BUS 640 week 2 assignment

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Market Demand Analysis and Estimation

Learning Objectives

A�er reading this chapter, you should be able to:

Iden�fy the rela�onship between the demand curve and the demand func�on and between the demand curve and the total and marginal revenue curves. Discuss the rela�onship between price elas�city of demand and the change in total revenue for a price reduc�on or increase. Explain the concepts and usefulness for managerial decision making of income elas�city, cross-price elas�city, adver�sing elas�city, and other elas�ci�es of demand. Describe how primary data required for the es�ma�on of demand func�ons and curves might be collected using marke�ng research methods. Explain how regression analysis can be u�lized to es�mate the demand func�on using secondary data and how these es�mates can be used to derive the demand curve and various elas�city of demand measure.

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Introduction

The firm’s market demand for a par�cular product is the aggrega�on (or horizontal summa�on) of the demand curves of individual consumers for that

product.1 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/ch04introduc�on#footernote1) Managers need to understand the underlying determinants of market demand and, in par�cular, how responsive it is likely to be to changes in the firm’s controllable variables (such as the four Ps of marke�ng) and to changes in uncontrollable variables (such as changes in consumer incomes or the strategic ac�ons of rival firms), since the firm’s revenues depend on the market demand for its products. The sensi�vity of quan�ty demanded to a change in an underlying determinant variable is known as an elas�city of demand. Elas�ci�es of demand convey important informa�on to managers about the impact on market demand (and hence on the firm’s revenues) due to changes in controllable and uncontrollable variables. In this chapter we will inves�gate several elas�ci�es of demand that are of interest to prac�cing managers.

In the second half of this chapter, we concern ourselves with the es�ma�on of market demand for the firm. Managers need to es�mate the volume of demand in the current and future periods so that they can plan effec�vely for hiring and training employees, ordering raw materials, expanding physical plant and equipment, introducing new products, replacing obsolete products, and so on. Es�ma�on of market demand involves gathering data and interpre�ng that data to provide a numerical es�mate of demand in the current and future �me periods. We consider the gathering of data via interviews, surveys, and market experiments, as well as the use of regression analysis to es�mate the responsiveness of quan�ty demanded to changes in the firm’s controllable and uncontrollable variables.

1. For example, hundreds of consumers might buy 0, 1, 2, 3 or more units each at the price of $10 per unit, and in aggregate the market demand might be, say, 680 units at price $10. At a lower price, for example, $9, these consumers might increase their quan�ty demanded by one or a few units each, such that market demand is, say, 920 units. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/ch04introduc�on#return1) ]

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4.1 The Demand Function and the Inverse Demand Curve

To clarify terms, note that the demand func�on refers to the rela�onship that exists between the quan�ty demanded of a par�cular product and all the determinants of that demand that we discussed in detail in the preceding chapter. The demand curve, on the other hand, refers to the rela�onship that exists between the quan�ty demanded of a par�cular product and the price of that product, with all other determinants held constant. The demand curve is thus a subset of the demand func�on where ceteris paribus applies to all determinants except price. As noted in Chapter 3, when we simply say "demand for a product," we will generally mean the demand curve for that product. So that if we say "a change in demand" or "demand has changed," we will mean that the demand curve for that product has shi�ed. To reiterate, changes in price cause movements along the demand curve, while changes in all other determining variables cause a shi� of the demand curve.

Controllable and Uncontrollable Variables That Affect the Demand Curve

In Chapter 3 we considered the main determinants of consumer demand. Those that are controllable by the firm are the four Ps of marke�ng, namely price, product design (or quality), promo�on, and the place of sale (distribu�on system). We saw that changes in price cause a movement along the consumer’s demand curve, while changes in the other controllable variables (and in uncontrollable variables) will cause a shi� of the consumer’s demand curve. Since the market demand curve is the horizontal summa�on of these individual consumer demand curves, we expect the market demand curve to shi� in the same direc�on (as individual demand curves) when these "demand shi�ers" change. The direc�on of the shi� for each of the other three Ps is summarized in Table 4.1.

Table 4.1: Controllable shi� variables for the firm’s demand curve Controllable shi� variable Demand curve will shi� outward for: Demand curve will shi� inward for:

Promo�on and adver�sing Promo�onal campaigns that mo�vate consumers to buy the product for the first �me, or to buy more of it

Reduc�ons in promo�onal ac�vity or unsuccessful promo�on that upsets people and turns them against the product

Product design or quality Product design changes that are perceived as enhancements by the market

Perceived reduc�ons in product design or quality aspects

Place of sale (distribu�on) Changes to the distribu�on system that makes purchasing more convenient for the customer

Changes to the distribu�on system that reduce convenience or accessibility

In addi�on, a variety of uncontrollable variables affect the firm’s demand. These uncontrollable variables can be discussed under three main headings, namely (a) ac�ons by related-product firms; (b) consumer variables; and (c) changes in the business environment.

Price and Nonprice Ac�ons of Related-Product Firms

As we saw in Chapter 3, related products are those that are either subs�tutes or complements for the focal firm’s product. Producers of subs�tute products are in direct compe��on with the focal firm—their ac�ons that increase demand for their products will simultaneously reduce the demand for the focal firm’s product. For example, if Ford reduces the price of its line of compact sedans it will sell more of these, but General Motors, Toyota, and other rivals will sell fewer compact sedans a�er consumers adjust their purchases to maximize their u�lity. The impact on quan�ty demanded due to a subs�tute

product’s price reduc�on may, in some market situa�ons,2 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#footernote2) lead to a retaliatory price reduc�on by the focal firm (and by other compe�tors), perhaps followed then by another price reduc�on by the firm that ini�ated the price cu�ng. We call this price compe��on, and if the price cu�ng con�nues it might degenerate into a price war. In extreme cases prices may be driven down to below costs and all firms might lose money. Since this is a predictable outcome, firms are usually sensible enough to avoid being drawn into a price war and usually try to increase their demand by adjus�ng one of the remaining three controllable variables.

Adjus�ng the nonprice controllable variables (i.e., product design, promo�on, and place of sale) is called nonprice compe��on and this is the most common form of compe��ve rivalry in most markets. Whereas price compe��on is reac�ve and immediate, nonprice compe��on is proac�ve and delayed—it takes �me and talent to design increased quality into the product, to develop and execute an effec�ve promo�onal campaign, or to set up new distribu�on channels. Since it takes �me to retaliate to nonprice compe��on, and since the success of such retalia�on is not at all assured (in prospect), firms that ini�ate nonprice compe��on usually benefit from the change they have ini�ated for a considerable period of �me and thereby earn financial payback on the investment they have made in changing product design, promo�on, or other nonprice variable.

Producers of complementary products should also be expected to adjust their controllable variables in their own best interests, but in this case what is good for the complementary firm is also good for the focal firm. As we saw in Chapter 3, ac�ons by complementary firms that increase the demand for their products will also increase the demand for the focal firm’s products, and oppositely, ac�ons that reduce demand for the complement will also reduce demand for the focal firm’s product. For example, if interna�onal airfares to France were reduced (increasing the quan�ty demanded of air travel to France) the demand curve for French hotel accommoda�on would shi� to the right, increasing the quan�ty demanded at any price. Conversely, if the price of French hotels went up significantly, for example due to the reduced value of the U.S. dollar in terms of the Euro, the demand

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Since consumers adjust their purchases to maximize their u�lity, when a subs�tute firm reduces its price, it will sell more, and the focal firm will sell less, leading to price compe��on.

Winning the Fare War

Purchasing behavior is shaped by consumer expecta�ons. A homeowner might take on a larger mortgage because he or she expects to afford the future loan payments.

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curve for air travel from the United States to France would shi� to the le�, causing a reduced quan�ty demanded at the current airfare levels.

Consumer Variables: Incomes, Tastes, and Expecta�ons

As we saw in the preceding chapter, increases in consumers’ incomes will cause increased quan�ty

demanded for superior3 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#footernote3) products (by defini�on), while increases in consumer income will cause reduced quan�ty for inferior products (by defini�on). Thus, if the focal firm’s product is an inferior product, then demand for this product will move oppositely to changes in consumer incomes. When consumers’ incomes are generally rising, as in a period of macroeconomic expansion, the firm’s demand should be expected to fall as its customers switch to a superior subs�tute, and conversely when consumers’ incomes are falling, as in a recession, the demand for an inferior good should be expected to increase. Macroeconomic expansions and recessions, also known as the business cycle, are likely to cause changes in the incomes of many (but not all) consumers, but note that consumers might at any �me receive salary increases or bonuses, or conversely work fewer hours or lose their jobs

and thus suffer reduced incomes, independent of the general trend of macroeconomic condi�ons.4

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#footernote4)

Consumers’ tastes may change and cause the quan�ty demanded of the firm’s product to increase when tastes change in favor of that product, or oppositely cause the quan�ty demanded to fall when tastes change against the firm’s product. As we learned in Chapter 3, consumer tastes relate to a�ributes of the product which consumers see as benefits offered by the product. Their "tastes" are really a euphemism for the u�lity they expect to gain from the consump�on of the product, and underlying that is the u�lity they expect to gain from the a�ributes of the product. Changes in tastes are usually prompted by new informa�on, such as a medical report showing that carotene is related to the preven�on of cancer, or that saturated fats are related to heart disease. Similarly, if the firm engages in "green" prac�ces to save the natural environment, its brand name may be viewed more favorably by at least some consumers and it should expect increased market demand as a result. Conversely, if a firm pollutes the environment or prac�ces discrimina�on in its workforce, it should expect a nega�ve change in tastes for the firm’s products for at least some of its customers, and hence, there will be a le�ward shi� of

its demand curve.5 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#footernote5)

Consumer expecta�ons underlie their purchasing behavior. For example, if a person expects to con�nue earning a salary, he or she might take on a large mortgage for a new house, or take a loan to buy an expensive luxury car, because he or she expects to be able to afford the loan payments into the future. If these expecta�ons change, for example due to a global financial crisis, he or she might want to proceed more cau�ously and subsequently defer or cancel such purchases. Consumers will also form expecta�ons about future price and quality levels and should be expected to defer purchases into a future period if they expect prices to fall substan�ally or quality to improve substan�ally. For example, if a firm announces that next month it will put its products on sale, it should expect to experience reduced demand in the current month because at least some consumers will defer their purchase of these products un�l next month. On the other side of the coin, expecta�ons of quality reduc�ons or price increases in future periods might arise and cause the consumer to accelerate purchases of some products rather than buy lesser quality or at higher prices in later periods. The same applies for expecta�ons of limited availability (shortages) of preferred products in the future—consumers will tend to stock up in advance rather than be unable to buy the product in a future period.

Changes in the Business Environment

In this sec�on we will discuss changes that could happen in the firm’s external business environment and consequently affect demand for its product (see Table 4.2). Ac�ons by governments may lead to changes in demand for the firm’s product. Governments pass new laws and regula�ons banning some products, legi�mizing others, and manda�ng consump�on of s�ll others, such as seat belts in cars. Governments take ac�on to discourage consump�on of cigare�es, alcohol, and drugs. A government might prohibit or place temporary restric�ons on trade with par�cular na�ons, or, oppositely, open trade rela�ons with na�ons that were previously closed. As an example of government regula�on, increasing social concern over global warming has led various governments to implement "carbon taxes" that will have a detrimental impact on the demand for products that have a rela�vely large carbon footprint as consumers switch to suppliers that have smaller carbon footprints. Similarly, new taxes in some countries on fat in food will reduce demand for foods with rela�vely high-fat content.

Growth in popula�on will typically mean more demand for a firm’s product, but demand for par�cular products is likely to be related to changes in the structure of total popula�on. Demographic change refers to variables such as age, ethnicity, gender, geographic distribu�on, and employment type thatProcessing math: 0%

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When severe snowstorms occur, sales o�en decline due to limited transporta�on and consumers choosing to stay at home or allocate their funds elsewhere.

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change over �me and are likely to affect the demand for products that are consumed more (or less) by a par�cular age, ethnic, gender, or regional group. For example, changes in the rela�ve size of an age cohort (i.e., people of the same age, or in the same five-year age bracket, such as 25–29 years old) occur due to changes in birth, death, immigra�on and emigra�on rates, such that a par�cular age cohort might be growing or shrinking in size. Thus, the market for things that a par�cular cohort consumes is likely to move in the same direc�on as the size of that age cohort. Where a firm’s product is targe�ng a rela�vely narrow age group (e.g., training wheels for bicycles typically used by kids 3–5 years old), changes in the size of this cohort (due to earlier changes in the birth rate) can be expected to significantly affect sales from year to year.

A third factor that impacts the external business environment for the firm is weather condi�ons. Severe snowstorms might paralyze the transporta�on system and cause electric power failures, meaning that sales will be lost as consumers stay at home or allocate their limited funds to blankets, snowplows, or household repairs. At the other extreme, heat waves cause a re-alloca�on of consumer expenditures toward air condi�oners and electricity to drive the air condi�oners at the expense of other expenditures. A recurring weather phenomenon with major economic impact is the cycle of El Niño and La Niña weather events that are due to the changing temperature of Pacific Ocean currents. In summary, products for which consump�on pa�erns are weather-related should expect to have increases or decreases in demand due to changing weather condi�ons. Finally, natural disasters, most prominently earthquakes and tsunamis, but also forest fires and floods, are low probability but high impact external events that cause massive infrastructure disrup�on and loss of life and property. They reduce demand for many firms as consumers delay or forego consump�on due to diver�ng their limited income towards other products that are necessary to rec�fy the damage caused by the natural disaster.

Table 4.2: Uncontrollable shi� variables for the firm’s demand curve Shi� variable Demand curve will shi� outward for: Demand curve will shi� inward for:

Prices of subs�tutes Price increases for subs�tutes Price reduc�ons for subs�tutes

Prices of complements Price reduc�ons for complements Price increases for complements

Nonprice compe��on by subs�tutes (rivals)

Changes in nonprice controllable variables that shi� the rival’s demand curve inward

Changes in nonprice controllable variables that shi� the rival’s demand curve outward

Nonprice compe��on by complements

Changes in nonprice variables that shi� the complement’s demand curve outward

Changes in nonprice variables that shi� the complement’s demand curve inward

Consumer incomes Increases in incomes (for superior goods) OR decreases in income (for inferior goods)

Decreases in incomes (for superior goods) OR increases in income (for inferior goods)

Consumer tastes Changes of consumer tastes in favor of the focal firm’s product (or its a�ributes)

Changes of consumer tastes away from the focal firm’s product (or its a�ributes).

Consumer expecta�ons Changes in expecta�ons that cause consumers to buy now rather than in a future period

Changes in expecta�ons that cause consumers to postpone purchases into a future period

Ac�ons by governments Changes to laws or regula�ons that encourage consump�on of the product

Changes to laws or regula�ons that discourage consump�on of the product

Demographic changes Increases in the age and gender cohorts that buy the focal firm’s product

Decreases in the age and gender cohorts that buy the focal firm’s product

Weather condi�ons Changes in weather pa�erns or condi�ons that cause more to be demanded

Changes in weather pa�erns or condi�ons that cause more to be demanded

Natural disasters Events causing damage that requires purchase of products necessary to cope with the damage caused by the event

Events that cause consump�on of a product to be impossible or inappropriate to consume

The Form of the Demand Function

We are now ready to consider the business implica�ons of the demand func�on, which we shall express in mathema�cal forms as shown in equa�on 4-1. You may be alarmed to think we are about to embark on a mathema�cal discussion; but fear not, the symbols are used as a shorthand way of iden�fying the variables and will serve to facilitate our discussion, which in turn will facilitate your understanding of the important issues. Let us express the demand

func�on6 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#footernote6) in symbols as:

QDx = α + β1PX + β2PY + β3AX + β4AY + β5GNI (4-1)

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Where QDx represents the quan�ty demanded of product X (the dependent variable); α (alpha) represents the part of QDx that is unexplained by the independent variables listed; β1 − β5 (the betas) show the impact of a one unit change in each independent variables (PX and PY; AX and AY) on QDx; PX and PY represent the prices of products X and Y, respec�vely; AX and AY represent the adver�sing expenditures for product X and Y, respec�vely; and GNI represents the level of Gross Na�onal Income.

Demand es�ma�on techniques (to be introduced later in this chapter) allow us to es�mate the values for a and the various bs, such that, if we know the current values of the independent variables (those on the right hand side), we can predict the value of the dependent variable, in this case QDx. For now,

let us suppose that we have collected data on the independent variables shown in equa�on 4-1 and have conducted mul�ple regression analysis to find the following values for a and the various bs for a par�cular product:

QDx = 5,030 − 3,806.2(PX) + 1,458.5(PY) + 256.6(AX) − 32.3(AY) + 0.18(GNI) (4-2)

Suppose we want to predict demand (QDX) for the current month using this demand func�on es�mated from recently collected data. First, we will subs�tute

into this equa�on the current values for the independent variables—suppose these are PX = $8; PY = $6; AX = $168 (thousands); AY = $182 (thousands), and

GNI = $12,875 (billions).7 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#footernote7) Mul�plying each of these variables by the appropriate β coefficient, and summing the results, we would find QDx = 22,879 units, and this would be our predic�on for quan�ty demanded in the current month.

Since a demand curve shows the impact on quan�ty demanded for a change in PX with all other determinants held constant, we can isolate the impact of

price on quan�ty demanded by amalgama�ng the impact of the other variables into a single quan�ty, which we shall call AOV (for "All Other Variables"), and express the demand curve in the form QDX = AOV + βPX as follows:

QDx = 53,328.7 − 3,806.2(PX) (4-3)

Note that this expression for the demand curve depends on all other variables remaining constant, and we require this so we can isolate the impact on quan�ty demanded of price, alone.

The Inverse Demand Curve

Economists, following the conven�on set by the classical economist Alfred Marshall, tradi�onally draw the demand curve with price (the independent variable) on the ver�cal axis and quan�ty (the dependent variable) on the horizontal axis, which is opposite to the way mathema�cians like to draw graphs —they would place the dependent variable on the ver�cal (Y) axis and the independent variable on the horizontal (X) axis. The economist’s conven�on makes it easier to compare prices and costs in later chapters, however. To express equa�on 4-3 in terms of PX we will add 3,806.2PX to both sides, take QDX from both sides, and divide both sides by 3,806.2 to find:

PX = 53,328.7/3,806.2 − 1/3,806.2(QDx) (4-4)

This simplifies to PX = 14.011 − 0.000263(QDx). This very small coefficient to QDx is hard to comprehend, so for convenience we shall now express QDx in

units of one thousand, and rewrite this as:

PX = 14.011 − 0.263QDx (4-5)

The demand for product X is now expressed in the form of an inverse demand curve of the generic form:

PX = a + bQDx (4-6)

where a = AOV/−β and b = 1/β. If we now plot this inverse demand curve on a graph with PX on the ver�cal axis, it will intercept the ver�cal axis at 14.011

(since PX = 14.011 when QDx = 0). Further, from equa�on 4-3 above, we would find the horizontal intercept by no�ng that QDx = 53,328.7 when PX = 0.

These intercept values of the inverse demand curve serve to locate the demand curve at the correct height within the graph, as shown in Figure 4.1, so that this demand curve will provide useful results within the relevant range of prices, that is, for prices around the current price level. Note that, henceforth, we shall simply refer to it as the demand curve rather than repeatedly saying the inverse demand curve.

Figure 4.1: The inverse demand curve

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Total Revenue and Marginal Revenue

In Figure 4.1 you can see the full range of prices and quan��es demanded for the market demand curve. The manager will want to know what happens to total revenue (TR) when price is changed and whether TR will rise or fall when price is increased (or reduced). There is a simple rela�onship between the demand curve, the total revenue curve and the marginal revenue curve, which we will now demonstrate. In Table 4.3 we show several levels of price ranging from $14.011 (when QDx = 0) to zero, (when QDx = 53.328). Note that total revenue is equal to price �mes the quan�ty demanded, that is:

TR = PxQDx (4-7)

In Table 4.3 you will note that TR starts from zero (when nothing is sold), rises to a maximum when price is $7, and then falls all the way to zero again as price is reduced further. No�ce that TR is maximized at $186,795 halfway down the demand curve (where PX = $7, which is half of the ver�cal intercept

value and QDx = 26.685, which is half of the horizontal intercept value). You can see that TR rises in a smooth curve to its maximum value and then falls in a

smooth curve, as shown in Figure 4.2.

Table 4.3: Price �mes quan�ty demanded equals total revenue Price Quan�ty demanded Total revenue

     $14.011 0      $0

  $12 7,654 $91,848

  $10 15,267 $152,670

 $8 22,879 $183,032

 $7 26,685 $186,795

 $6 30,492 $182,952

 $4 38,104 $152,416

 $2 45,716 $91,432

 $0 53,329      $0

Now we consider marginal revenue (MR), which is defined as the change in total revenue for a one-unit change in quan�ty demanded. MR is important because it indicates "where the firm is" on the TR curve and the firm surely does not want to be on that part of the TR curve where total revenue is falling. Given the defini�on of MR above, we can express it in terms of TR and quan�ty demanded, as follows:

MR = ΔTR/ΔQDx (4-8)

where the symbol Δ (uppercase delta) signifies a discrete change in each of the variables indicated. You will quickly appreciate that MR is a measure of the slope of the TR curve, since ΔTR represents the rise of the TR curve and ΔQDx represents the run of that curve. Clearly the slope (and hence MR) is posi�ve

but falling as the TR curve rises at a decreasing rate (becoming progressively less steep) un�l MR = 0 when TR is maximized, and therea�er MR is nega�ve and takes increasingly larger nega�ve values as TR falls toward zero. In Figure 4.2 the MR curve is shown as star�ng at the ver�cal intercept and falling exactly twice as fast as the demand curve (since it cuts the horizontal axis at half the quan�ty demanded, i.e., about 26,685 compared to 53,328). The MR curve starts at about $14, frac�onally below the intercept value (which is 14.011) where the first unit is demanded, because the first unit sold caused TR to increase from zero to about $14. Thus, the MR curve can be represented as having the same ver�cal intercept as the demand curve and twice the slope of

the demand curve8 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#footernote8) as follows: Processing math: 0%

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MRx = a + 2bQDx (4-9)

Figure 4.2: Demand, total revenue and marginal revenue curves

What we learn from all this is that there is a happy medium in terms of the price to be set by the firm. If price is set "too high" on the demand curve, TR could be increased by reducing price, and oppositely, if price is set "too low" on the demand curve, TR could be increased by increasing price. But note that TR is not profit—we have not yet considered the costs of produc�on, so we are not yet ready to say exactly where on the demand curve the price should be set to maximize profits. We can readily see that the lower half of the demand curve is a bad idea. Marginal revenue would be nega�ve, so TR would be increased by moving to the upper half of the demand curve. But, the profit-maximizing price level will depend on the level of costs, as we shall see in Chapter 7.

2. Price wars are likely to happen in oligopoly markets (where there are rela�vely few compe�ng firms, such as the automobile market), which we examine in Chapter 7. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#return2) ]

3. Some texts use the term normal products to describe what we are calling superior products here. Later in this chapter we will see that superior (also known as normal) products can be divided into necessi�es, which increase by a lesser propor�on than does income, and luxuries, that increase by a greater propor�on than does income. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#return3) ]

4. The macroeconomic system tends to follow a cyclical pa�ern of faster growth followed by slower (or nega�ve) growth of gross na�onal product (GNP), followed by faster growth again. These cycles of economic expansion followed by recession are known as business cycles. Thus, we say that the demand for superior products is procyclical, meaning that it is generally in synchroniza�on with the business cycle, whereas the demand for inferior products is an�cyclical, meaning that it generally moves oppositely to the changes in GNP. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#return3) ]

5. Note that the firm’s brand name is an a�ribute of the product because it connotes informa�on about the firm’s a�tudes to business ethics, product quality, the natural environment, social equity and jus�ce, and so on. A brand name is effec�vely a stock of knowledge held by the consumer, so that new informa�on that enhances the brand is likely to result in increased demand for the firm’s product. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#return5) ]

6. Note that only some of the controllable and uncontrollable determinants of market demand are listed in this par�cular demand func�on. We suppose that either data could not be collected on the other independent variables, or that data collected on the other poten�al determinants revealed that these variables had insignificant impact on QDx for this product.

Also note that the linear (i.e., addi�ve) demand func�on depicted by equa�on 4-1 is just one form of the demand func�on—the actual form is an empirical issue, demand could be a nonlinear func�on of some variables, for example, it depends on what the data reveals when we es�mate the demand func�on. We use a linear demand func�on here for simplicity of exposi�on. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#return6) ]

7. We are using gross na�onal income (a macroeconomic concept) here as a proxy measure of the income levels of consumers of product X, assuming that their incomes would rise or fall in synchroniza�on with GNI. This is an oversimplifica�on, of course, but we note that GNI data is readily available and allows the manager to avoid the search costs of gaining actual data on changes in consumers’ incomes, which may be only slightly more accurate. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#return7) ]Processing math: 0%

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8. This is because TR is a quadra�c expression in Q, which we can specify by recalling from equa�on 4-6 that Px = a + bQDx and subs�tu�ng for Px into equa�on 4-7 we find TR = aQDX +

bQDx 2. Marginal revenue (MR) is the deriva�ve of the TR expression, so MR = a + 2bQDX. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.1#return8) ]

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4.2 Elasticities of Demand

Managers will be interested in the elas�city of demand with respect to each of the determining variables because these measure the rela�ve responsiveness of quan�ty demanded to a small change in a par�cular determining variable. Because many independent variables operate to determine quan�ty demanded, there are many elas�city measures that the manager will be interested in. We shall look at the main ones here, but you will see that an

elas�city value can easily be calculated for any variable that significantly influences demand.9 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#footernote9)

Price Elasticity of Demand

Price elas�city of demand is defined as the percentage change in quan�ty demanded divided by the percentage change in price. That is:

(4-10)

where ε (the Greek le�er epsilon) is the conven�onal symbol for price elas�city and Δ (the Greek le�er [capital] delta) represents a discrete change in the relevant variable. Expanding this out, we can equivalently say:

(4-11)

Cancelling the 100/1 terms and rearranging we find:

(4-12)

Now note that the first term in this expression (ΔQDx/ΔPx) is equal to β1 from the demand func�on, so:

(4-13)

Note that β1 shows the responsiveness of QDx to a small change in Px. Since β1 = −3,806.2 in our earlier example, we can say that a $1 increase in the price

of product X will cause a decrease in quan�ty demanded of 3,806.2 units. But note that elas�ci�es of demand are measures of rela�ve responsiveness, so

the β1 coefficient is weighted by the ra�o of price to quan�ty demanded to find the price elas�city value. 10

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#footernote10) Evalua�ng equa�on 4-14 for β1 = −3,806.2, Px = $8, and QDx = 22,879 we find ε = −1.331.

So, price elas�city is equal to the coefficient to price from the demand func�on weighted by the ra�o of price to quan�ty demanded. Since the ra�o of Px to QDx varies from infinity (when QDx = 0) to zero (when Px = 0) price elas�city must vary from very high nega�ve numbers to very low nega�ve numbers as

we move down the demand curve. We can see this in Table 4.4, using the data from the previous example.

Table 4.4: Price elas�city at various price levels PX QDx PX/QDx β1 ε

$14.011 0 ∞ −3,806.2 ∞

$12 7,654 1.568 −3,806.2 −5.967

$10 15,267 0.655 −3,806.2 −2.493

$8 22,879 0.350 −3,806.2 −1.331

$7 26,685 0.262 −3,806.2 −1.000

$6 30,492 0.197 −3,806.2 −0.749

$4 38,104 0.105 −3,806.2 −0.400

$2 45,716 0.044 −3,806.2 −0.167

$0 53,329 $0 −3,806.2 0

Note that the price elas�city values are nega�ve because β1 is nega�ve (due to the inverse rela�onship between price and quan�ty demanded). Also note

that the price elas�city rises from high nega�ve numbers to smaller nega�ve numbers as we move down the demand curve, and that ε = −1 at the midpoint of the demand curve. Talking about numerically larger nega�ve values can be confusing. A be�er way of communica�ng about price elas�city is to talk about it in absolute terms, ignoring the nega�ve sign. Thus, economists say the price elas�city gets higher (in absolute terms) as we move up the demand curve. For example, we say that price elas�city at price $12 is higher than it is at price $10, and so on. By conven�on we say demand is price elas�c above the midpoint of the demand curve (for ε > |1|, i.e., for values of ε greater than one in absolute terms) and conversely is price inelas�c below the midpoint

of the demand curve (for ε < |1|, i.e., for values of ε less than one in absolute terms).11 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#footernote11)

We can now summarize the rela�onships between price, price elas�city, total revenue, and marginal revenue that are apparent in Figure 4.2. If price elas�city is greater than 1 (in absolute terms) then the current price must be on the upper half of the demand curve; MR must be posi�ve; and TR willProcessing math: 0%

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Although caviar is a luxury good for many, this is not the case for everyone since everybody’s tastes and income levels are different.

© iStockphoto/Thinkstock

decrease for a price increase (or increase for a price decrease). Oppositely, if ε < 1 (in absolute terms) then the current price must be on the lower half of the demand curve; MR must be nega�ve; and TR will increase for a price increase (or decrease for a price reduc�on). Thus, price elas�city is a number that conveys a lot of useful informa�on to the managerial decision maker.

Income Elasticity of Demand

Income elas�city of demand is defined as the percentage change in quan�ty demanded divided by the percentage change in income (that caused the change in demand). That is:

(4-14)

where θ (the Greek le�er theta) is the conven�onal symbol for income elas�city. Following the earlier example we are using GNI (gross na�onal income) to represent the income level. Following the same procedure as before we can "cut to the chase" and simply say that:

(4-15)

where β5 is the coefficient to GNI from the demand func�on es�mated earlier as equa�on 4-1. Evalua�ng equa�on 4-15, using the earlier values of β5 =

0.18, GNI = 12,875, and QDx = 22,879, we find θ = 0.1013. Thus, according to our data, we expect that the responsiveness of demand to a one-unit change

(i.e., one billion) in GNI will be about 0.18 units of product X (i.e., the value β5), but that the rela�ve responsiveness (i.e., the income elas�city) is 0.1013.

The income elas�city implies that quan�ty demanded would increase by only about one tenth of 1% for a 1% increase in GNI (or 1.013% for a 10% increase in GNI), which is to say that quan�ty demanded is virtually unresponsive to changes in GNI. As with price elas�city, economists use the income elas�city value (θ) to provide informa�on over and above the responsiveness value, as we shall soon see.

From our earlier discussion of superior and inferior goods we know that product X must be a superior good since its quan�ty demanded increases when income increases. Indeed we could have concluded that simply by looking at the posi�ve sign of the β5 coefficient to income in the demand func�on. If on

the other hand, β5 had been a nega�ve number, we would know that the product was an inferior good. Note that some consumers may indeed consider

product X to be an inferior good but on balance the income elas�city shows it is a superior good, since the overall effect of an income change on quan�ty demanded is slightly posi�ve, and this overall effect is what the manager will want to know.

Luxury and Necessity Goods

We can make a further dis�nc�on within superior goods based on the size of the income elas�city. If θ is greater than 1, we say that the product is a luxury good. Values of θ > 1 mean that demand for the product increases by a larger percentage than the percentage increase in consumer incomes. For example, suppose your income is currently $100,000 and you buy caviar four �mes a year, spending say $400 a year on 20 ounces of caviar. Suppose your income rises by 10% to $110,000 a year, and you then increase your caviar consump�on to six �mes (30 ounces total) a year. The percentage increase in your demand for caviar is 50% and the percentage increase in your income is 10%, so θ = 5. As we suspected of course, this makes caviar a luxury good for you, but not necessarily for everyone, since everybody’s tastes and income levels are different. Extraordinarily rich people may already be buying as much caviar as they can eat and may respond to an increase in their incomes by not buying more, and most people on lower incomes will not be buying any caviar at all. Again, the manager will look at the aggregate change

in market demand when incomes change rather than the varia�on across consumers within his or her market.12

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Conversely, if θ is posi�ve but less than one we say that the product is a necessity good. In our earlier example product X would be classified as a necessity good, since θ = 0.1013. For necessity goods, demand certainly increases when income rises, but its rela�ve responsiveness is less than one. Examples of necessity goods include all basic foodstuffs, ordinary clothing, basic housing and transporta�on services, and other basic things that consumers need to buy to stay warm and stay well as they go about their normal lives whether working, unemployed, or re�red. Luxury goods are those subs�tute products that one aspires to but cannot afford while on rela�vely low incomes. For example, as income rises people might want to replace a low-status brand handbag with a high-status brand handbag, or replace cheap Scotch whisky with single-malt Scotch whisky. No�ce that the low-status handbag and the cheap Scotch are inferior goods for these people in these examples, since their quan�ty demanded for these products decreases as their incomes rise. But also note that these products are not necessarily inferior goods at the aggregate market level—for very poor people they might be luxury goods that can only be purchased as incomes rise from very low levels. Managers will want to predict changes in the market demand for their products when incomes change, and while this will include some people increasing and some people reducing their quan�ty demanded, they will want to be able to predict that the net effect will go one way (superior goods) or the other (inferior goods).

Cross-Price Elasticity of Demand

Cross-price elas�city of demand is defined as the percentage change in quan�ty demanded for product X divided by the percentage change in the price of a related product Y. That is:Processing math: 0%

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Price Elas�city

(4-16)

where η (the Greek le�er eta) is the conven�onal symbol for cross-price elas�city of demand. Following the same procedure as before we can say that:

(4-17)

where β2 is the coefficient to PY in the demand func�on shown earlier as equa�on 4-1. Evalua�ng equa�on 4-17 for the values of β2 = 1,458.5, PY = 6, and

QDx = 22,879, we find η = 0.382. Thus, according to our data, we expect that the responsiveness of QDx to a one-unit increase in PY (i.e., from $6 to $7), will

be 1,485.5 addi�onal units of X, but that the rela�ve responsiveness (i.e., the cross-price elas�city) will be 0.382. This implies that a 10% increase in the price of product Y would cause the quan�ty demanded for X to increase by about 3.82%, or conversely a 10% price reduc�on for product Y would cause the demand for product X to decline by about 3.82%. Thus product X and product Y are subs�tutes for each other—increases in the price of one would cause some consumers to switch from that product towards the other in order to maximize their u�lity.

To summarize, the sign of the coefficient to the price of a related product in the demand func�on (β2 in this example) and the sign of the cross-price

elas�city measure (η) indicates whether that product is a subs�tute or a complement for the focal product X. If the β coefficient and hence the cross-price elas�city had shown a nega�ve sign, we would know that product Y is a complement for product X, that is, X and Y are complementary in consump�on, meaning they are typically consumed together. The size of the coefficient will show the responsiveness of QDx to a one unit change in PY, and the size of the

cross-price elas�city measure will imply the percentage change in QDx for a one-percentage change in PY.

Other Elasticities of Demand

Because the es�mated demand func�on we introduced earlier provides data on the responsiveness of demand for product X to changes in adver�sing for product X, we can calculate the elas�city of demand with respect to the firm’s adver�sing expenditures. Again, the elas�city measure will be the percentage change in QDX divided by the percentage change in adver�sing,

but is more quickly calculated by weigh�ng the coefficient to the adver�sing variable in the demand func�on (β3) by the ra�o of the adver�sing expenditure (Ax) over the dependent variable

(QDx). Evalua�ng for β3 = 256.6, Ax = 168 (in thousands) and QDx = 22,879 we find the adver�sing

elas�city to be 1.884.

Thus, the responsiveness of quan�ty demanded to adver�sing expenditures is expected to be 256.6 addi�onal units of product X for every addi�onal $1,000 of adver�sing expenditure. The rela�ve responsiveness of demand to adver�sing is that a 1% increase in adver�sing would lead to a 1.884% increase in quan�ty demanded. But whether the firm should do any more adver�sing depends on how much each addi�onal unit of product X would contribute to the firm’s expenses

or contribu�on margin.13 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#footernote13)

Obviously it is only worth spending another $1,000 on adver�ng if the extra sales (256.6 units) contribute at least $1,000 (i.e., about $4 each per unit) to overhead and profit. The informa�on gained from the es�mated demand curve, plus informa�on gained from cost es�ma�on (see Chapter 6) will help the manager make the decision whether to change the adver�sing level or not. We shall also consider the firm’s adver�sing decision in Chapter 11.

Cross-Adver�sing Elas�city

The es�mated demand func�on also provided data on the impact of firm Y’s adver�sing on the quan�ty demanded of product X. The cross-adver�sing elas�city will be the coefficient (β4) to the AY variable in the demand func�on weighted by the ra�o of the independent variable (AY) over the dependent

variable (QDx). Evalua�ng for β4 = −32.3, AY = 182 (in thousands) and QDx = 22,879 we find the cross-adver�sing elas�city to be −0.257. Thus, the

responsiveness of quan�ty demanded of X to increased adver�sing expenditures by Y is expected to be −32.3 units of product X for every addi�onal $1,000 spent on adver�sing by firm Y, and the rela�ve responsiveness of demand for X to adver�sing by Y is that a 10% increase in adver�sing by Y would lead to a 2.57% decrease in the quan�ty demanded of X. Thus, the firm’s demand is not very sensi�ve to changes in the adver�sing of this rival firm. But managers at firm X need to know how vulnerable they are to increases in adver�sing (or promo�onal efforts more generally) by related-product firms, so they can decide on their own adver�sing policy. Should they spend more on adver�sing to win these customers back? Would it be worth it? That depends, again, on the contribu�on margin for product X. If it is thousands of dollars per unit of X (such as it might be for heavy machinery, MBA programs, or sales of luxury cars) then firm X may well find it more profitable to increase its own adver�sing, or reduce their price, to increase market share. On the other hand, if the contribu�on margin is rela�vely small it will not be worth either adjustment, given the costs of changing prices or moun�ng an adver�sing campaign. We defer resolu�on of this decision problem to Chapter 11.

Quality Elas�city of Demand

Finally, we will briefly consider the firm’s quality elas�city of demand. Quality elas�city is defined as the percentage change in quan�ty demanded of product X divided by the percentage change in the quality of product X. We argued in Chapter 3 that a perceived increase in quality would cause an outward shi� in the demand curve for individual consumers, and that this, in aggregate, would cause an outward shi� in the market demand curve. The manager will want to know "how far will the demand curve shi� if I increase product quality?" Keep in mind that increased product quality will typicallyProcessing math: 0%

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cause per unit costs to be higher, so again the manager will want to know "will an increase in quality lead to an increase in my profits?" In a simple example, suppose that increased quality causes variable costs to rise by $1 per unit, but the market will buy the same or greater volume at a price that is $1.25 higher than before, you can see that the firm will be more profitable as a result. In Chapter 11 we will look at more complex examples where there

are diminishing returns to adver�sing effec�veness and also where variable costs increase at higher levels of produc�on.14

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9. Elas�ci�es of demand are deduced from the values found in the demand func�on. Thus, although we have for convenience expressed QDx in thousands in the demand curve, we will

con�nue to express QDx in single units in the calcula�ons of the various elas�ci�es. Alterna�vely, we could divide each of the β coefficients by 1000 (e.g., β1 which was found to be

3,806.2 would be 3.8062), and so on, for the other coefficients. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#return9) ] 10. This is an important difference between the jargons of marke�ng and economics. When marketers speak of "price responsiveness," they usually mean the β1 value. Economists use the

term "price elas�city" to show the rela�ve responsiveness of ΔQDx to ΔPx and they use ε value to convey informa�on about the change in total revenue that is associated with a price

change, as we will see. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#return10) ] 11. Note that firms do not want to have their prices fall on the lower half of the demand curve, since MR is nega�ve and TR would be increased by raising price un�l it was higher than the

midpoint of the demand curve. As we shall see in Chapter 7, only firms opera�ng in oligopolies (few compe�ng firms) who expect heavy sales reduc�ons if they raise prices (because they expect their rivals to not follow their price increases) have to worry about that. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#return11) ]

12. Of course all caviars are not the same. There are quality differences that reside in the different a�ributes and a�ribute ra�os for the various brands of caviar. So a brand manager pursuing a niche marke�ng strategy will be very interested in the tastes and preferences of consumers in the targeted niche market, and it is the niche market’s demand, rather than the total market demand for all caviars, that is important to the manager. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#return12) ]

13. The contribu�on margin is the difference between price and variable cost per unit and represents the contribu�on that each unit of product X makes toward the firm’s overhead (fixed) costs and profits a�er the incremental variable costs have been covered. We will spend more �me talking about the contribu�on margin in the next two chapters. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#return13) ]

14. To include product quality as an independent variable in an es�mated demand func�on, the firm would need to have reliable data that reflects product quality. Assuming efficiency in produc�on (see Chapter 6), and other things remaining the same, such as the output rate, wages, and other input costs, the cost of goods sold per unit might be a sufficiently reliable indicator of product quality. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.2#return14) ]

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Focus groups are useful for uncovering new informa�on about buyers’ probable reac�ons to changes in price and other determining variables.

© Digital Vision/Thinkstock

4.3 Estimating Market Demand From Primary Data

In the remainder of this chapter, we will discuss methods that are used to obtain data rela�ng to the firm’s demand func�on so we can derive the coefficients that indicate the responsiveness of quan�ty demanded to each of the independent variables that collec�vely determine the firm’s demand. We begin by discussing direct methods of demand es�ma�on whereby primary data is collected from actual or poten�al buyers via interviews, surveys, and market experiments. Indirect methods of demand es�ma�on involve the sta�s�cal examina�on of data previously collected for official government sta�s�cs, or found in reports researched and wri�en for other purposes (so-called secondary data). We will discuss the use of regression analysis as a tool to quan�fy the dependence of quan�ty demanded on the independent variables in the demand func�on. Special a�en�on is given to the interpreta�on of the regression results and the avoidance of six major pi�alls of regression analysis.

Interviews, Focus Groups, and Surveys

The most direct method of demand es�ma�on is to simply ask buyers or poten�al buyers about their probable reac�ons to changes in price or other determining variables. Interviews usually follow a ques�onnaire to ensure that respondents provide answers to specific ques�ons. Ques�onnaire design is an art form and should not be treated lightly—unless the ques�ons are asked in words that the respondent fully understands, the results might not be reliable. Focus groups are less structured and are useful for finding new informa�on about what consumers want in terms of product design or their collec�ve response to planned price changes, for example. Usually the researcher will let conversa�on range freely within the focus group, le�ng people’s ideas and opinions emerge, and occasionally redirec�ng discussion back to issues of concern to the researcher. Surveys u�lize structured ques�onnaires and are administered either by mail, by telephone, by email, or via online survey tools such as SurveyMonkey.

Let us work through a simple example of a survey to find the demand curve for a new product. Suppose a firm plans to introduce a new product and wants to know how much would be demanded at various price levels. From the popula�on of poten�al buyers a random sample of 500 people is drawn, perhaps by contac�ng every 10th name on a list of probable buyers. Suppose we then contact these people a�er dividing them into five groups of 100 each. For each group we would describe the new product and its usefulness in the same way, but would state a different price for each group, as shown in Table 4.5. We would then ask them whether they would buy the product at the

price stated, and list the number of posi�ve responses in the table as shown.15

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.3#footernote15)

Table 4.5: Survey results for various suggested prices Sample Group 1 2 3 4 5

Price stated $6 $4 $5 $7 $8

Quan�ty demanded 198 305 262 155 97

These price–quan�ty coordinates would then be plo�ed, as shown in Figure 4.3, and a line of best fit would be drawn freehand across the data points. A line of best fit summarizes the apparent rela�onship between the two variables. We should not expect all (or any) of the observa�ons to lie exactly on the line of best fit. There is likely to be random varia�ons among the five groups that cause them to demand a li�le more, or a li�le less, than another group would have at the same price. We posi�on the line of best fit such that we think it minimizes the gap between the data points and the line. Then we note the intercept point on the price axis and the slope of the line of best fit. The intercept appears to be close to $10 and the slope appears to be roughly −1/50 = −0.02. Thus, our es�mate of the sample’s demand curve for this new product is Px = 10 − 0.02QDx.

Figure 4.3: Freehand line of best fit to price-quan�ty data pairs

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Hiring a marke�ng research firm to design a professional ques�onnaire is money well spent for managers contempla�ng large investments in new products, reposi�oning of product prices or quali�es, and product line extensions.

© iStockphoto/Thinkstock

But note that these results relate to a sample of only 500 people. To es�mate the demand curve for the en�re market we would mul�ply the slope term by the sampling propor�on. Suppose 5% (or one in 20 people) of the popula�on was sampled, so we need to mul�ply the slope term by 1/20 to arrive at an es�mate of the market demand curve, which would be PX = 10 − 0.001QDX. From this, we can easily determine that the horizontal intercept of the

es�mated demand curve occurs at about 10,000 units. Thus, marginal revenue would cut the horizontal axis at about 5,000 units, so that the total revenue curve would rise to a maximum of about ($5 × 5,000 units =) $25,000 (per period) and would then fall if price were to be reduced below $5.

Poten�al Problems With Interview and Survey Data

Survey methods may not lead to reliable results if any one of the seven following problems exists. First, we may not have a random sample of our target consumers. Methods exist to ensure that samples are sufficiently random, and tests can be made to ensure that sample selec�on bias or nonresponse bias are not likely to be present in the data (Hair, Black, Babin, & Anderson, 2010). A second problem is that answers reported to you directly (o�en called espoused data) by the survey respondent may be unreliable. The presence of the interviewer, or even the fact that someone later will see the answers given, may cause the respondents to be less than fully frank with their answers, which is known as interviewer bias. For example, people may overstate their income in order to seem more successful than they really are. A third problem is social desirability bias, that is, if the researcher asks a personal ques�on, the respondents might understate or overstate the true amount because they would be embarrassed to reveal the truth. Ques�ons about poli�cs, religion, income, and lifestyle are likely to induce a social desirability bias. A fourth problem is self-serving bias, where interviewees have the incen�ve to not reveal the exact truth since it might adversely affect future outcomes for them. For example, if a firm were to ask how much more would consumers pay for a 20% improvement in quality, respondents would have an incen�ve to say an amount smaller than what they really would be prepared to pay. A fi�h problem is disinterested or busy par�cipants who give random answers or rush through �cking boxes without really considering the ques�ons asked. Even if the answers given are completely truthful, a sixth problem is the best-of-inten�ons problem whereby the respondents say what they believe they will do (e.g., I will buy the product at a price of $7) but do not subsequently actually buy it due to the interven�on of other issues, such as losing a job or discovering another product that is a be�er value proposi�on. Finally, the responses may be unreliable if the ques�ons are confusing, misinterpreted, or unknowable. New products, when described briefly for the first �me, may not easily be imagined by consumers as part of their lifestyle or work environment. For example, IBM vastly underes�mated the demand for its personal computers in the early 1980s a�er surveying hundreds of business execu�ves who saw the desktop computer simply as a fancy typewriter for their secretaries.

To combat these problems, it is important to design the ques�onnaire carefully, which is best done by experts. Marke�ng research firms, or freelance consultants specializing in survey design, can be u�lized to design ques�onnaires that will minimize these problems; for example, rather than asking ques�ons about price directly, the ques�on might ask about "value" (recall that value equals quality over price) that consumers perceive in a series of price–quality combina�ons. Money spent on professional ques�onnaire design will be money well spent for managers contempla�ng large investments in new products, reposi�oning of product prices or quali�es, product line

extensions, and so on (Hair et al., 2010).16 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.3#footernote16)

Simulated Market Situations

Marketers o�en conduct simulated market situa�ons, also known as consumer clinics, where they construct an ar�ficial shopping environment and observe the choices of customers, while varying the prices of some products, the shelf placement of products, and point-of-purchase informa�on about product quality, for different groups of shoppers. Par�cipants are usually a�racted to these experiments by the promise of free products; for example, they may be given $100 of "monopoly money" to spend as they wish within an hour. Researchers monitor hidden cameras to observe shopping behavior and tally up the purchases at the cash register on the way out. If the par�cipants are randomly drawn from theProcessing math: 0%

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Direct marke�ng occurs when the producer of the product sells directly to the consumer. This can be accomplished through Internet sales, newspapers adver�sements, or direct mailings sent in the mail.

© Jerry Arcieri/Corbis

popula�on of poten�al customers for the focal products, market researchers may conclude that the en�re market would react to price changes and changes in other product a�ributes in the same way. The quan�ta�ve results of a simulated market experiment (e.g., how many units of X were purchased by each sample of 100 shoppers) can be analyzed in the same manner as above for the survey data, with an es�mated line of best fit scaled up to reflect the ra�o of sample size to the popula�on of poten�al customers for the focal product. Similarly, for different quali�es of the same product, higher shelf placement, and end-of-aisle placement, the researchers could mul�ply the sample groups’ responses to es�mate the overall market’s response to changes in these

variables.17 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.3#footernote17)

Market Experiments

Market experiments involve real people in real markets spending their own money on the products they probably really do want. The firm will select a specific city or region that is representa�ve of other ci�es or regions or perhaps is representa�ve of the en�re na�on (e.g., San Diego is said to be quite representa�ve of southern California). The firm then introduces a new price, or new quality (i.e., changed a�ributes) of its product, or new promo�onal campaign into all stores in this test market (via its established distribu�on systems), and observes the impact on quan�ty demanded in that city or region. The firm then predicts a similar result will occur in other ci�es or regions that are similar to the test market, perhaps proceeding to a "na�onal rollout" to the en�re market. Such experiments are obviously very large scale and will require a large investment that may be lost if the experiment is not successful or conducted well. On the other hand, such market experiments limit the poten�al loss to only some frac�on of what it might be if the firm had gone directly to a na�onal rollout. Thus, market experiments can be used to validate managers’ decisions about changes in controlled variables in a limited context before they embark on full-scale implementa�on of the changes. As we saw in Chapter 2, managers will want to integrate such risk considera�ons into their decision making.

Direct Marke�ng Experiments

Direct marke�ng occurs when the producer of the product sells directly to the consumer of the product rather than u�lizing conven�onal distribu�on channels that involve wholesalers and retailers as intermediaries between the producer and the consumer. An example of direct marke�ng is Internet sales direct from the manufacturer to the consumer, and many retailers also sell products via their Internet websites. However, many people s�ll read newspapers, magazines, and le�ers sent to them via "snail mail," and these remain effec�ve vehicles for direct marke�ng experiments. Researchers send different price and quality offers to different poten�al customers, who then decide whether to buy the product at the price and quality they have been offered. Researchers expect to find a nega�ve price effect and a posi�ve quality effect, of course, but it is a measure of the extent of those effects (i.e., the responsiveness of demand to the changes made) that they seek. For example, a firm might want to test three different price points and two different quality points before choosing one price–quality combina�on to commit to full-scale produc�on. It would send mail to, call, or email all six possible combina�ons as an offer (only one offer to each person) to individuals on its mailing, telephone, or email list, or social network. By making different offers to different poten�al customers and tallying up the actual sales made for each combina�on, the firm’s managers would es�mate the price effect and the quality effect and decide which combina�on to proceed with.

Internet websites allow firms to compile a list of poten�al customers by encouraging people to ask for further informa�on or a price quote, and consumers must supply their email address to receive an answer. Since those customers are typically not connected to each other, or are not likely to communicate with each other effec�vely, they are not likely to know that the firm is making mul�ple offers and will typically make up their own mind on the basis of the offer made to them. Similarly, special-interest magazines and na�onal newspapers that are printed in two or more loca�ons to save freight and postage cost, or are printed in two or more print runs, can contain different adver�sements for the same product being read by different poten�al customers, with subsequent sales data providing informa�on on the price effect, quality effect, impact of packaging or promo�onal changes, and so on.

15. Rather than a Yes/No answer, we might ask the respondent to choose a point on a 1–5 scale where 1 = not at all likely to buy; 2 = somewhat likely to buy; 3 = not sure; 4 = quite likely to buy; and = 5 very likely to buy. We would then record in a table the number of people who chose either 4 or 5. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.3#return15) ]

16. Market researchers o�en use "conjoint analysis" to provide data that is revealed by choices among alterna�ves, rather than simply espoused. Respondents consider several product a�ributes conjointly (i.e., together, in the context of each other). For example, the manager might want to know whether consumers value higher product quality and increased purchasing convenience enough to warrant charging a higher price. In the experiment, the level of price, quality, and convenience of purchasing are varied across mul�ple scenarios. For example, scenario 1 might be stated as high price, high quality, and high convenience (i.e., high-high-high), while scenario 2 might be stated as low-high-high; scenario 3 as high- high-low; and so on. Respondents are asked to rate the a�rac�veness of each scenario on a 1–7 scale ranging from 1 = highly una�rac�ve to 7 = highly a�rac�ve. The conjoint method assigns values to the high se�ng for each of the three variables to find revealed a�tudes to high price, high quality, and high convenience. These will reveal whether the disu�lity of the higher price is offset by the increased u�lity associated with the higher quality and higher convenience. See Hair, J.F., Black, W.C., Babin, B.J., and Anderson, R.E. Mul�variate Data Analysis, Pearson, 2010. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.3#return16) ]

17. Again, such results are not always reliable, for three main reasons: First, the samples may not be a random sample of the overall market, perhaps under-represen�ng consumers who (a) are working and cannot par�cipate during the day, or (b) that have higher incomes and don’t consider $100 worth of free products worth the trouble, or (c) that value their privacy highly. Second, people may spend other people’s money differently than how they spend their own, and might decide to buy luxury goods in the market simula�on that they would not buy from their own income. A third problem is that these market simula�ons are very expensive. Hundreds of shoppers take away thousands of dollars worth of products. It is expensive to set up ini�ally and to monitor the "store." [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.3#return17) ]

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4.4 Regression Analysis of the Demand Function

Regression analysis calculates a mathema�cal equa�on that best summarizes the rela�onship exis�ng between two or more variables. Bivariate regression analysis, also known as correla�on analysis, calculates the rela�onship between two variables, such as price and quan�ty demanded, and provides an equa�on that specifies the intercept and slope terms of the line of best fit to the data. In the simple two-variable case, it is quite easy to sketch in a freehand line of best fit for a small number of observa�ons as we did in Figure 4.3. But imagine if you had 100 or more data points; it would take a long �me to carefully plot them on a graph before you even got to the point of sketching in the line of best fit, and so we rely on computers to quickly and accurately produce the parameters of the line of best fit. Mul�ple regression analysis, that is, with mul�ple independent variables, effec�vely provides the responsiveness coefficients (β) of the rela�onships between quan�ty demanded and each of the independent variables in the demand func�on, so that the impact on demand of all the independent variables can be found simultaneously, with all other independent variables effec�vely held constant. The Excel spreadsheet package (with a sta�s�cal add-in module) can accomplish bivariate or mul�ple regression analysis in milliseconds once you have arranged the data in columns. More powerful sta�s�cal so�ware packages, such SPSS or STATA, are generally used by academics and other researchers, but these rather expensive programs are less likely to be provided in a business firm, or, if you are self-employed you would have to buy one of those packages separately.

For our purposes here, Excel is more than enough.18 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#footernote18)

To illustrate how a computer regression program finds the line of best fit, we shall start with a simple two-variable (bivariate correla�on) case, where Y depends on X. In Figure 4.4, we show several Y,X data points plo�ed on a graph with the line of best fit shown as Y = A + βX. The ordinary least squares method posi�ons the line of best fit such that it minimizes the sum of the squared devia�ons of the observa�ons from the line—the devia�ons are squared to avoid posi�ve devia�ons offse�ng nega�ve varia�ons and to more heavily weight the larger devia�ons. A computer regression program calculates the sum of the squared devia�ons in a few milliseconds, and effec�vely compares different loca�ons of the line of best fit (or the mul�variate analog) and selects the one that minimizes the sum of these squares. Essen�ally, the mathema�cal procedure passes the line through the point represen�ng the mean values of the Y and X observa�ons (which we call Y-bar and X-bar), and then pivots that line around this mean–mean point to find the slope (and thus the intercept) that minimizes the sum of the squared devia�ons from the line. A similar process is involved for mul�ple regression analysis. The mathema�cal procedure can be imagined to pivot the lines of best fit between the dependent variable Y and each of the mul�ple independent variables simultaneously un�l it finds the values for the various β coefficients that minimize the sum of the squares of the devia�ons (which are also known as the residuals or error terms).

Figure 4.4: Ordinary least-squares method of fi�ng the line of best fit

Statistics Provided by Regression Software

Before we use Excel to find the coefficients for a demand func�on, we need to consider some sta�s�cs that are provided by regression analysis and that allow us to judge how well the line of best fit actually fits the data, and how reliable are predic�ons that are made based on the data.

The Coefficient of Determina�on (R2)

The coefficient of determina�on indicates the explained variance of Y, that is, the propor�on of the varia�on in Y (from its mean value) that is explained by

the variance in X (or mul�ple X variables) from its (their) mean value(s). In effect the coefficient of determina�on, commonly called R2, tells us how well the

regression equa�on fits the data.19 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#footernote19) The value of R2 will be between 0 and 1; for example, an Processing math: 0%

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R2 of 0.98 would indicate an amazingly good fit to the data, such as we saw in Figure 4.3. By contrast, the R2 for the data shown in Figure 4.4 is probably only about 0.6, indica�ng that only 60% of the variance in Y is explained by variance in X. That means there is 40% of the variance that is unexplained by the X. This unexplained variance will be largely a�ributed to missing variables, that is, other determinants of Y for which data has not been collected or that were not entered into the regression analysis. A second cause of unexplained variance could be measurement error in the data. We have to be sure we are

measuring the variables correctly or we will introduce variance into the analysis.20 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#footernote20) For example, the use of GNI in the earlier example as a proxy for the incomes of the consumers in the target market is a fairly imprecise measure that almost certainly contains measurement error, since GNI includes business profits as well as household incomes and not all profits are paid out as dividends. To minimize measurement error we need to seek the most precise measure we can get for each variable and only use proxy variables when we have no be�er data available.

The Standard Error of Es�mate

The standard error of es�mate (Se) is a measure of the dispersion of the data points from the line of best fit. Using this sta�s�c we can calculate

confidence intervals around the predicted value of Y given a set of values for the independent variables. A confidence interval is a range of values that we expect the actual value of Y to fall within for every value of X within a par�cular sta�s�cal confidence level. We commonly use the 95% confidence interval to indicate the range, between a lower es�mate and an upper es�mate of the Y value (associated with any X value), within which we expect the actual value of Y to fall 95% of the �me.

Assuming that the error terms are normally distributed around the line of best fit, we can use the proper�es of the normal distribu�on to calculate the upper and lower points of the 95% confidence interval. As we saw in Chapter 2, a normal distribu�on will be a symmetric bell-shaped distribu�on of data points around the mean of those data points, and the height of the bell will be such that 68% of the observa�ons will lie within plus or minus one standard devia�on from the mean; and 95% of the observa�ons will lie between plus or minus two standard devia�ons from the mean; and 99.7% of the observa�ons will lie between plus or minus three standard devia�ons from the mean. Note that a standard devia�on is the square root of the variance of the observa�ons around the mean of a single variable. The standard error of es�mate is the analog when there are two or more variables—it measures the square root of the variance of the Y values around the predicted value given the observed values of the independent variables that cause that variance in Y. So, the 95% confidence interval around the predicted value of Y will be given by the predicted value of Y plus or minus two standard errors of es�mate. Put another way, there is only a 5% chance of the predicted value of Y falling outside that confidence interval for any selected value of X.

The Standard Error of the Coefficient

The standard error of the coefficient (Sβ) is a measure of the accuracy of the calculated value of the β coefficient generated by the regression analysis. For

mul�ple regression there is a Sβ value for each one of the independent (X) variables. If Sβ is rela�vely small, we can be more confident that the es�mated

value of β is close to the true value of β, and conversely, if it is rela�vely large we can have less confidence that the es�mated β is close to the true value. (The true value of the coefficients could be found if we were to survey the en�re popula�on of customers rather than just a sample). In short, Sβ is the

standard devia�on of the mean β observed for each independent variable from the sample. Again, using the proper�es of a normal distribu�on, we can establish confidence intervals around the es�mated value of β, and be confident at the 95% confidence level that the responsiveness of the dependent variable to changes of an independent variable will lie within the range described by the relevant β plus or minus two standard errors of the coefficient.

Using Excel to Conduct Regression Analysis

There are many sta�s�cs add-in modules that work with the Microso� Excel spreadsheet program that will make you quite capable of conduc�ng basic

regression analyses.21 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#footernote21) Let us now work through how to set up and conduct regression analysis using Excel. You would first open a new worksheet in Excel. Supposing you have 100 observa�ons, leave the top row empty and enter the numbers 1–100 down the first column (in cells A2, A3, A4, and so on down to cell A101). This allows us to refer to specific observa�ons by their iden�fying

observa�on number in case we later find there are serious outliers that need to be removed.22

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#footernote22) Then label the columns across the top of the spreadsheet with the variable names, star�ng with the dependent variable in cell B1, and the names of the independent variables in cells C1, D1, E1, and so on. Enter the data for the dependent variable observa�ons all the way down the second column (cells B2–B101), and then enter the independent variables corresponding to each observa�on down each of the columns to the right, as shown in Table 4.6.

Table 4.6: Se�ng up an Excel spreadsheet to conduct mul�ple regression analysis Obs’n Sales of X Price of X Price of Y Advert X Advert Y Income Avg. temp Exch. rate

1  9,637 6.99 6.99 128.4  96.3 3,100.2 48.4 1.0434

2 10,815 6.49 6.99 143.1  98.1 3,327.1 52.4 1.0889

3 12,886 5.99 5.99 165.9 120.8 3,654.7 64.8 1.1054

4  9,847 6.49 5.99 132.5 105.6 3,229.3 58.8 1.0226

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Leave a spare row below the last observa�on, and calculate the mean and standard devia�on for the dependent variable by entering =avg(B2-B101) and =stdev(B2-B101) in cells B103 and B104, respec�vely. Then enter =min(B2-B101) and =max(B2-B101) in cells B105 and B106, respec�vely to find the smallest and largest values for the dependent variable. To drag these formulas over to the right for the other data columns, highlight the cells B103–106, locate the small square in the bo�om right hand corner of cell B106 and drag it to the right, out to the last column of data. This should immediately produce the means, standard devia�ons, minima and maxima of the independent variables. We want to take a quick look at these sta�s�cs of the data to give us a feel for the data and to iden�fy any outliers. Looking down each column and comparing the data points with the above sta�s�cs might also reveal obvious data entry errors that we can fix before moving on.

To conduct the regression analysis we first move the cursor to a loca�on below the data so that the results will be posted there. We then go to the "Sta�s�cs" menu and pull down the "Regression" tab to iden�fy the algorithm we need. Clicking on that algorithm will place it in the chosen cell, and we then click on the column heading for the dependent variable (or highlight the data down that column), then in sequence iden�fy which of the independent variables are to be entered into the regression analysis. A�er all have been entered, close the bracket in the algorithm and press "Enter" and the calcula�ons will proceed. A table showing the results will appear in the chosen area of the spreadsheet. This will include the value of the α and the various

β sta�s�cs, as well as the R2, Se , and Sβ sta�s�cs.

We then observe and interpret these sta�s�cs. The α sta�s�c represents that part of the dependent variable that is due to all other variables that are not included in the regression equa�on. Each of the β sta�s�cs shows the responsiveness of the independent variable to the relevant independent variable, and the signs (posi�ve or nega�ve) should be as hypothesized; that is, nega�ve for the price effect; posi�ve for the other three Ps (if entered into the

equa�on)23 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#footernote23) ; either posi�ve or nega�ve for the income effect; posi�ve for the price of subs�tutes; nega�ve for the price of complements; nega�ve for the nonprice strategic variables of subs�tutes; posi�ve for the nonprice strategic variables of complements; posi�ve for suppor�ng business environment variables (such as popula�on growth) and nega�ve for damaging business environment variables (such as bad weather or new legisla�on).

From this data we are able to calculate the inverse demand curve (P = a + bQDx) by first calcula�ng the compressed form of the demand func�on (QDx =

AOV + β1Px) where AOV includes the impact of all other variables except Px, as detailed earlier in this chapter. The intercept term in the demand curve

expression is calculated as a = −AOV/β1 and the slope term of the demand curve is b = 1/β1. The marginal revenue curve is then MR = a + 2bQDx and the

total revenue func�on is TR = aQ + bQ2. We can also calculate the elas�city value for each independent variable as the responsiveness coefficient (β) �mes the ra�o of the relevant independent variable and the value for QDx, such as ε = β1. Px /QDx.

Pitfalls of Regression Analysis

There is an old expression "garbage in, garbage out" that certainly relates to regression analysis. If your data is garbage, your regression results will be too! I will briefly men�on here six common pi�alls of regression analysis that may compromise the accuracy of your results. Specifica�on errors relate to the hypothesized func�onal form of the regression equa�on. If you set up the equa�on in linear form, but in reality the dependent variable has a curvilinear rela�onship with any independent variable, or there are important missing variables, the output sta�s�cs of the regression analysis must be inaccurate. We have also previously men�oned measurement errors whereby the data collected is not an accurate measure of the variable that you want to measure. Next, if there is a simultaneous equa�on rela�onship, such as Y depends on X and simultaneously X depends on Z, we cannot expect a single equa�on to be a true reflec�on of a mul�ple-equa�on rela�onship. Mul�collinearity occurs when there is a significant correla�on between two or more of the supposedly independent variables—this violates a basic assump�on of regression analysis that the independent variables are independent of each other. Heteroscedas�city occurs when the variance of the error terms depends on the magnitude of the independent variables and is therefore not as assumed by the mathema�cs of regression analysis. Finally autocorrela�on (also known as serial correla�on) might occur in �me–series data and indicates that the error terms are serially related, that is, get progressively larger or smaller as �me increases.

Any one of these problems will seriously compromise your regression results. Fortunately, most of these problems can be fixed by respecifying the func�onal form of the equa�on; by collec�ng be�er data; by using a structural equa�on model (with mul�ple equa�ons); by elimina�ng one of the colinear independent variables; or by plo�ng and observing the error terms and subsequently respecifying the regression model. But these "fixes" would take us

beyond a managerial economics course into a quan�ta�ve methods course or a research method textbook.24

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#footernote24) Our purpose here was to show that basic regression analysis can be conducted easily using the readily available Excel spreadsheet package (with a sta�s�cal module added in) to provide a first level es�mate of the demand func�on and the responsiveness of quan�ty demanded to each of the independent variables for managerial decision-making purposes.

18. Computer programs have turned the old fashioned way of compu�ng the regression equa�on by hand into an unnecessary waste of �me, and also eliminate calcula�on errors. Accordingly, students in managerial economics courses do not need to learn the complex equa�ons that allow the regression parameters to be calculated by hand. We can rely on computers and concentrate on ensuring that the input data quality is high. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#return18) ]

19. Note that a "good fit" does not confirm causality, however, since other factors might be driving this, such as misspecifica�on of constructs, poor measurement of variables, endogeneity of variables, and so on. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#return19) ]

20. Unexplained variance could also be due to the pure randomness. Note that the same consumer may end up with different decisions on the same product with the same price on different days. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#return19) ]

21. One such "sta�s�cs add-in" is Statpro, developed to accompany a popular Sta�s�cs textbook by Albright et al. This add-in is free to download and will allow you to conduct mul�ple regressions using Excel spreadsheets. Use Google to find the Statpro website and follow the instruc�ons to download it into your Excel program. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#return21) ]

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22. An outlier is an observa�on that has a value for one or more variables that is way outside what appears to be the normal range of devia�ons from the line of best fit (i.e., the regression equa�on). It is important not to delete observa�ons that include large varia�ons that might reasonably be correctly measured but simply include a large random error term —that would amount to falsifying the data. As a simple rule of thumb, and mindful of the proper�es of a normal distribu�on, you might decide to delete observa�ons that are more than three standard devia�ons from the mean value of the variable, assuming an approximately normal distribu�on of the data. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#return21) ]

23. If the β for any of the other three Ps (product design, promo�on, or place of sale) is nega�ve, this would indicate that that variable has been taken too far, beyond the op�mum, and is having a nega�ve impact on quan�ty demanded, so should be reduced if the firm wishes to maximize its profits. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#return23) ]

24. For example, Hair et al., 2010, Mul�variate Data Analysis text, cited earlier. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec4.4#return24) ]

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Summary

In this chapter we began by reviewing the impact of various factors on the firm’s demand func�on, and stated the demand func�on as a linear equa�on that showed quan�ty demanded as a func�on of the independent variables that collec�vely determine market demand. Market demand is influenced by the firm’s controllable variables (price, promo�on, product design, and place of sale) and by other variables that are uncontrollable by the firm (the 4 Ps of other firms, consumer incomes, consumer tastes, consumer expecta�ons, ac�ons by governments, demographic changes, weather events, and natural disasters). We converted the demand func�on to an inverse demand curve of the form P = a + bQDx, which states the price in terms of a ver�cal intercept

term (a) and a slope term (b). We then derived the rela�onships between the demand curve, the total revenue curve and the marginal revenue curve. The marginal revenue (MR) curve has the same intercept value but twice the slope of the demand curve. The total revenue (TR) curve has an inverted-U shape, increasing up to the point where MR falls to zero, and then falling. Next we introduced price elas�city of demand (denoted by the Greek le�er epsilon, ε) and related this to the above curves—price elas�city is a summary measure that indicates what will happen to marginal and total revenue when price is either increased or decreased. We say that demand is price elas�c when price elas�city measure is greater than one in absolute terms, that is, ε > |1|, and that demand is price inelas�c when ε < |1|. We know that TR will be rising (for price reduc�ons) when demand is price elas�c and falling (for price reduc�ons) when demand is inelas�c.

Similarly, other elas�ci�es were introduced as summary measures of the rela�ve responsiveness of quan�ty demanded to changes in variables that affect the quan�ty demanded. In each case the responsiveness of quan�ty demanded is shown by the sign and size of the relevant β coefficient in the demand func�on, and the elas�city (rela�ve responsiveness) measure is the β coefficient weighted by the ra�o of the relevant independent variable to the quan�ty demanded. Managers need to be aware of these elas�ci�es because they each communicate relevant informa�on to the decision maker. Income elas�city of demand (denoted by theta, θ) is a measure of the rela�vely responsiveness of quan�ty demanded to changes in consumers’ incomes. Normal or superior goods have posi�ve income elas�city (θ > 0) while inferior goods have nega�ve income elas�city (θ < 0). Superior goods can be further categorized as luxury goods if income elas�city exceeds one (θ > 1), necessity goods if income elas�city value lies between zero and one (0 < θ < 1). Cross-price elas�city of demand was denoted where η (the Greek le�er eta) was posi�ve for price changes of subs�tute goods and nega�ve for price changes of complementary goods. Cross-adver�sing elas�city of demand was similarly posi�ve for subs�tute goods and nega�ve for complementary goods. We also considered the firm’s own adver�sing elas�city of demand and quality elas�city of demand, no�ng that when these are posi�ve it means that addi�onal adver�sing or quality will lead to addi�onal quan�ty demanded, but where nega�ve it means that the market has responded badly to the firm’s change in that controllable variable.

In the second half of the chapter we introduced methods for es�ma�ng demand func�ons and demand curves. We considered primary data collec�on methods such as interviews, surveys, and market experiments and sketched in the line of best fit to indicate the responsiveness of quan�ty demanded to changes in price or whichever other determining variable the manager may be interested in. We then considered mul�ple regression analysis to compute the dependency of quan�ty demanded on each of the independent variables simultaneously. Regression analysis generates sta�s�cs that provide a measure (β) of the responsiveness of quan�ty demanded to changes in each of the independent variables included in the regression equa�on, as well as the

coefficient of determina�on (R2) that indicates how well the regression equa�on fits the data. The standard error of es�mate (Se) indicates how confident

we can be in the predic�on made for the magnitude of quan�ty demanded, with a range of plus or minus 2 �mes the Se indica�ng the 95% confidence

interval around that predic�on. The standard error of the coefficient (Sβ) similarly indicates how confident we can be that the β coefficients derived from

the sample data reflect the true rela�onship between the variables that would be found in the popula�on as a whole. We concluded by briefly considering six common pi�alls of regression analysis and emphasizing the need to call in the experts when conduc�ng regression analysis in a business situa�on when the stakes are high and the cost of making a mistake is likely to be higher than the cost of the consultant who could design and implement a study that would gain sufficiently accurate data.

In the next two chapters we turn our a�en�on to the cost side of the profit equa�on (where profit equals revenues minus costs), and again we will u�lize regression analysis to es�mate cost func�ons, so that the manager will have the data required to make profit-maximizing price and other strategic decisions, and that in turn is the subject ma�er for the following four chapters of this book.

Ques�ons for Review and Discussion

Click on each ques�on to reveal the answer.

1. What independent variables do you think should enter the demand func�on for �ckets to the home games of a Na�onal Football team? (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

The determinants of demand for �ckets to home games of a football team probably include price; loca�on in the stands of the seats available; whether under cover or not; whether reserved for that teams members/supporters or not; whether well-served with food and beverages or not; whether the team is winning games or not; and whether the games are early, mid-season or final series games. Maybe you can think of other a�ributes of football games that increase demand from your perspec�ve.

2. Assign the value "rela�vely high" or "rela�vely low" to the price elas�city of market demand for each of the following, and explain why you chose one or the other value. (a) Coca-Cola (b) Dr Pepper (c) Ar�ficial limbsProcessing math: 0%

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(d) Levi’s jeans (e) Cure for AIDS (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

(a) Coca-Cola: rela�vely low price elas�city due to strong product differen�a�on supported by incessant adver�sing. (b) Dr Pepper: rela�vely low, due to strongly differen�ated taste (li�le or no close subs�tutes) and fana�cally loyal customers. (c) Ar�ficial limbs: rela�vely low, due to li�le or no close subs�tutes and the strong need for customiza�on to suit individuals. (d) Levi's jeans: rela�vely high, despite strong brand differen�a�on there are many other brands of jeans, each claiming be�er design, with strong promo�onal campaigns. (e) Cure for AIDS: rela�vely low price elas�city of demand due to no subs�tutes and strong need for the product by those afflicted with the disease.

3. If you knew that, for a par�cular product, the current price is $45, current quan�ty demanded is 250 (thousand units per month), and the price elas�city of demand is equal to −1.5, explain how you would find the expression for the demand curve (in the form P = a + bQ). (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

Since elas�city can be expressed as ε = 1/b . P/Q we can subs�tute data provided and know that −1.5 = 1/b (45/250) so we can solve for b = 1/−8.333 = 0.12. Then values for P, b, and Q in the demand curve expression P = a + b Q to write 45 = a − 0.12(250). Solving for a, we find a = 75, and thus the expression for the demand curve is P = 75 − 0.12Q.

4. Given your knowledge of the elas�city concept, define the rainfall elas�city of umbrellas. What possible usefulness could such a concept have? (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

An elas�city is a measure of the rela�ve responsiveness of one variable to changes in another variable, so the rainfall elas�city of umbrellas would be the percentage change in umbrella sales divided by the percentage change in rainfall; we expect that the more it rains the more umbrellas would be demanded. The value of this informa�on to umbrella vendors would be to es�mate how much stock they need to have in hand when rain is predicted. This would be especially valuable when the stock of umbrellas must be moved from a place of storage (e.g., a warehouse) to the place of sale (e.g., downtown shops) without delay, since umbrella demand is usually an impulse purchase, and if the vendor runs out of stock poten�al sales are lost.

5. Why would you expect the market demand for luxury goods, such as jewelry, to be more vola�le in periods of fluctua�ng incomes, as compared to items such as milk and bread? (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

The demand for luxury goods, such as jewelry, will fluctuate more than in propor�on to changes in the income levels because it serves a want rather than a need and when incomes go down people can postpone the sa�sfac�on of their wants. Necessity goods, such as milk and bread, sa�sfy the more urgent need for food. People are reluctant to cut back on their purchases of these goods and do so only slightly when their incomes fall.

6. List 10 ques�ons you would ask people in a survey designed to es�mate the demand func�on for a par�cular brand of toothpaste. (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

There is no defini�ve answer to this ques�on. You might suggest ques�ons such as: What is your current brand of toothpaste? What other brands would you consider? Why do you prefer brand X? Why do you prefer it to brand Y and brand Z? What do you like about the taste of your toothpaste? Would you prefer it was different in some way? How do you think brand X toothpaste could be improved? What is your income level (in broad categories)? How much could the price of your brand (X) rise before you would switch to another brand?

7. Suppose you had annual data on the price and quan�ty demanded of newsprint over the past 20 years and plo�ed these (or conducted bivariate regression analysis) to find a line of best fit. Why would this be an unreliable es�mate of the demand curve? What other data would you need to make a more reliable es�mate of the demand curve for newsprint? (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

Annual data on price and quan�ty demanded would need to be supplemented by "control variables" that take account of other things that might be different from year to year, or might have changed over the 20-year data collec�on period. Changes in these variables would have caused the demand curve to shi� from �me to �me, such that the observed PQ data would not be on a single demand curve. Annual data on Gross Na�onal Income (as a proxy for customer incomes); newspaper circula�on numbers; and propor�on of the popula�on who buy newspapers (which would have been declining) would be a minimal requirement to control for such shi�s of the demand curve.

8. Summarize the issues you would need to check before concluding that the results of a regression analysis were a reliable basis for es�ma�ng the demand func�on. (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

The coefficient of determina�on (R2) should be reasonably high to imply an apparent rela�onship between the dependent variable (DV) and the independent variables (IVs); the standard error es�mate should be rela�vely small to allow a rela�vely narrow range of vales within which we can expect the DV value to fall at the 95% confidence level; the standard error of the coefficient for each of the IVs should be rela�vely small to assure us that the es�mated b values are close to the true (popula�on) values; and the six pi�alls of regression analysis (specifica�on errors, measurement errors, simultaneous rela�onships, mul�collinearity, heteroscedas�city, and autocorrela�on) should be absent.

Decision Problems

1. The demand for Fritz Reinhart premium beer in a par�cular city has been es�mated to be:

Qx = 37,986.5 − 4,476.9Px + 2,994.2Py + 668.2Ax − 849.7Ay

Where Qx is quan�ty demanded (per month) and Px is the price of Fritz Reinhart beer (in six-packs); Py is the price of the main compe�tor beer,

Urquhart Pilsner; Ax is the adver�sing expenditure for Reinhart (in thousands of dollars per month) and Ay is the adver�sing expenditure of Urquhart

(thousands of dollars per month). The current values of the independent variables are Px = 9.95; Py = 8.95; Ax = 36; and Ay = 22. Processing math: 0%

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a. Calculate the price elas�city of demand for Fritz Reinhart beer, and comment on the extent to which demand and total revenue would change if the price of this beer (per six-pack) were to be raised by a dollar.

b. Calculate the cross-price elas�city of demand and speculate how a price decrease to $8.50 for Urquhart beer would impact the quan�ty demanded of Reinhart beer.

c. Would it be profit maximizing for Fritz Reinhart to increase its adver�sing expenditures by another $1,000 per month? (Assume the cost of produc�on is constant at $4 per six-pack.)

d. What can Fritz Reinhart do to reduce the nega�ve impact of Urquhart’s adver�sing on its quan�ty demanded? 2. The demand func�on for Crispie Chips has been es�mated as follows:

Qx = −27.6887 − 37.73585Px + 44.1177Py + 0.2315Ax

Where Qx represents thousands of packets of chips; Px is the price per packet; Py is the average price per packet of the many other brands of similar

chips; and Ax represents thousands of dollars spent adver�sing Crispie Chips. The current values of the independent variables are Ax = 216.0; Px = 0.85;

Py = 0.79.

a. Calculate the price elas�city of demand for Crispie Chips and comment on its value. b. Derive an expression for the (inverse) demand curve for Crispie Chips and sketch this on a piece of paper. c. Suppose the cost of producing Crispie Chips is constant at $0.19 per packet. Should they reduce price and produce more (assuming they want to

maximize profit)? d. Should Crispie Chips spend more on adver�sing? e. What assump�ons have you made regarding the reliability of the data and the accuracy of the es�mated demand func�on?

3. Jose Hermanos Tequila (JHT) has conducted an experiment in six different liquor stores that are spread around the suburbs of a major southwestern city, with approximately similar customers for each store. JHT set different prices in each of the stores for its Hermanos Gold product, as follows, in each case with its product prominently displayed between the two other major tequila brands. Fortunately for JHT’s experiment there were no changes in the prices or promo�on of any other liquor products during the week of the experiment.

Store Price ($) Quan�ty demanded

A B C D E F

19.10 15.70 16.50 21.50 12.90 13.90

17 24 21 10 32 28

a. Sketch the line of best fit represen�ng the demand curve for Hermanos Gold in the typical liquor store in that city. b. What price promises to maximize total revenue (TR) for the JHT company? c. What is the price elas�city of demand at that price?

4. Axton Auto Accessories (AAA) has manufactured a new a product—a high-mounted rear brake light to replace the one that typically sits on the back window shelf of a passenger car. AAA’s product offers several new features, however, such as the ability to scroll messages across the light-emi�ng diode (LED) screen. These prerecorded messages are designed to facilitate communica�on between vehicles, with displays such as "Sorry!"; "Thank You!"; "Please let me in!"; and "This car for sale." The memory of the device can also be loaded (via your computer) with new messages such as your phone number, adver�sements for products, and support for sports teams or poli�cal par�es. This device is about a foot wide, and these messages only scroll across the screen when the vehicle is accelera�ng. The display reverts to bright red when the vehicle is braking, but also offers another innova�on by displaying the word "CAUTION" when the driver li�s his or her foot off the accelerator. Trial marke�ng of the product at different prices for a month in 10 stores of a major auto parts retail company has returned the following data:

Retail store Retail price ($) Quan�ty demanded

1 2 3 4 5 6 7 8 9

10

33.90 25.00 49.98 27.98 37.75 45.90 23.98 31.00 25.50 29.98

2,208 2,682 2,061 2,526 2,158 1,732 2,877 2,312 2,606 2,488

a. Load this price and quan�ty data into columns in an Excel spreadsheet and conduct bivariate regression analysis to determine the demand func�on in the form Qx = AOV + βPx.

b. Convert the demand func�on to an inverse demand curve expressed in the form Px = a + bQx.

c. At what price level is total revenue (TR) maximized? Processing math: 0%

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d. Assuming that the cost of produc�on is constant at $8 and that the auto parts store marks up the wholesale price (its cost) by 100% to arrive at the retail price for its customers, what wholesale price should AAA set to maximize its profit?

5. The consul�ng firm that you work for has been hired by the U.S. Government to provide an independent analysis of the demand-side effects of a contemplated increase in the tax on gasoline. It provide you with a data set rela�ng to the period 1962–1987, which contains valuable historic lessons rela�ng to the impact of vola�le pump prices due to the supply restric�ons imposed by the Organiza�on of Petroleum Expor�ng Countries (OPEC) and the Corporate Average Fuel Economy (CAFE) regula�ons that required car manufacturers to increase the fuel efficiency of the cars they sold, while at the same �me Real Disposable Income (RDI) per capita was rising, the number of passenger cars (NPC) almost doubled, and infla�on was pushing up the Consumer Price Index (CPI).

Year QDx Px NPC MPG RDI CPI

1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1084 1985 1986 1987

43,771 45,246 47,567 50,273 53,312 55,110 58,524 62,448 65,784 69,514 73,463 78,011 74,217 76,457 78,847 80,677 83,233 80,233 73,375 71,718 72,848 73,156 71,180 69,450 71,404 70,984

 20.36  20.11  19.98  20.70  21.57  22.55  22.93  23.85  24.55  25.20  24.46  26.88  40.41  45.44  47.44  50.70  53.09  74.33  104.73  112.75  102.65  95.36  91.46  89.64  63.63  66.33

 66,638  69,842  72,969  76,634  80,106  82,367  85,793  89,156  92,095  96,144  100,658  106,119  109,823  111,679  115,170  118,711  121,717  125,750  127,448  129,123  129,500  131,723  133,751  137,308  140,693  142,209

14.37 14.26 14.25 14.15 14.10 14.05 13.91 13.75 13.70 13.73 13.67 13.29 13.65 13.74 13.93 14.15 14.26 14.49 15.32 15.68 16.36 16.81 17.80 18.28 18.35 19.29

 6,271  6,378  6,727  7,027  7,280  7,513  7,728  7,891  8,134  8,322  8,562  9,042  8,867  8,944  9,175  9,381  9,735  9,829  9,722  9,769  9,725  9,930  10,419  10,662  10,947  10,976

 90.6  91.7  92.9  94.5  97.2 100.0 104.2 109.8 116.3 121.3 125.3 133.1 147.7 161.2 170.5 181.5 195.4 217.4 246.8 272.4 289.1 298.4 311.1 322.2 328.4 340.4

Where: Qx is the gasoline consump�on by passenger cars (in millions of gallons);

Px is the retail (pump) price of gasoline, in cents per gallon;

NPC is the number of registered passenger cars (in thousands);

MPG is the na�onal average of miles travelled per gallon of gasoline;

RDI is Real Disposable Income per capita (in 1982 dollars); and

CPI is the Consumer Price Index (base year 1967).

This data illustrates some very interes�ng issues that were happening over that tumultuous period of our history. You will note that the pump price of gasoline more than doubled five-fold from the mid-1960s to the mid-1970s, and then doubled again in the early 1980s, due to the OPEC crisis. The number of passenger cars climbed relentlessly with the love affair with "muscle cars" despite the increasing pump price of gasoline, and indeed outpacing the increases in real disposable income per capita. The average MPG climbed only slowly as manufacturers increased the fuel efficiency of new cars and consumers slowly traded up to the more efficient new cars and re�red their older vehicles. The changes in CPI show that the rate of infla�on was generally much greater than the rate of increase of pump prices as the increased produc�on and transporta�on costs, due to rising fuel prices, pervaded the en�re economy, pushing up the prices of food and other household items that drive the CPI.

a. Reconcile the fact that while the quan�ty demanded of gasoline and pump prices both rise over this period generally, they are inversely related along a demand curve.

b. Conduct a mul�ple regression analysis to explain the quan�ty demanded of gasoline in terms of the other data provided. (Enter this data into an Excel spreadsheet and use the Excel regression tool, if loaded, or alterna�vely, download an add-in regression program such as Statpro to find the regression sta�s�cs.)

c. What propor�on of the variance in Qx is explained by these other variables? What missing variables might account for the remainder of the variance in the quan�ty demanded of gasoline?

d. Use the regression equa�on to predict the quan�ty demanded of gasoline in 1988 for the values Px = 68.5; NPC = 145,885; MPG = 20.36; RDI = 11,192;

and CPI = 354.6. e. What is the 95% confidence interval for your predic�on?

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Key Terms

Click on each key term to see the defini�on.

absolute terms (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

An expression meaning that we ignore the nega�ve sign in front of a number, such that we say, for example, that −5 is larger than −4, typically used when dealing with price elas�city values, which are always nega�ve.

autocorrela�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The dependence of data values in the current period on their value in the preceding period. Autocorrela�on violates an assump�on of regression analysis that the dependent variable is determined by the independent variables alone, not also by its own prior value.

business cycle (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The pa�ern of growth of the macroeconomy, typically with alterna�ng periods of expansion and recession (or at least slower growth rates) with associated fluctua�ons in macroeconomic variables such as interest rates, infla�on rates, and unemployment rates.

coefficient of determina�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A sta�s�c produced by regression analysis that indicates what propor�on of the total variance in the dependent variable (Y) is explained by varia�ons in the independent variables (Xs).

confidence interval (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A range of values around the value of the dependent variable (Y) that is predicted (by the regression equa�on) for par�cular values of the independent variables (Xs), within which range we can be confident that the actual value of Y subsequently observed will fall (for example) 95% of the �me.

consumer clinics (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Ar�ficial shopping environments created by marketers to conduct simulated market situa�ons. Marketers observe the choices of customers, while varying the prices of some products, the shelf placement of products, and point-of-purchase informa�on about product quality, for different groups of shoppers.

contribu�on margin (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The excess of price per unit over average variable costs per unit, which contributes towards the firm’s fixed costs and profit.

cross-adver�sing elas�city (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The rela�ve responsiveness of one firm’s quan�ty demanded to changes in another firm’s adver�sing expenditures. It can be calculated as the percentage change in quan�ty demanded divided by the percentage change in the other firm’s adver�sing expenditures.

demand func�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The func�onal rela�onship that exists between the quan�ty demanded of a par�cular product (dependent variable) and all determinants of that demand (the independent variables).

demographic change (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Changes over �me in variables such as age cohort size, ethnicity propor�ons, gender balance, geographic distribu�on, and employment type. These changes are likely to affect the demand for products that are consumed more (or less) by a par�cular age, ethnic, gender, regional, or employment group.

dependent variable (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A variable (such as quan�ty demanded in different �me periods) that is dependent on the concurrent values of independent variables (such as price, adver�sing, consumer incomes, and so on).

direct marke�ng (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

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Directly selling goods and services to consumers through direct marke�ng channels (such as the Internet, mailing campaigns, and telemarke�ng) rather than indirectly via wholesale and retail firms (who interface directly with the consumer).

direct methods (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Demand es�ma�on whereby primary data is collected from actual or poten�al buyers via interviews, surveys, and market experiments.

elas�city of demand (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The rela�ve responsiveness of quan�ty demanded to a change in one of the independent variables that help to determine quan�ty demanded. For example, price elas�city of demand is measured by the percentage change in quan�ty demanded divided by the percentage change in the price level.

es�ma�on of market demand (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A process by which the volume of demand in the current and future periods is es�mated. This process involves gathering and interpre�ng data to provide a numerical es�mate of demand in the current and future �me periods.

heteroscedas�city (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The circumstance where the error terms associated with a regression equa�on vary in a systema�c manner rela�ve to the magnitude of an independent variable, rather than occurring randomly as assumed by the mathema�cs of the regression equa�on. It introduces unreliability into the standard error of es�mate and the coefficient of determina�on.

independent variables (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Variables included on the right-hand side of a regression equa�on because they are expected to exert a determining influence on the dependent variable.

indirect methods (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Demand es�ma�on involving the sta�s�cal examina�on of data previously collected for official government sta�s�cs, or found in reports researched and wri�en for other purposes (so-called secondary data).

inverse demand curve (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Expresses price as a func�on of quan�ty demanded for product X, in the form Px = a + bQDx. This form is derived from the demand func�on which expresses quan�ty demanded as a func�on of the various independent variables, including price.

line of best fit (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A line best summarizing the apparent rela�onship between two variables. We should not expect any of the observa�ons to lie exactly on the line of best fit as there are likely to be random varia�ons within the data.

luxury good (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Items for which the quan�ty demanded increases more than propor�onately when consumer incomes increase. For example, income rises 5% and demand for caviar increases 10%.

marginal revenue (MR) (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A measure of how much the total revenue changes when one more unit is sold.

market demand (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The aggregate sum of the quan�ty demanded by all consumers of a par�cular product within a period of �me.

missing variables (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Other determinants (Xs) of the dependent variable (Y) for which data has not been collected or that were not entered into the regression analysis.

mul�collinearity (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

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The circumstance where the independent variables in a regression equa�on are in fact not independent of each other but instead are significantly correlated with each other. This causes the regression sta�s�cs to be unreliable.

necessity good (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A product that has an income elas�city value that is posi�ve but less than one, meaning that when incomes rise, quan�ty demanded of that product rises but by a lesser percentage than income has risen.

nonprice compe��on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Compe��on among rival firms that does not involve cu�ng price but rather involves the other three Ps of marke�ng, namely product design, promo�on, and place of sales.

ordinary least squares method (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A process that posi�ons the line of the best fit so that it minimizes the sum of the squared devia�ons of the observa�ons from the line. The devia�ons are squared to avoid posi�ve devia�ons offse�ng nega�ve varia�ons and to more heavily weight the larger devia�ons.

price compe��on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A situa�on among two or more rival firms, where each sets its price in an a�empt to maximize its profits.

price elas�city (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The rela�ve responsiveness of quan�ty demanded to changes in the price level, for a par�cular product. It allows an es�mate of by what propor�on demand is likely to change when an item’s price is increased or decreased by a par�cular propor�on.

quality elas�city (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The rela�ve responsiveness of quan�ty demand to a change in the quality of a par�cular product. It is measured as the percentage change in quan�ty demanded of product X divided by the percentage change in the quality of product X.

regression analysis (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A method of analysis that determines the sta�s�cal rela�onship between a par�cular dependent variable and the independent variables that are expected to determine the value of that dependent variable.

simultaneous equa�on rela�onship (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Exists when a dependent variable Y depends on X but simultaneously X depends on Z. Thus, a single regression equa�on cannot reliably be es�mated for the dependence of Y on X or Z.

specifica�on error (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Occurs when the hypothesized func�onal form of the regression equa�on does not reflect the true rela�onship between the variables. Linear regression equa�ons are most commonly used, but some�mes there will be a nonlinear rela�onship (e.g., a quadra�c func�on) between the dependent variable and at least one of the independent variables.

standard error of es�mate (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A measure of the dispersion of the data points from the line of best fit. Using this sta�s�c we can calculate confidence intervals around the predicted value of Y given a set of values for the independent (X) variables.

standard error of the coefficient (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A measure, for each of the independent variables, of the accuracy of the calculated value of the β coefficient generated by the regression analysis.

total revenue (TR) (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The combined sum of the revenues collected from all the buyers during a par�cular period of �me. It is equal to the price per unit mul�plied by the number of units sold.Processing math: 0%