

b. How do your answers to part a affect your decision about whether to expand your manufacturing facilities?

Answer

a. Because J-Phone competes in a monopolistically competitive market, you must expect that your wildly popular phone will soon face new competition from other cell phone companies, causing the price of a cell phone with a camera to fall. (In fact, prices fell quickly from $500 in 2000 to less than $300 in 2005.) You also must expect that J-Phone’s market share will decrease when other companies market their new phones. (Indeed, that is precisely what occurred: J-Phone’s market share initially rose from 16.4 percent in 2001 to 18.5 percent in 2003 before falling back to approximately 15.5 percent in 2005.)

b. Your answers to part a must give you pause when it comes to expanding your manufacturing plant. You should worry that once your demand and price fall with the arrival of new competition, you will be stuck with an uneconomically large production facility if you expand.

SOLVED PROBLEM

Figure 6.15 Long-Run Equilibrium for a Monopolistically Competitive Firm

The managers maximize profit by producing 100 million smartphones, the quantity that sets MR = MC . The price, $400 per smartphone, is determined using the demand curve (D). In the long run, competition from new producers decreases the demand for smartphones sufficiently that the firm no longer makes an economic profit. The price equals the firm’s average total cost.

D MR

MC

ATC

Price and cost (dollars per smartphone)

Quantity (millions of smartphones per year)

$900

$0

$100

$200

35030025020015010050

$300

$400

$500

$600

$700

$800

2$200

2$100

Profit-maximizing price

Profit- maximizing quantity

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6.5 Managerial Application: The Monopoly, Dominant Firm, and Monopolistic Competition Models  257

6.5 The Monopoly, Dominant Firm, and Monopolistic Competition Models

Learning Objective 6.5 Apply what you have learned about monopolies, dominant firms, and monopolistically competitive firms to make better managerial decisions.

The most crucial managerial lesson about monopolies, dominant firms, and monop- olistically competitive firms has been presented repeatedly throughout this chapter: Use marginal analysis to determine the profit-maximizing quantity of production. Managers in virtually all types of firms can reach the profit-maximizing quantity by comparing the estimated marginal revenue to the estimated marginal cost and then increasing production if marginal revenue exceeds marginal cost or decreasing pro- duction if marginal revenue falls short of marginal cost.

A second, almost equally significant lesson is the importance of barriers to entry, which enable you to maintain your firm’s economic profit indefinitely. If your barri- ers to entry disappear, so, too, will your economic profit. Successful managers search for ways to strengthen existing barriers or erect new ones, such as lobbying the gov- ernment to impose regulations or requirements for new suppliers to fulfill.

Using the Models in Managerial Decision Making As a manager, it is unlikely that you will have a figure showing marginal revenue, marginal cost, and demand. But you still need to make decisions about the quantity to produce and the price to charge. Section 5.4 pointed out that for perfectly compet- itive firms, the profit-maximization rule, can be restated as “Produce all the units for which MR - MC 7 0, and stop when you hit the unit with MR - MC = 0.” This same result applies to firms with market power. In other words, managers of monop- olies, dominant firms, and monopolistically competitive firms can all use the profit- maximization rule to determine their profit-maximizing quantity.

Determining the Profit-Maximizing Price The second part of the profit-maximization rule, “Set the highest price that sells the quantity produced,” is immediately applicable if you have an estimate of your demand. You can use your profit-maximizing quantity in your estimated demand function and solve for the price. If you do not have an estimate of demand, you have additional tools at your disposal: the relationships among price, marginal cost, and elasticity of demand shown in Equation 6.4 and 6.5 and summarized in the following box.

You can use estimates of your marginal cost and price elasticity of demand to set the profit-maximizing price or, perhaps more realistically, to set a range of prices for your product. Suppose that you again work for a pharmaceutical firm and your

MANAGERIAL APPLICATION

• Price and marginal cost: The profit-maximizing relationship between price and

marginal cost is 1P = MC * ee - 12. • Markup equation: The profit-maximizing markup of price over marginal cost is

PMC = e

e - 1.

RELATIONSHIPS AMONG PRICE, MARGINAL COST, AND ELASTICITY OF DEMAND

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258  CHAPTER 6 Monopoly and Monopolistic Competition

company has another, newly developed drug with a marginal cost of $1,000 per dose. As a manager, you believe that the price elasticity of demand for this drug is likely to lie between 1.5 and 1.1. You can use the first equation to set a range for the price you will charge. If the price elasticity of demand is 1.5, the price should be

$1,000 * a 1.5 1.5 - 1

b = $3,000

If the price elasticity of demand is 1.1, the price should be

$1,000 * 1.1

1.1 - 1 = $11,000 6.6

In other words, if you are confident that your estimates are correct, your profit- maximizing price will be between $3,000 and $11,000 per dose.

If you have already set a price for the product, you also can determine if you are maximizing your profit. Suppose that after you set a price of $8,000 per dose, you refine your estimate of the price elasticity of demand to 1.1. Equation 6.6 shows that you have not set the profit-maximizing price. In this case, you must think carefully about whether your estimates are correct. If you are confident that the price elasticity of demand is 1.1 and the marginal cost is $1,000 per dose, you know that the price of $8,000 is too low. To maximize profit, you should raise the price to $11,000 per dose.

The second relationship in the box shows how the profit-maximizing markup of price over marginal cost depends on the price elasticity of demand. This equation shows that the smaller the value of e, the larger the markup. If you know that there are only a few substitutes for your product, you know that its price elasticity of demand is small, which gives you greater ability to mark up your price over the marginal cost. Consequently, managers often focus their marketing efforts on con- vincing consumers that their firm’s product is unique and has no substitutes. If this approach succeeds, the managers can increase the markup and the firm’s profit.

Erecting Barriers to Entry Barriers to entry allow a firm already in the market to protect its economic profit. You must be alert to opportunities to erect such a barrier to protect your firm. Some are outside of a manager’s control: You cannot affect the presence of economies of scale or gain immediate control over a vital input. On the other hand, patents, copyrights, and trademarks are relatively easy to obtain and can serve as important barriers to entry.

Lobbying the government to make entry of new firms difficult can also help pre- serve some of your firm’s market power. Although the government is unlikely to create a monopoly, it may require new firms to present some sort of difficult-to-ob- tain certification or costly permit, which helps create a barrier to entry. For example, when Internet sales of contact lenses first became possible, lobbyists descended on some state regulatory boards, suggesting that online sellers should be required to obtain a state-issued optician’s license. Requiring these licenses would have served as a barrier to entry but those efforts generally failed. A more recent example involves Uber, an app-based ride-sharing service that competes with taxi companies. Taxi drivers in both the United States and other countries have lobbied local authorities to require Uber to obtain government licenses or certifications for its drivers. These requirements are an attempt to make it difficult for the new competitor, Uber, to enter the market for rides. Indeed, in 2015 and 2016, France jailed and fined Uber’s two highest-ranking French executives for violating licensing laws passed in response to successful lobbying by French cab companies!

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Keep in mind that as a matter of social policy, economists generally oppose firms’ efforts to erect barriers to entry because they can give a firm market power, which leads to a deadweight loss. From your perspective, however, that same barrier to entry also increases your firm’s economic profit.

Applying the Monopolistic Competition Model The most basic lesson from monopolistic competition is familiar: Barriers to entry protect economic profit. The absence of barriers to entry means that in the long run your firm will make only a competitive return. In the smartphone market, Apple’s managers tried to erect barriers to entry by applying for patents and then suing HTC, Samsung, and other manufacturers for patent infringement in the United States, the European Union, China, Japan, and many other countries.

Without barriers to entry, managers of monopolistically competitive firms can try to increase the demand for their product and/or increase the difference between their product and those of their competitors. Any increase in demand or differentia- tion will be temporary, since rivals will soon step in to produce their version of the product, but the firm can temporarily make an economic profit.

Innovation Managers of monopolistically competitive firms often strive for innovation, creation of a novel product that meets consumers’ needs. As long as your firm’s product stays one step ahead of those of its competitors, you have the opportunity to make an economic profit. Apple’s innovative iPad tablet, first sold in 2007, serves as a good example. The initial introduction of the iPad was a huge success. Nothing similar existed in the mar- ketplace, and the demand was strong—Apple sold 300,000 iPads on their first day of availability. Continuing its success, in 2014, Apple sold three recently designed, different full-size iPads. By 2016, the number of different full-size iPads was down to two, and only one (the iPad Pro) had been designed within the previous two years. Apple faced tremendous competition from other companies, each producing its own variation of a tablet. The first generations of the iPad were widely acclaimed as bringing something new, fresh, and exciting to the market. As product innovations became more costly, it became more difficult for Apple to fend off the competition. Samsung, Asus, Lenovo, and others entered the market, making similar tablets. Apple’s share of the tablet market fell from approximately 60 percent in early 2012 to 30 percent in early 2014 to 25 percent in early 2016. The demand for Apple’s iPads decreased, and Apple’s total revenue from these products fell, from approximately $70 billion in 2013 to $46 billion in 2016.

Marketing The tale of Apple’s iPad demonstrates how difficult it is to consistently increase the demand for your products by innovation alone. So managers also extensively mar- ket their products to keep the demand for the products robust. For example, Apple’s annual Worldwide Developers Conference (WWDC), during which Apple execu- tives highlight new technologies, receives extensive publicity on all Internet technol- ogy websites, as do Apple’s widely publicized new product introductions. These marketing events increase the demand for Apple’s products. During such events, Apple’s managers strive to differentiate their products, making the case that they are different from and superior to those of their competitors. (Chapter 13 is devoted to a more detailed examination of marketing and advertising decisions.)

Apple’s efforts show that marketing is crucial for any type of firm with market power. Marketing generally has two related objectives: (1) increase the demand for the product; and (2) convince consumers that the product is unique, with no close substitutes,

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260  CHAPTER 6 Monopoly and Monopolistic Competition

thereby reducing its price elasticity of demand. Successful marketing accomplishes both goals. Increasing the demand and/or decreasing the price elasticity of demand allows the producer to increase the markup and, consequently, increase the profit.

Green marketing is becoming more prevalent (as is the similarly named—but very different—concept of greenwashing, falsely claiming green attributes for a product— see Section 13.3). Green marketing refers to marketing that emphasizes the positive environmental aspects of a product. Ben & Jerry’s, an ice cream, frozen yogurt, and sorbet company that is now a division of Unilever, has consistently marketed itself as following green values. Unilever’s executives determined that such advertising boosts the demand for Ben & Jerry’s products, particularly among consumers who are concerned about the environment, so Ben & Jerry’s advertises the use of non- GMO ingredients (those without genetically modified organisms) and cage-free eggs. Ben & Jerry’s, however, also runs marketing campaigns stressing other product attributes, such as its Instagram campaign for its Scotchy Scotch Scotch ice cream and its stop-motion television advertisements for various flavors. Clearly, Ben & Jer- ry’s uses a diverse mixture of themes in its marketing because the firm’s managers want to appeal to a wider customer base beyond “green consumers.”

Green marketing is similar to other types because its goal is to increase demand and differentiate the product. It differs from other marketing efforts because of the major role played by certification. For example, Ben & Jerry’s uses Fairtrade-certified sugar, coffee, bananas, and other inputs. Fairtrade International is an organization that creates fair trade standards, designed to ensure that producers get a “fair” price for their product, and certifies that products used by different companies meet these fair trade standards. Other green certifications are provided by government programs, such as the USDA Organic label for food and Energy Star standards for appliances, as well as by nongovernment organizations, such as the U.S. Green Building Council’s LEED (Leadership in Energy & Environmental Design) certification for buildings.

Overexpansion You learned in Section 5.4 that as a manager of a perfectly competitive firm, you must be careful about increasing your capacity simply because your profit has increased. The same advice holds true for managers of monopolistically competitive firms. If you successfully introduce a new product or create a marketing campaign that yields an economic profit, keep in mind that economic profit in a monopolistically competi- tive market is not permanent. If you overexpand your production capacity, you might wind up with an economic loss in the long run as the entry of new firms decreases the demand and price for your product. Starbucks initially started growing rapidly in the early 1990s and by 2007 had grown to over 7,000 U.S. stores. It had grown too rapidly, however, and was facing new competition from McDonald’s, Dunkin Donuts, and smaller, regional competitors that had all entered the premium coffee market. So in 2008, with its profit falling, Starbucks retrenched and closed over 8 percent of its U.S. stores. The executives at Starbucks, however, did not let this negative experience shape their company’s future. Instead, they innovated new ways to sell coffee. In par- ticular, Starbucks partnered with Target and Safeway to open smaller stores within large Target and Safeway locations. These innovative smaller stores have lower costs than stand-alone locations and have allowed Starbucks to resume growing.

Additionally, if you are a supplier of an input to a monopolistically competitive firm with a hot new product, you, too, must be alert to overexpansion. When competi- tors for your customer arrive on the scene, your customer will decrease production and reduce purchase of inputs. Unless you think you can pick up business by providing your input to the new rivals, hesitate before increasing the scale of your operation.

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Revisiting Premature Rejoicing by the Managers at KV Pharmaceutical

Recall that the managers at KV Pharmaceutical cele-brated after the FDA gave them a seven-year period of marketing exclusivity for the drug 17P because they thought it made them a monopoly for the next seven years. They knew that the price elasticity of demand for Makena, their name for 17P, was small because of the absence of substitutes. Suppose that the managers believed that the price elasticity of demand was 1.01 and the marginal cost was $15 per dose (the same as the competitive price).

Using the equation P = MC * 1 ee - 12 , the profit- maximizing price would be $15 * 1 1.011.01 - 12 = $1,515. KV Pharmaceutical’s actual price was $1,500 per dose, which was approximately 100 times the competitive price.

Unfortunately for the managers, setting such a high price immediately alienated groups that had previously supported their efforts to create a standardized version of 17P. Many believed that the managers’ actions were immoral. Within just a few days of KV Pharmaceutical’s price announcement, the March of Dimes, which had lobbied the FDA to approve Makena, abandoned its support and called for a lower price. More importantly, the FDA turned against KV Pharmaceuti- cal by announcing that it would not take action against com- pounding pharmacies that continued to make 17P. The FDA’s action—or, perhaps more accurately, inaction—changed KV Pharmaceutical from a monopoly to, at best, a dominant firm. As you have learned by reading this chapter, a dominant firm’s price is lower than that of a pure monopoly. Within a week after the FDA’s response to the pricing announcement, the managers at KV Pharmaceutical lowered the price from $1,500 to $690 per dose.

If you use the equation relating price, marginal cost, and

price elasticity of demand, P = MC * 1 ee - 12, you will see that KV Pharmaceutical’s managers believed that with the competition from compounding pharmacies, the price elas- ticity of demand had risen to 1.02. Their estimate was, how- ever, surely wrong. The initially high price alienated so many potential demanders who deemed it highly unethical—from the doctors who would prescribe the drug to the insurance companies that would help pay for it—that the demand was lower than they thought it would be and the price elasticity of demand was larger than they expected. Even at $690 per dose, few patients purchased Makena. Within a year and a half of receiving FDA approval to exclusively market the drug, KV Pharmaceutical declared bankruptcy.

The managers at KV Pharmaceutical made an important miscalculation when they set their initial price: When they calculated the profit-maximizing price, they did not consider the furiously negative response to the 100-fold price hike or the FDA’s decision to allow compounding pharmacies to pro- duce the drug. Both of these reactions drastically decreased the demand and increased the elasticity of demand for Mak- ena, and they led to a bad outcome for KV Pharmaceutical. The managers should have considered the possibility that demanders and regulators would consider their extremely large price hike both immoral and unjustified and that these views would lead radically decrease the demand for Makena. The managerial lesson from KV Pharmaceutical’s experience is clear: When setting a price, managers must determine whether the price will cause other factors to change and thereby affect demand.

Summary: The Bottom Line 6.1 A Monopoly Market • A monopoly market has three characteristics: a single

seller, a product with no close substitutes, and insur- mountable barriers to entry.

• A monopoly firm’s demand curve is the same as the market demand curve, so it is downward sloping. Due to the downward-sloping demand curve, the marginal revenue curve lies below the demand curve.

• The firm’s marginal revenue (MR), price (P), and price elasticity of demand 1e2 are related to one another

using the equation MR = P * 11 - 1e2.

6.2 Monopoly Profit Maximization • Monopoly managers maximize profit via the profit-

maximization rule: Produce the quantity that sets the marginal revenue equal to the marginal cost, and charge the highest price that sells the quantity produced.

• The profit-maximizing price (P), marginal cost (MC), and price elasticity of demand 1e2 are related according

to P = MC * 1 ee - 12, which can be rearranged to show that the markup of price over marginal cost equals PMC =

e e - 1.

Summary: The Bottom Line  261

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262  CHAPTER 6 Monopoly and Monopolistic Competition

Key Terms and Concepts Competitive fringe

Deadweight loss

Dominant firm

Market power

Markup equation

Monopolistic competition

Monopoly market

Natural monopoly

Residual demand

• A monopoly makes an economic profit if P 7 ATC, makes a competitive return if P = ATC, and incurs an economic loss if P 6 ATC.

• Because barriers to entry protect a monopoly by prevent- ing other firms from entering the market, the monopoly can make an economic profit indefinitely. Barriers to entry include legal barriers, control of an essential raw material, large economies of scale, and substantial sunk costs.

• Competitive markets are better for society because monopolized markets create a deadweight loss and give society a smaller total surplus of benefit over cost.

6.3 Dominant Firm • A dominant firm market has one large firm competing

with a number of smaller firms, collectively called the competitive fringe.

• The dominant firm’s demand is the residual demand, the market demand minus the quantity produced by the competitive fringe. Managers of dominant firms maximize profit by producing the quantity that sets residual marginal revenue equal to marginal cost and setting the price from the residual demand curve.

• The presence of the competitive fringe decreases the dominant firm’s profit.

6.4 Monopolistic Competition • Monopolistic competition is a market with many firms,

with no barriers to entry, and in which each firm pro- duces a differentiated product.

• Monopolistically competitive firms use the same profit- maximization rule as firms in other market structures:

Produce the quantity that sets the marginal revenue equal to the marginal cost, and charge the highest price that sells the quantity produced.

• Because there are no barriers to entry, monopolistically competitive firms making an economic profit in the short run can make only a competitive return in the long run, since new firms enter the market and com- pete away the short-run economic profit.

6.5 Managerial Application: The Monopoly, Dominant Firm, and Monopolistic Competition Models

• Two results are key for managerial decision mak- ing: (1) Regardless of market structure, apply the profit-maximization rule, and (2) the presence of barriers to entry is necessary for your firm to con- tinue to make an economic profit, so you should look for ways to sustain barriers to entry or create new ones.

• You can use the relationship among the profit-maxi- mizing price, marginal cost, and price elasticity of

demand, P = MC * 1 ee - 12, along with estimates of the marginal cost and elasticity of demand, to deter-

mine your profit-maximizing price. • As a manager of a monopolistically competitive

firm, successful innovation and/or marketing can allow you to make a short-run economic profit. But the economic profit is only temporary, so you must be careful to not overexpand your scale of operations.

Questions and Problems

6.1 A Monopoly Market Learning Objective 6.1 Explain the relation- ship between a monopoly’s demand curve and its marginal revenue curve.

1.1 As a manager, do you want to possess market power? Why or why not?

1.2 “Only one firm produces Kellogg’s Corn Flakes, so Kellogg’s is a monopolist.” Is this assertion correct? Explain your answer.

1.3 What role do barriers to entry play in determin- ing whether or not a firm is a monopoly?

1.4 The table shows part of a monopoly’s demand. Complete the table, and then plot the demand curve and marginal revenue curve in a dia- gram with price on the vertical axis and quan- tity on the horizontal axis. Assuming that both curves are linear, extend the demand and mar- ginal revenue curves to the vertical axis. What is the vertical intercept of the demand curve? Of the marginal revenue curve? What is the slope of the demand curve? Of the marginal revenue curve?

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that unit. To maximize your profit, should you increase, decrease, or maintain the current level of production? Explain your answer.

2.4 The first two columns of the table show a monopoly’s marginal revenue, and the last two columns show its marginal cost.

Marginal Revenue,

MR

Quantity, Q

Marginal Cost, TC

Quantity, Q

$11.00 10 $5.00 10

10.00 11 5.50 11

9.00 12 6.00 12

8.00 13 6.50 13

7.00 14 7.00 14

6.00 15 7.50 15

5.00 16 8.00 16

a. What is the firm’s profit-maximizing quantity? b. Assume that the marginal revenue and mar-

ginal cost curves are linear. Draw them in a diagram. Draw the firm’s demand curve in the diagram. (Hint: Recall that the demand curve and the marginal revenue curve have the same vertical intercept and the slope of the marginal revenue curve is twice that of the demand curve.) What is the firm’s profit- maximizing price?

2.5 The figure illustrates the demand for soybean seeds, which your firm’s scientists genetically mod- ified to be resistant to herbicide sprays. The figure shows the demand curve (D), the marginal revenue curve (MR), the average total cost curve (ATC), and

1.5 For a monopoly, P 7 MR. For a perfectly com- petitive firm, P = MR. What accounts for this difference?

1.6 Use the definition of marginal revenue to explain why marginal revenue is negative over some range of the demand curve for a monopoly.

1.7 You are a manager of a pharmaceutical firm that has a monopoly for a particular drug. Your staff has esti- mated the price elasticity of demand for the drug. When the price of the drug is $1,000 per dose, the price elasticity of demand is 3.0, and when the price is $400 per dose, the price elasticity of demand is 2.0. a. What is the marginal revenue when the price

is $1,000 per dose? b. What is the marginal revenue when the

price is $400 per dose?

6.2 Monopoly Profit Maximization

Learning Objective 6.2 Discuss how managers of a monopoly can determine the quantity and price that maximize profit and how they com- pare to those of a perfectly competitive firm.

2.1 Why do the managers of a monopoly produce the quantity that sets marginal revenue equal to marginal cost?

2.2 “If a monopolist maximizes its profits, at the profit-maximizing quantity the demand for its product must be elastic.” Do you agree with this statement? Why or why not?

2.3 You are managing a pharmaceutical company that makes a patent-protected drug. According to your calculations, at the current level of pro- duction the marginal revenue of one unit of the drug is less than the marginal cost of producing

Questions and Problems  263

Price, P

Quantity, Q

Marginal Revenue, MR

$30 12

29 13

28 14

27 15

26 16

25 17

24 18

23 19

22 20

21 21

20 22

19 23

Accompanies problem 1.4.

D

MR

MC

ATC

Price and cost (dollars per ton of soybean seeds)

Quantity (millions of tons of soybean seeds)

$90

$0

$10

$20

1,4001,2001,000800600400200

$30

$40

$50

$60

$70

$80

2$20

2$10

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264  CHAPTER 6 Monopoly and Monopolistic Competition

the marginal cost curve (MC). Your supervisor wants to produce 600 million tons of seeds, the quantity that minimizes the average total cost. a. Explain why your supervisor’s approach is

incorrect. b. How can you determine the profit-maximizing

quantity? c. According to the figure, what is the profit-

maximizing price and quantity?

2.6 The following figure illustrates the demand for a new, patented memory chip. a. To maximize profit, what price do you set,

and what quantity do you produce? b. What is your economic profit or economic loss? c. Do you expect your current economic profit

or economic loss to continue? Explain your answer.

In a figure, plot this demand curve, and label it D. Then plot the corresponding marginal revenue curve and label it MR. (Recall that that the marginal revenue curve has the same vertical intercept as the demand curve and has a slope twice that of the demand curve.) Assume that the marginal cost and average total cost equal $2 for all levels of production. Draw the marginal cost curve and the average total cost curve. What is the profit-maximizing price and quantity? How much economic profit will you earn?

2.9 Suppose that the demand for a monopoly firm’s product is given by

Q = 80 - P a. If the firm’s marginal cost is constant at $10,

what is the profit-maximizing price and output?

b. Suppose that the demand changes to Q = 100 - P. After this change, what is the new profit-maximizing price and quantity?

c. If the demand changes to Q = 160 - 2P, what is the new profit-maximizing price and quantity?

2.10 Biotech companies employ many highly skilled workers. a. Suppose the wage rate paid these workers

falls, perhaps because more students gradu- ate from college with the necessary skills. In the short run, how does a fall in the wage rate affect the firm’s marginal revenue and marginal cost curves?

b. If each of the biotech companies produces a unique drug so each is a monopoly in its market, how does the fall in wages change the managers’ decisions about the profit- maximizing quantity and price?

2.11 The demand for a monopoly’s product increases. In a diagram, show how the increase in demand changes the monopoly’s price and quantity.

2.12 “When the managers of a monopoly maximize its profit, the price always exceeds the marginal cost.” Is this assertion true or false? Explain your answer.

2.13 You are the manager of a monopoly. a. If the marginal cost of your product is $100

and the price elasticity of demand for your product is 2, what markup of price over marginal cost do you set?

b. If the price elasticity of demand is 3 rather than 2, what markup do you set?

c. Use your knowledge of factors that affect the magnitude of the price elasticity of demand to your answers to parts a and b.

D

MR

MC

ATC

Price and cost (dollars per memory chip)

Quantity (millions of memory chips per month)

$9

0

$1

$2

14012010080604020

$3

$4

$5

$6

$7

$8

2.7 Your marketing research department has esti- mated the demand for your firm’s product to be

Q = 10,000 - 100P and the marginal revenue to be

MR = 100 - 0.02Q If marginal cost and average total cost are constant

at $40, a. How much would you produce? b. What price would you charge? c. How much economic profit would your

firm earn? d. Illustrate your answers to parts a through c

in a diagram.

2.8 Suppose that the market demand curve for your product is given by

Q = $25 - 0.5P

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2.14 A monopolist’s profit-maximizing price is $10, and its profit-maximizing output is 300 units. a. If the average total cost of production is $7.50

per unit, what is the firm’s economic profit? b. What happens to economic profit if man-

agers change price and output?

2.15 Would you expect a profit-maximizing monopo- list to produce the quantity of output that is socially efficient? Explain your answer.

2.16 It is possible for chemists to determine the chem- ical composition of many pharmaceutical drugs. With this fact in mind, why do you think that pharmaceutical companies patent their drugs rather than keep their formulations as trade secrets?

2.17 Biotech drugs are those produced within living biological systems. Making these drugs is quite complicated and can be very sensitive to small manufacturing changes. The Food and Drug Administration (FDA), which must approve any drug before it is marketed, is trying to determine the procedures it will require to allow the produc- tion and sale of generic copies of biotech drugs that can be labeled as interchangeable with the original brands (called biosimilar interchangeability). a. As a manager of a biotech company that

manufactures an approved biotech drug with an expired patent, what arguments would you make to the FDA regarding approval of interchangeable biosimilar drugs?

b. If you are a manager of a generic drug com- pany, what arguments would you make to the FDA?

2.18 You are a manager of a natural monopoly with the costs and demand illustrated in the figure.

a. What is the minimum efficient scale of production?

b. If you are free to maximize profit, what price do you set, and what quantity do you pro- duce? What is your economic profit or loss?

c. Suppose that a new firm enters the market and produces one-fourth of your produc- tion. What is the firm’s average cost? If you do not change your price, is the new firm likely to make an economic profit or incur an economic loss? Explain your answers.

2.19 In a small city, you are the owner of the only plumbing company offering in-home service. You run your operation from a small hole-in- the-wall office, with your plumbers arriving at their job sites in their own, unmarked vehicles. You catch wind that another rival might enter the market, so you schedule a presentation with the city commissioners. During this presenta- tion, you can make one of two arguments: (1) Plumbers offering in-home service should be required to purchase a plush office (in case consumers wish to complain about the service), or (2) plumbers must pass a costly certification test given at the local community college (so that consumers are assured of quality service). Of course, as a long-time, proven business, you would be exempt from either regulation. You believe that if you argue for both policies, the commission will see it for what it is—an attempt to erect barriers to entry—so you must argue for only one. Suppose that both would increase your rival’s costs by $100,000. Does one of these proposals have a significant advantage over the other? Carefully explain your answer.

6.3 Dominant Firm Learning Objective 6.3 Describe how managers of a dominant firm determine the quantity and price that maximize profit.

3.1 In 1911, American Tobacco produced over 90 percent of the cigarettes sold in the United States. Small, competitive firms produced the remaining 10 percent. a. How did American Tobacco’s managers

determine the profit-maximizing quantity? b. How would the decisions change if the com-

pany eliminated the competitive fringe?

3.2 In 1936, Alcoa sold 90 percent of the aluminum ingot sold in the United States. The rest was imported. a. As a manager at Alcoa, how would you

determine the price to charge? b. How would your decision change if the gov-

ernment barred all imports?

D

LAC LMC

MR

Price and cost (cents per kilowatt hour)

Quantity (billions of kilowatt hours per year)

18¢ 20¢

0

2¢ 4¢

3530252015105

6¢ 8¢

10¢ 12¢ 14¢ 16¢

Questions and Problems  265

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266  CHAPTER 6 Monopoly and Monopolistic Competition

3.3 The table shows the market demand and compet- itive fringe supply for a market with a dominant firm. Complete the residual demand column of the table.

Price (dollars per unit)

Market Demand (units)

Competitive Fringe Supply (units)

Residual Demand (units)

$50 40 30

45 50 25

40 60 20

35 70 15

30 80 10

25 90 5

3.4 The following table shows the market demand and competitive fringe supply for a market with a dominant firm. a. From Chapter 3, an equation for the price

elasticity of demand is e = � b * 1P>Qd2 � , where b is the change in the quantity demanded from a $1 change in price. (For any two points on the demand curve, b is equal to the change in quantity demanded divided by the change in price.) Use this formula to calculate the price elasticity of demand at the three different prices on the market demand curve and on the residual demand curve. Record your answers in the table.

b. How does the price elasticity of demand on the market demand curve compare to the price elasticity of demand on the residual demand curve?

Price (dollars per unit)

Market Demand (units)

Price Elasticity of Demand for

Market Demand

Competitive Fringe Supply

(units)

Residual Demand (units)

Price Elasticity of Demand for Residual

Demand

$50 70 50 20

45 80 30 50

40 90 10 80

Accompanies problem 3.4.

D

SCF MC

Price and cost (dollars per unit)

Quantity (thousands of units per day)

$90 $100

0

$10 $20

35030025020015010050

$30 $40 $50 $60 $70 $80

3.5 The figure shows the market demand curve (D), the competitive fringe’s supply curve (SCF), and the dominant firm’s marginal cost curve (MC). a. Use the figure to draw the residual demand

curve, the market marginal revenue curve, and the residual marginal revenue curve.

b. If the firm is a monopoly, so that the compet- itive fringe does not exist, what price and quantity will its managers select?

c. If the firm is a dominant firm, what price and quantity will its managers select?

d. Is the firm’s markup higher when it is a monopoly or a dominant firm? Explain your answer.

e. Is the firm’s profit larger when it is a monop- oly or a dominant firm? Explain your answer.

3.6 How does the presence of a competitive fringe affect the profit of the dominant firm? Why does the competitive fringe have this effect?

3.7 In India, Cisco’s market share of the Ethernet switch and router market is approximately 67 percent. Juniper and HP each have market shares of about 6.5 percent, and several other firms have somewhat smaller market shares. Draw a diagram showing the equilibrium in this dominant firm market. Identify the equilibrium price and the equilibrium quantity produced by the dominant firm and the competitive fringe firms. Illustrate what happens to the equilib- rium price and the equilibrium quantity pro- duced by the dominant firm and the competitive fringe firms if additional fringe firms enter the market.

Accompanies problem 3.5.

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6.4 Monopolistic Competition Learning Objective 6.4 Explain how manag- ers of a monopolistically competitive firm determine the quantity and price that maximize profit.

4.1 How is a monopolistically competitive firm sim- ilar to a perfectly competitive firm? How is it similar to a monopoly?

4.2 Suppose that you are a manager in Whirlpool’s appliance division. Your accountants provide you with a report on costs and revenues. You determine that the cost to produce another top-loading washing machine is $200 and its marginal revenue is $250. Presuming Whirlpool is competing in a monopolistically competitive market, how do you change the quantity and the price of the washing machines?

4.3 The figure shows the demand curve (D), marginal revenue curve (MR), and marginal cost curve (MC) for a monopolistically competitive ham- burger restaurant. What is the profit-maximizing quantity and price of hamburgers?

4.5 Australian yogurt is a new product that is not strained and is made from whole milk, so it is creamier than regular or Greek yogurt. Suppose that you are a manager for Publix supermarkets and some colleagues suggest that the company produce a Publix-brand Australian yogurt. They explain that producing Australian yogurt is cur- rently very profitable, and they predict this trend will continue. How do you respond to your colleagues, and why?

6.5 Managerial Application: The Monopoly, Dominant Firm, and Monopolistic Competition Models Learning Objective 6.5 Apply what you have learned about monopolies, dominant firms, and monopolistically competitive firms to make better managerial decisions.

5.1 Explain how marginal analysis can help deter- mine the profit-maximizing quantity for man- agers of monopolies, dominant firms, and monopolistically competitive firms.

5.2 The price elasticity of demand for your product is 2.0, and your marginal cost is $30. What is your profit-maximizing price? Suppose that you can run a new advertising campaign and differentiate your product by emphasizing its unique features, thereby decreasing the price elasticity of demand to 1.8. What is your new profit-maximizing price?

5.3 You are managing a firm with market power, and you think the price elasticity of demand for your product is between 1.3 and 1.5. You esti- mate that your marginal cost is between $50 and $70. In what range should you set your price? If you refine your estimate of the mar- ginal cost to $60, in what range should you set your price?

5.4 As a manager of a monopolistically competitive firm like Starbucks, you are pleased that your green advertising, which proclaims your coffee is ethically and sustainably grown, has con- vinced consumers that your coffee is vastly superior to anything else sold by your competi- tors. The demand for your coffee has increased, and at every price, the price elasticity of demand has decreased. Presuming that your marginal cost is the same for every cup of coffee— say $2 per cup—and has not changed, illustrate these changes in a diagram, showing how they affect your profit-maximizing price and quan- tity of coffee.

D MR

MC

Price and cost (dollars per hamburger)

Quantity (hamburgers per day)

$6

$7

0 1,2001,000800600400200

$1

$2

$3

$4

$5

Questions and Problems  267

4.4 You are a manager of a firm like J.P. Licks, a monopolistically competitive ice cream store in Boston. You are determining the price and quan- tity of your Cookies ‘n’ Cream Pie. Economists you have hired report that the marginal cost of an ice cream pie is constant and is equal to $10 per pie. They also report that the demand is given by Q = 300 - 10P, where Q is the quan- tity of ice cream pies demanded per day and P is their price. What is the profit-maximizing price and quantity of Cookies ‘n’ Cream Pies?

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268  CHAPTER 6 Monopoly and Monopolistic Competition

MyLab Economics Auto-Graded Excel Projects 6.1 1880 Town is a tourist attraction in Midland, SD.

Its owners have collected buildings built between 1880 and 1920, filled them with antique furniture and collectables, and charge admission for tour- ists to experience history. Because of its exclusivity and location, this tourist attraction enjoys some market power power.

Suppose you run a tourist attraction similar to 1880 Town. After running some tests with pric- ing, you have determined the daily demand schedule for admission as given. In addition to tracking demand at various prices, you also monitor costs closely. a. Using the demand schedule provided, find

total revenue and marginal revenue at each point.

b. Using total costs, find the marginal cost at each point. (Just as marginal revenue is the change in total revenue divided by the change in Q, remember that marginal cost is the change in total cost divided by the change in Q.)

c. How much should you charge for entrance to the tourist attraction and how many visi- tors do you expect to have?

d. What is the economic profit when you maxi- mize profit?

6.2 Casey’s General Stores, Inc. is a convenience store chain based in Ankey, IA and has conve- nience marts all over the midwest. In small towns, there may only be one or two gas stations; however, in larger towns many gas stations compete with each other. One signature of gas stations is that the prices per gallon are displayed on large signs making it easy for customers to compare prices and select the cheapest station. Many chains, like Casey’s, have very loyal cus- tomers so when they have slightly higher prices, they don’t lose all business. Suppose you are in charge of pricing products at a convenience store similar to Casey’s in a larger town with a number of gas stations and convenience marts. You are provided with the elasticity and marginal cost information in the Excel file in the figure. a. Using the markup rule, determine the price

you should charge for each product. b. Why is the price elasticity of gasoline so

high? c. With the high price elasticity of gas, why do

other products have lower price elasticities? d. What is the relationship between elasticity

and the amount of the markup on a product.

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269

The profit-maximization rule, MR = MC, is the same for all firms. It applies equally well to the firms with no market power that you learned about in the last chapter (perfectly competi- tive firms) and to the firms with market power, including monopoly, monopolistically com- petitive, and dominant firms.

A. Marginal Revenue Curve The chapter stated that for a linear demand curve, the marginal revenue curve has the same vertical intercept and a slope equal to twice the slope of the demand curve. Using calculus, we can prove this claim. Start by using the definitions of total revenue as the price multiplied by the quantity, P * Q, and marginal revenue as the change in total revenue (TR) that results from a change in quantity (Q), MR = dTRdQ . Of course, the quantity must equal the quantity

consumers demand, so total revenue equals P * Qd and marginal revenue equals dTR dQd

.

Demand is typically written as a function of the price, Qd = a - 1b * P2, but it can be inverted to express P as a function of Qd, which is called the inverse demand function:

P = a b

- a1 b

* Qdb = c - 1d * Qd2 A6.1

For simplicity, the term after the second equal sign uses c = ab and d = 1 b to eliminate the fractions.

In the demand function in Equation A6.1, c is the vertical intercept of the demand curve and d is its slope.

Because total revenue equals P * Qd, multiplying Equation A6.1 by Qd gives

TR = P * Qd = 3c - 1d * Qd24 * Qd = c * Qd - 3d * 1Qd224 A6.2 Marginal revenue equals the derivative of total revenue with respect to quantity. Use the

power rule to take the derivative of total revenue in Equation A6.2:

dTR

dQd = MR = c - 12 * d * Qd2 A6.3

Equation A6.3 is the equation for the MR line. It is a straight line with its vertical intercept equal to c, which is the same as the vertical intercept for the demand curve, and its slope equal to 2 * d, which is twice the slope of the demand curve.

One important point to keep in mind: These results hold only if the demand curve is a straight line, which, of course, is not always the case.

B. Elasticity, Price, and Marginal Revenue The definition of marginal revenue is the same for both perfectly competitive firms and firms with market power. However, the relationship between the demand and marginal revenue is quite different. For perfectly competitive firms, MR = P. But for firms with market power, the equation in the chapter (Equation 6.2) shows that the relationship between the marginal reve- nue and price is more complicated:

MR = P * a1 - 1 e b = P * a e - 1

e b A6.4

CHAPTER 6 APPENDIX

The Calculus of Profit Maximization for Firms with Market Power

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Calculus makes deriving this equality straightforward. Total revenue again equals price multiplied by quantity, P * Qd, so using the product rule to differentiate total revenue with respect to quantity, the marginal revenue is

MR = dTR

dQd =

d1P * Qd2 dQd

= a dP dQd

* Qdb + aP * dQ d

dQd b = a dP

dQd * Qdb + P A6.5

In Equation A6.5, dP dQd

is the slope of the demand curve. This slope is negative, so

1 dP dQd

* Qd2 is negative. If you take the absolute value of this term, you must add a minus sign to account for the negative sign; that is, a dP

dQd * Qdb = - ` a dP

dQd * Qdb ` . You can now use this

term in Equation A6.5 to yield

MR = - ` a dP dQd

* Qdb ` + P = P - ` a dP dQd

* Qdb `

Next, multiply the absolute value term by 1 in the form PP. Then distribute the P term in the denominator of this fraction into the denominator of the term in the absolute value. That leaves a P multiplying both terms, which can be moved outside the parentheses. Equation A6.6 shows these changes step-by-step:

MR = P - ` a dP dQd

* Qdb ` * P P = P - ` adP * Q

d

dQd * P b ` * P = P * c1 - ` adP * Q

d

dQd * P b ` d A6.6

Finally, recall the equation for the price elasticity of demand from the appendix to Chapter 3,

e = ` dQd * P Qd * dP ` . In Equation A6.5, however, the term in the absolute value, ` a

dP * Qd

dQd * Pb ` , is not the price elasticity of demand, e, but rather its reciprocal, 1>e. Use this result in Equation A6.6 to arrive at Equation A6.4:

MR = P * a1 - 1 e b = P * a e - 1

e b

C. Maximizing Profit The profit-maximization rule from Chapter 5—produce so that MR = MC—remains true in this chapter even though the firms in this chapter possess market power. Profit equals total revenue minus total cost, or

Profit1Q2 = TR1Q2 - TC1Q2 As in the previous chapter, to maximize profit take the derivative of Profit(Q) with

respect to Q, and set it equal to zero:

dProfit

dQ =

dTR dQ

- dTC dQ

= 0 A6.7

In Equation A6.7, dTRdQ is MR and dTC dQ is MC, so Equation A6.7 can be rewritten as

MR - MC = 0 1 MR = MC A6.8

which is, of course, the same result presented in this chapter as well as in Chapter 5. This der- ivation shows that producing so that MR = MC maximizes profit for any type of firm with market power—a monopoly, a dominant firm, or a monopolistically competitive firm—even though their demand curves differ. For example, a dominant firm faces the residual demand, while a monopoly faces the market demand. Although these demands differ, producing where MR = MC maximizes profit for both types of firms.

For perfectly competitive firms as well as firms with market power, the profit-maximizing price is the highest price that allows the firm to sell the quantity produced. For perfectly

270  CHAPTER 6 APPENDIX The Calculus of Profit Maximization for Firms with Market Power

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competitive firms, that price is determined by the market. Firms with market power, however, must determine what price to set. The method you can use depends on the information you possess. If you have an estimate of the demand for your product, you can use the profit- maximizing quantity in the demand to determine the price to set. Alternatively, if you know your price elasticity of demand and marginal cost, you can use the results in Equations A6.4 and A6.8 to determine your price. In particular, using the profit-maximization condition in A6.8, MR = MC, as a substitute for MR in Equation A6.4 gives

MC = P * a e - 1 e

b

Then, as in the chapter, divide both sides by e - 1e :

P = MC * e

e - 1 A6.9

Equation A6.9 shows you that the profit-maximizing markup of price over marginal

cost is e e - 1.

D. Maximizing Profit: Example Vertex is a medium-sized pharmaceutical company. One of Vertex’s major products is Kalydeco, the first drug to treat a genetic cause of cystic fibrosis rather than just its symptoms. For the patients with the specific genetic flaw treated by Kalydeco, no other drug is a close substitute. The patents protecting Kalydeco have over a decade before they expire, so Vertex has a monopoly in the production of Kalydeco. Suppose that you are working for a company similar to Vertex with a monopoly in the production of a lifesaving drug. You are in the department charged with setting the price and quantity for your company’s drug.

The profit-maximizing quantity sets MR = MC, so you need to determine the marginal revenue and the marginal cost. Your research analysts estimate that the demand for your drug is equal to

Q = 2,050 - 0.002778P A6.10

where Q is the quantity of prescriptions demanded per year and P is the price. The analysts also estimate that the total cost of producing your drug is equal to

TC = 0.086Q3 - 124Q2 + 8,000Q + 50,000,000 A6.11

To calculate the marginal revenue, dTRdQ , start by solving Equation A6.10 for P. Subtract

2,050 from both sides of the equation and then divide by -0.002778 to obtain

P = 737,941 - 360Q A6.12

The inverse demand function in Equation A6.12 shows the price, P, as a function of the quantity, Q. Total revenue equals P * Q, so multiply the expression for P in Equation A6.12 by Q to get total revenue:

TR = 1737,941 - 360Q2 * Q = 737,941Q - 360Q2 A6.13 Finally, use the power rule to take the derivative of total revenue in Equation A6.13 with

respect to quantity to find the marginal revenue function:

MR = 737,941 - 720Q A6.14

Next, use Equation A6.11 to calculate the marginal cost, dTCdQ , by differentiating the total

cost in Equation A6.11 with respect to Q. Once again, using the power rule for derivatives gives the marginal cost function:

MC = 0.258Q2 - 248Q + 8,000 A6.15

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To maximize profit, you must produce the quantity that sets MR = MC; using Equations A6.14 and A6.15,

737,941 - 720Q = 0.258Q2 - 248Q + 8,000 A6.16

Rearrange Equation A6.16 by moving the terms on the left side to the right side:

0 = 0.258Q2 + 472Q - 729,941 A6.17

Finally, use the quadratic formula to solve Equation A6.17 for the profit-maximizing quantity, Q. This shows that Q equals 1,000 prescriptions per year.1

You also need to determine the profit-maximizing price. You do not have an estimate of the price elasticity of demand, but you do have the inverse demand function in Equation A6.12. Given Q = 1,000, you can use the inverse demand function to determine the profit-maximizing price: P = 737,941 - 1360 * 1,0002 = $377,941. Consequently, the profit-maximizing price is $377,941 for a yearly prescription for your company’s drug.

1 The other root of Equation A6.17 is −2,820, which is meaningless because the quantity must be positive.

Calculus Questions and Problems A6.1 Suppose that GNV Pool owns the only community

pool in Gainesville, Florida. The market demand for annual passes to this pool is

Qd = 600 - 2P

where Qd is the quantity of annual passes demanded and P is the per-pass price. GNV Pool knows that its total cost of providing annual passes is

TC1Q2 = 25,000 + 0.25Q2

a. What is the profit-maximizing price and quantity? b. What is the amount of economic profit or loss?

A6.2 You are a manager for PetCarry, a manufacturer of high-quality pet carriers. Your research department has given you the demand function for your pet carriers as

Qd = 10,000 - 100P

where Qd is the quantity of carriers demanded and P is the price. You know that your total cost of pro- ducing carriers is

TC1Q2 = 30,400 + 4Q a. What is the profit-maximizing price and quantity? b. What is the amount of economic profit or loss?

A6.3 Walter is an antitrust consultant. He currently works in a large European city with many other antitrust consultants. Walter is considering moving to Tampa, Florida, where there are currently several other anti- trust consulting firms. If Walter makes this move, he

will be competing in a monopolistically competitive market. Walter knows that the demand for his anti- trust consulting services in Tampa is

Qd = 1,700 - 5P

where Qd is the number of hours of antitrust con- sulting services demanded and P is the hourly price of antitrust consulting services. Walter’s total cost of setting up an antitrust consulting firm in Tampa and producing consulting services is

TC1Q2 = 20,000 + 160Q where Q is the number of hours of antitrust consult-

ing services that Walter supplies. a. If Walter were to open an antitrust consulting

firm in Tampa, what would be his marginal reve- nue from an additional hour of antitrust consult- ing services?

b. If Walter were to open an antitrust consulting firm in Tampa, what would be his marginal cost of an additional hour of antitrust consult- ing services?

c. What is Walter’s profit-maximizing number of antitrust consulting hours if he opens an anti- trust consulting firm in Tampa?

d. What is Walter’s profit-maximizing price for an hour of consulting services?