Economics Problems - Market Structures and Pricing Decisions Applied Problems

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Market Structures and Price Determination

Learning Objectives

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

Dis�nguish among the four main types of markets (or market structures). Explain how markets work and how they determine the market-clearing prices. Dis�nguish between price-taking and price-making situa�ons for individuals and firms. Discuss how the extent of product differen�a�on is cri�cally important for price-making. Iden�fy how the firm selects the price and output levels that maximize profit under various market structures.

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A market is a tangible place or an intangible situa�on in which buyers and sellers communicate for the purpose of exchanging value. Purchasing items at a grocery store is an example of a tangible market.

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Introduction

In this chapter, we are primarily concerned with the manager's problem of choosing the appropriate price and output level in order to maximize the firm's profits. As you know, profits are the excess of revenues over costs. In the preceding four chapters we have been concerned with the demand and revenue side (Chapters 3 and 4) and the produc�on and cost sides (Chapters 5 and 6). In this chapter, we bring together the cost and demand sec�ons of this course to help the manager make be�er pricing and output decisions.

Business firms operate in markets; they sell their outputs of products or services in markets, and they buy their fixed and variable inputs in markets. Their inputs are in turn the outputs of other firms and individuals that supply products and services (such as direct materials, direct labor, buildings and equipment) to these input markets. Before proceeding with the firm's pricing and output decisions, it seems prudent to clarify what we mean by "markets."

What Is a Market?

A market can be defined as a tangible place or an intangible situa�on in which buyers and sellers communicate for the purpose of exchanging things of value. Buyers exchange money for goods or services, and sellers exchange goods or services for money. In barter markets, buyers and sellers exchange goods or services that they own for other goods or services that they want. Since the earliest �mes, people would gather in the village marketplace to buy and sell (or exchange by barter) food, clothing, animals, tools, weapons, and so on. Such physical market loca�ons s�ll exist, of course; even in modern ci�es you will find vegetable markets, fish markets, and so on. Other market loca�ons are visited only by those directly engaged in the transac�on, such as a person ge�ng a haircut at the hairdresser's shop, or a farm laborer going out to a farm looking for work. Market transac�ons can take place without the buyer or the seller physically mee�ng: For example, you can use a telephone to call a roofer to fix your roof while you are at work, and later pay his invoice. To do this you (metaphorically) enter the market for roof repairs and choose one or more roof repairers who give you a price quota�on (or assurance that the price for the repair job will be fair), a verbal or wri�en contract is then entered into, and the transac�on is subsequently completed.

The Internet has provided buyers and sellers with quick and effec�ve online access to millions of markets. Prospec�ve buyers can easily find out who sells the item they wish to purchase, what price and quality features are associated with the offer made by each seller, when and how delivery and payment will take place, and so on. Buyers and sellers can nego�ate the transac�on price online without mee�ng, or mul�ple and anonymous buyers can compete for the sale of a specific item via online auc�ons (on sites such as eBay). Similarly, buyers and sellers rou�nely enter into contracts to purchase and sell items, or to provide services for remunera�on, using text messaging or email correspondence.

The extent of a market is limited by �me, space, and informa�on. First, markets take place at certain �mes, and it is too late tomorrow to enter today's market expec�ng to get yesterday's prices—prices (and perhaps also quali�es) may have changed considerably compared to yesterday's market outcomes. For example, if we hear on the news that Facebook stock prices fell today, trying to buy Facebook stock tomorrow we might find that its stock prices have risen considerably. Second, markets take place at par�cular loca�ons, real or virtual, which in many cases limits the number of par�cipants if buyers and sellers have to be physically present to buy or sell the product or service, or if buyers need to follow specific processes to access a virtual market environment. For example, ge�ng a haircut requires the buyer to travel to a hairdresser, and there may be only three or four service providers within a convenient distance for the buyer, notwithstanding that there may be hundreds of barbers and hairdressers spread around the city and across the state. Similarly, a mobile mechanic may consider taking automobile repair jobs only within a radius of 20 miles, despite there being thousands more poten�al buyers of auto repairs outside that radius. Thirdly, markets are limited by the availability of informa�on to poten�al buyers and sellers. For example, poten�al home buyers may not know that their dream home has been put up for sale, and thus they do not a�end the auc�on at which it is sold. Similarly, poten�al sellers may not know that someone would be willing to offer them thousands of dollars for their an�que furniture, if only both par�es knew about the other's willingness to buy or sell. Markets require that par�cipants be informed about the market's existence and be able to enter (personally or by proxy) the marketplace (real or virtual) at the �me that the market transac�on is to occur.

Thus, a market is a means by which buyers and sellers can get together in some sense to allow them to enter into and complete a transac�on. In any market, a transac�on can occur if a price can be agreed upon between the buyer and the seller. Our major concern in this chapter is how the structure of the market influences the ability of the selling firm to set the price level for its output.

The Four Basic Market Structures

Economists iden�fy four basic market structures as follows:

pure compe��on markets in which there are many sellers supplying iden�cal products, such as farmers selling milk, eggs, or corn, or individuals selling shares on the Stock Exchange; monopolis�c compe��on markets in which there are many sellers each supplying differen�ated products, such as coffee shops in the central business district of a large city;Processing math: 0%

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Market Structures

oligopoly markets in which rela�vely few sellers each supply iden�cal or differen�ated products, such as automobiles, aircra�, steel, and other building materials; and monopoly markets in which there is only one seller of the product or service which has no direct subs�tutes, such as your local gas or electricity u�lity.

The number of compe�ng sellers and the degree of product differen�a�on interact to give rise to an expecta�on, by the focal firm, of what rivals will do in reac�on to its price changes. When there are many firms (i.e., in pure compe��on and in monopolis�c compe��on), we expect that firms will not expect rival firms to react to their pricing decisions. Note that by "many firms" we mean a number sufficiently large that the produc�ve capacity of any one firm is a very small propor�on of the total produc�on capacity of the firms opera�ng in the market. Because of this rela�ve insignificance of any one supplier in pure compe��on and monopolis�c compe��on, none of these firms expects its ac�ons to be reacted to (or perhaps even no�ced) by other firms.

Conversely, by "few firms" we mean a number small enough such that any one firm can produce a rela�vely large propor�on of market demand and consequently can influence the market price upwards (by withholding supply) or downwards (by flooding the market). Being a significant en�ty in such markets, the firm must expect reac�on from those affected by its compe��ve moves; we shall expand upon the expecta�ons of oligopolists regarding their rivals' reac�ons to their compe��ve moves later in this chapter. Monopolists do not have to worry about rivals' reac�ons because they have no direct rivals, but they do have to be concerned with the reac�ons of public regulatory bodies to their pricing and other compe��ve moves. Many public u�li�es that provide ci�es and communi�es with water, electric power, and household gas supplies are regulated monopolies that are subject to con�nual scru�ny by their regulators. Monopoly suppliers of services based on new technologies, such as Microso� and Google, must also heed the monopoliza�on sec�ons of the Federal An�-Combines Act. The dis�nguishing differences of the four basic market structures are summarized in Table 7.1, along with examples of each type.

Table 7.1: The four market structures

Pure compe��on

Monopolis�c compe��on

Oligopoly Monopoly

Number of compe�ng firms

Many, due to no barriers to entry of new rivals

Many, due to no barriers to entry of new rivals

Few, due to high barriers to entry of new rivals One, due to an absolute barrier to entry for poten�al rivals

Degree of product differen�a�on

Zero (iden�cal products)

Small (slightly differen�ated products)

Zero to substan�al (ranges from iden�cal to highly differen�ated products)

Extreme (unique product with no direct subs�tutes, due to entry barrier)

Expecta�on of rivals' reac�ons

No reac�on expected due to very small share of total supply of the product

No reac�on expected due to very small share of total supply of the product

Rivals are generally expected to match price increase but to ignore price reduc�ons1 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/ch07introduc�on#Ch7footNote1)

No rivals, but does expect government regula�on if behaving "badly"

Examples Agricultural commodi�es; stock markets; financial markets; foreign exchange markets

Personal services; clothes retailers; foodservice providers (e.g., Coffee shops and restaurants)

Steel, aluminum, cement, and glass building materials; car and airplane manufacturers; local oligopolies

Pharmaceu�cal firm with patents; electricity and gas u�li�es; unique items; labor unions; cartels

The degree of product differen�a�on refers to the extent to which compe�ng suppliers' products contain the same or different product a�ributes, or more or less of these a�ributes, as discussed in Chapter 3. Product differen�a�on is as perceived by the customer and implies a preference ranking between and among compe�ng suppliers, that is, the customer would expect to gain more u�lity from some product variants than from others offered in the same market. In pure compe��on, the compe�ng sellers provide iden�cal products, meaning that their products are completely undifferen�ated, such as the shares in a company that might be offered for sale in the stock market by many small stockholders. In monopolis�c compe��on, the sellers compete in the same product category providing basically similar products which are more or less differen�ated in terms of their loca�on or the other product a�ributes offered. For example, the various coffee shops and fast-food stores that are sca�ered around a big city all offer food, snacks, and beverages but in slightly different formats and combina�ons, with be�er or worse service quality, and in more or less convenient loca�ons.

In oligopoly markets, the degree of product differen�a�on can range from none to quite substan�al. It will be quite low in markets where a few sellers provide iden�cal products (such as tendering to buyer specifica�on for steel, aluminum, and other building materials) and the only elements of differen�a�on might be the firms' more-or-less convenient loca�ons, proposed delivery �mes, reputa�on for service quality, or personal rela�onships between the buyer (or purchasing agent) and the seller. Taking the a�ribute view of product quality, as we did in Chapter

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3, we can see that these loca�on, �ming, and service differences among compe�ng suppliers cause the buyer to differen�ate the quality of one seller from another when the basic product (e.g., steel supplied to exac�ng specifica�ons) is otherwise iden�cal. Conversely, product differen�a�on in oligopoly markets may be quite substan�al because the sellers' products or services are quite different or would be delivered in different ways by firms that are equally convenient or pleasant to deal with. Examples include the markets for automobiles, passenger flights, university degrees, suburban houses, and so on. In these examples, the different brands and models of cars, different classes of air travel, different subject ma�er to study, and different design features and loca�ons of homes cause the poten�al buyer to restrict their choice to a subset of the suppliers or service providers in the broader market.

In monopoly markets, the products of the monopolist are totally differen�ated from those available in other markets—by defini�on, a monopoly is the single supplier of a par�cular product category. Monopolies usually occur due to barriers to entry—meaning there are obstacles to the entry of compe�ng firms. These barriers include legal restric�ons preven�ng new entrants (such as for the post office and for gas and electricity u�li�es); restricted access to the technology necessary to compete effec�vely (such as trade secrets or patents); or control of necessary raw materials or human skills (such as control of all the bauxite deposits for making aluminum, or employment of the only person with a unique talent). Barriers to entry also operate to prevent entry of new firms into oligopoly markets, thus preserving the fewness of firms in those markets. For example, the barriers to entry preserving the fewness of firms in the automobile industry are due to the huge cost of establishing an automobile manufacturing plant and the associated network of distributors and service facili�es; the strong and established reputa�ons for quality of the

exis�ng sellers; and the limited access to the latest and patented technology held by the incumbent firms.2

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/ch07introduc�on#Ch7footNote2)

1. This refers to one par�cular oligopoly situa�on. During a "price war" for example, price reduc�ons by one firm should be expected to be matched or exceeded by rival firms. Alterna�vely, with price leadership, the price leader expects the price followers to match both price increases and price reduc�ons—we discuss these oligopoly situa�ons later in this chapter. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/ch07introduc�on#return1) ]

2. Another reason for the preserva�on of monopolies is that some markets are natural monopolies, meaning that they are rela�vely small markets and are most efficiently served by only one firm, due to the economies of plant size (introduced in Chapter 5). They are "natural" in the sense that although there are not insurmountable barriers to entry, if a new entrant did enter it would soon realize that it would be more profitable to sell out to, or merge with, the exis�ng firm and thus revert to the monopoly structure of the market. We consider natural monopoly later in this chapter. Similarly, some would argue that the automobile industry and the airplane manufacturing industry (for example) are natural oligopolies due to the massive economies of scale and economies of scope available to exis�ng firms, such that new entrants would ul�mately sell out to or merge with exis�ng firms (or perish due to price compe��on). [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/ch07introduc�on#return2) ]

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Due to the fact that excess demand drives prices upward and excess supply drives prices downward, profit-maximizing sellers of undifferen�ated products must be price-takers.

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7.1 Short-Run Price and Output Decisions in Pure Competition

In iden�cal–products markets, prices are determined by what we call market forces. These market forces are the pressure exerted by buyers and sellers to move the market price level upward or downward, and occur due to either excess supply or excess demand. Excess supply at the market price means that the quan�ty supplied exceeds the quan�ty demanded at that price, and thus sellers are unable to sell all that they want to sell at the exis�ng price. Because products are iden�cal in undifferen�ated product markets, a very slight reduc�on in price would allow the firm to offer a be�er value proposi�on to poten�al buyers. When products are undifferen�ated, price is necessarily the only difference between the various sellers' products, so all poten�al buyers would flock to any seller offering a lower price. That firm would soon sell out, and other sellers would be similarly mo�vated to also reduce their price slightly, so that they too would sell more output (and make more profit). When all firms have slightly reduced their prices, the market price will have moved to the new slightly lower level. If there remains excess supply at this price level, the process would con�nue: Each firm is again mo�vated to reduce price slightly to sell all their output (rather than a lesser amount) at a price just below the market price. This process con�nues un�l the excess supply disappears, and it disappears when the quan�ty supplied by the sellers (at the market price) is just equal to the quan�ty demanded by all the buyers at that same price.

Excess demand occurs when the quan�ty demanded by buyers at the market price exceeds the quan�ty that suppliers wish to provide at that price. Excess demand causes upward pressure on the market price level, and this occurs because any firm will see that it could sell all it wants to at a slightly higher price and will be mo�vated to raise its price to maximize its profits. Since all firms are similarly mo�vated to gain more revenue for the same quan�ty of output, the market price is pushed upwards slightly. If there remains excess demand at this higher price, it means that some buyers are s�ll seeking to buy the product but are unable to do so, so the profit- maximizing firm will see the opportunity to again raise price slightly and sell all it wants to at a slightly higher price. This process will be repeated un�l the excess market demand (and the upward pressure on market price) disappears and market quan�ty demanded equals market quan�ty supplied.

This principle—that excess demand drives the market price upward, and conversely, excess supply drives the market price downward—is the fundamental reason why profit-maximizing sellers of undifferen�ated products must be price-takers; that is, they simply accept the market-determined price (see Chapter 1). If a firm sets price above the market price, it would sell no product at all (and that will not be profit-maximizing). Conversely, if it sets price below the market price, buyers would want to buy all the firm could produce, but the rising marginal cost of the la�er units (due to the law of diminishing returns; see Chapter 5) would exceed the price and it would not be profit-maximizing to serve all the demand at the lower price. Although the seller opera�ng in pure compe��on can change its own price upward or downward, the profit-maximizing thing for the individual seller to

do is to accept the market price level (unless there is evidence of excess demand or excess supply).

There are many markets with many sellers of undifferen�ated products that fulfill the characteris�cs of pure compe��on. Examples are:

the (stock) market for ownership shares in listed public companies, which determines the price of one unit of stock in a par�cular company at any par�cular �me; the loanable funds market, which determines the interest rate (borrowing price) for loans of any specific period and risk profile, issued in any specific currency; the bond market which determines bond prices for the bonds of a specific company with a specific dura�on remaining before those bonds are redeemed; the foreign exchange market, which determines the exchange rate for a par�cular na�onal currency (i.e., price of that currency in terms of other currencies); and

the market for undifferen�ated agricultural products such as milk, eggs, corn, and co�on.3

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#Ch7footNote3)

In all these markets, price determina�on takes place all day every day, and prices move upwards or downwards many �mes each day according to whether there is temporarily excess demand or temporarily excess supply in the market at the prevailing price level.

In Figure 7.1, we show the market demand and supply curves for a par�cular iden�cal products market. The market demand curve is the summa�on of the demand curves of individuals, as we saw in Chapters 3 and 4. Note that it slopes downward to the right so more will be demanded at lower prices than at higher prices. This follows from the u�lity-maximizing behavior of individuals who, as we saw in Chapter 3, will a�empt to equalize the ra�o of marginal u�lity to price (MU/P) for all products and services they consume. If the price of product X has fallen, other things being equal, the MUx/Px ra�o

for the last unit purchased of product X must have increased, so consumers will buy more of X to restore the u�lity-maximizing balance of MU/P across all goods and services purchased. This subs�tu�on in favor of product X does not go on forever because the MU of any par�cular product or service declines (due to the law of diminishing marginal u�lity) as the individual consumes more of that item. So MUx falls as more of product X is consumed un�l a new

u�lity-maximizing combina�on of products and services is found (for each consumer) that necessarily includes more of product X than it did at the higher price. Thus, the market demand curve slopes downward to the right because more units are demanded at lower prices than at higher prices.

Conversely, the market supply curve slopes upward and to the right so more is supplied to the market when the price is higher than when it is lower. The market supply curve reflects the summa�on of the supply of all the firms opera�ng in the market for a par�cular product or service. It slopes upward to the

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right because of the profit-maximizing behavior of suppliers who are subject to the law of diminishing returns in their produc�on processes. This law, you will recall from Chapter 5, reflects the declining marginal product (MP) of the variable input factors as these are applied progressively and more intensively to the fixed factors of produc�on. We saw in Chapter 5 that diminishing marginal produc�vity causes the marginal cost (MC) of produc�on to rise

progressively as the output rate increases.4 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#Ch7footNote4) The profit-maximizing firm will not want to supply output at levels where the MC (which equals incremental cost in this case) is higher than the price (which equals incremental revenue in this case). But at a higher market price the profit-maximizing firm would willingly supply more units of output, since the incremental revenue would exceed MC for at least one more unit of output. When all sellers act in this same way, it is clear that the aggregate amount they supply to the market must increase when the market price is higher and decrease when the market price is lower—thus the market supply curve slopes upward and to the right.

In Figure 7.1, we demonstrate the existence of excess demand at price P1, where Q2 is demanded but only Q1 is supplied. This excess demand will leave a

quantum of demand (equal to Q2–Q1) unsa�sfied and you can see that all of those poten�al buyers would be willing to pay P1 or more to purchase the

product.5 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#Ch7footNote5) These unsa�sfied buyers will offer to purchase at prices higher than P1 and the

price will dri� upwards toward the price (P*) at which there is no excess demand le�. For example, suppose that in the egg market there is an automated auc�on system to determine the market price. The auc�oneer would first propose an ini�al price, such as P2 (per dozen of a par�cular quality, such as

extra-large free-range eggs) and the poten�al buyers (i.e., food stores) enter their bids to buy various quan��es at that price, and the poten�al sellers enter their bids to supply various quan��es at that price. Suppose the automated system then calculates that quan�ty demanded (Q2) exceeds quan�ty supplied

(Q1). The auc�oneer (or the automated system) then proposes a somewhat higher price and the poten�al buyers and sellers adjust their offers accordingly.

We expect the buyers to want to buy somewhat less at the higher price as they will be ac�ng to maximize their profits and know that they face a downward-sloping demand curve for this product in their retail stores. Conversely, we expect the sellers to offer somewhat more eggs to the market at a

higher price because, although they face increasing marginal costs of produc�on, the higher price will cover the incremental costs of addi�onal supply.6

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#Ch7footNote6) If there is s�ll excess demand at the higher price, the auc�oneer again proposes a s�ll higher price, and this process con�nues un�l the quan�ty demanded just equals the quan�ty supplied (i.e., Q*) at the equilibrium market price (P*).

Figure 7.1: Market supply and demand curves and the equilibrium market price

Oppositely, if the price is ini�ally at the higher level, P2, the quan�ty supplied will greatly exceed the quan�ty demanded by the amount shown in Figure 7.1

as "Excess supply." Suppliers will find that there is insufficient demand for their products and they will have unplanned accumula�on of inventory (if the product is tangible) or underemployed workers and facili�es (if the product is a service). This will induce suppliers to reduce their quan�ty supplied (or

output levels if supplied in real �me) while offering excess inventory of the product for sale at lesser prices.7

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#Ch7footNote7) Because (in pure compe��on) the firms' products are perceived to be iden�cal, the buyers will buy from any seller asking a lower price causing sellers who maintain the higher price to sell nothing at all. Thus, prices will fall un�l the excess supply situa�on is removed, and this occurs at price P*. At price P* there is neither excess demand nor excess supply, and thus there are no longer any market forces opera�ng to either raise or lower the price, and thus we say that P* is the equilibrium price. As noted in Chapter 1, the equilibrium price is also known as the market-clearing price, as its clears the market of all products to be sold.

The Profit-Maximizing Output for Firms in Pure Competition

We have argued above that the profit-maximizing firm will want to raise its output rate if the market price is higher and reduce its output rate when the market price is lower. We will now explain more fully how the price-taking firm, opera�ng in an undifferen�ated market where price is determined by market forces, makes its output-rate decision. In Figure 7.2, we show the market price determina�on in the le�-hand graph and the firm's output rate decision in the right-hand graph. We extend a line across from the market graph to the firm's graph to signify the price level that the firm must set; in effect, that line becomes the demand curve for the purely compe��ve firm. A demand curve shows how much a firm can sell at various price levels—in this case the purely compe��ve firm can only use one price level, but it can sell any amount (i.e., all that it wants to) at the market price level. Thus, we showProcessing math: 0%

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The foreign exchange market is an example of pure compe��on. Price determina�on occurs daily, and prices shi� several �mes each day according to whether there is temporarily excess demand or supply in the market at the prevailing price level.

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the firm's demand curve as the horizontal line labeled d. Since the firm can sell any number of output units at the market price, its marginal revenue, which is defined as the change in total revenue (TR) due to a one-unit change in the output rate, or MR = ΔTR/Δq, must be equal to price, and thus the MR curve, shown as mr, is depicted by the same line as the demand curve for firms opera�ng in pure compe��on.

Now, to maximize profit at the market-determined price the firm must choose its output level such that marginal costs (MC) are equal to marginal revenue (MR). To understand why profits are maximized when MC = MR, consider a situa�on where MC > MR; this would mean that the last unit of output adds more to total cost (TC) than it adds to total revenue (TR) and thus it must reduce profit. Conversely if MR > MC this would mean that the last unit of output adds more to TR than it adds to TC, and thus its produc�on and sale must increase profit. It follows that produc�on should be increased to the output level where MC = MR (but not beyond this output level) if the firm wishes to maximize profit. In Figure 7.2, we can see this occurs at the output rate depicted as q*. Note that if the firm produced even one extra unit beyond q*, the point on the MC curve would lie above the mr curve, and thus profits would be reduced. Conversely, if the firm produced one less unit than q* the relevant point on the MC curve would be less than the MR and the firm would have foregone an opportunity to make a small addi�onal contribu�on (since incremental revenue would be higher than incremental costs) to the firm's profit. Thus, the profit-maximizing rule is to set output level such that MC = MR, which in the case of the firm in pure compe��on is the same as se�ng output such that MC = P.

Figure 7.2: The firm's choice of output rate in pure compe��on

No�ce that the area of the shaded rectangle in Figure 7.2 represents the firm's profits. The area of a rectangle equals height by width, of course. The height of the shaded box is equal to the difference between price and the short-run average cost at output level q*, that is P*–SACʹ, which is the (average) profit per unit at output level q*. The width of the box is equal to the number of units produced. Thus, total profits are equal to average profit per unit �mes the number of units, shown as the area of the shaded rectangle. The difference between price and SAC (i.e., P* – SACʹ) is also known as the price–cost margin or simply the profit margin.

Also no�ce that in Figure 7.2 we have used lowercase le�ers to depict the firm's demand, marginal revenue, and output levels to avoid confusion with the market-level demand and output variables. The rela�onship between big Q* and li�le q* is interes�ng, however. Since we have shown a representa�ve or average firm, we can say that Q* = nq* where n is the number of firms in the industry—the profit-maximizing outputs of the many small firms must add up to the total amount supplied to the market at price P*, namely Q*. (Obviously the scales on the horizontal axes in Figure 7.2 are different for the market graph and the firm's graph.)

Shifts of Market Demand and Supply Curves

The equilibrium market price is temporary, however, since any shi� of either the market supply curve or the market demand curve will cause a situa�on of either excess demand or supply to arise, and thus price will move towards a new equilibrium level. Such price adjustments happen con�nually in the stock markets, funds markets, bond markets, foreign exchange markets, and in agricultural commodity markets. So, firms that operate in purely compe��on markets should expect market price to change from �me to �me, and will need to respond quickly to adjust their output levels so that they can maximize profits under the new market condi�ons.

In Figure 7.3, we show a shi� in the market demand curve due to a change that has happened in the consumers' world. Perhaps their incomes have increased, or they have had a change in tastes towards this product. Or, perhaps the price of another product complementary in consump�on has fallen, or for some other reason (as discussed in Chapters 3 and 4), individual demands for this product have increased and thus the aggregate or market demand has shi�ed to the right. Since this demand shi� will cause excess demand at the former equilibrium market price P*, the price will be quickly adjusted upwards towards a new equilibrium price P**.

Figure 7.3: Output adjustments by firms due to a shi� in market demand curve

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Law of Demand and Supply

The individual firm's response to the higher market price will be to increase its output up to the point where MC equals the new marginal revenue level, which is shown as mrʹ in Figure 7.3. You can observe that the firm's profit has increased substan�ally, being equal to the much larger rectangle (in darker shading) defined by its height (the ver�cal distance between the new price level P** and the somewhat higher SAC level at output level q**) and its width (the number of units at the new profit-maximizing output level q**).

Also, note that the increase in the equilibrium market supply (from Q* to Q**) must be equal to n �mes the increase in supply of the individual firm (from q* to q**), where n is again the number of firms in the industry. Note that we have now explained both the ini�al (Q*) and the subsequent (Q**) market equilibrium quan��es supplied as the aggregate of the amounts supplied by the many firms in the industry in each situa�on. What is true for two aggregate output levels can be shown for other output levels as well. Thus, you will appreciate that the market supply curve S is

actually the horizontal summa�on of the MC curves of the many firms in the industry.8

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#Ch7footNote8) Indeed, the MC curve (for firms in pure compe��on) is effec�vely the individual firm's supply curve, since it shows what output level the individual will supply at various price levels. We saw in Chapter 3 that the market demand curve D is the horizontal summa�on of the individual consumers' demands at various price levels. Thus, individual suppliers and individual consumers jointly determine the market price in markets for undifferen�ated products. These market forces that cause price to rise when there is excess demand and to fall when there is excess supply are simply the result of individual consumers and suppliers trying to maximize their u�li�es and their profits, respec�vely.

3. Just as in the stock market example where we view the market for one company's stock (e.g., Google) to be a separate market from the market for another company's stock (e.g., Facebook), in these other markets, we view different quali�es of product (e.g., eggs from hens in cages versus eggs from free-range hens) as separate markets. In the market for free- range eggs, for example, most consumers will regard the various suppliers of free-range eggs to be supplying iden�cal products (in the absence of significant brand name recogni�on that would differen�ate these products of compe�ng suppliers). So, although buyers will compare the products offered across a product category as differen�ated subs�tutes (e.g., bonds with different maturi�es issued by different firms) they will choose the bond that offers the superior value proposi�on from their point of view, and in that bond market (e.g., for a bond issued by a par�cular organiza�on with a par�cular maturity) they will expect to pay the market-determined price. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#return3) ]

4. The output rate refers to the number of units of output produced per period of �me, shown as Q/t in the figures, to refer to output levels in any one produc�on period. An increased rate of output necessarily requires increased input of the variable inputs and involves the law of variable propor�ons (or the law of diminishing returns to the variable inputs). For the most part, we will simply say increases or decreases in output, or in output levels, but keep in mind that in the short-run context we mean the output rate per period of �me. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#return4) ]

5. The demand curve not only shows the maximum quan�ty buyers will demand at any price, but simultaneously shows the maximum price they will pay for any quan�ty. Note that all of the buyers between Q1 and Q2 are willing to pay a price higher than P1 (except for the very last buyer who is prepared to pay only P1). [return

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#return5) ] 6. Note that eggs can be held in cold storage for weeks and that the sellers can decide to supply more eggs from storage if the price is high enough or conversely, take some or all their

eggs back into storage if the price is not high enough. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#return5) ] 7. The upward-sloping supply curve reflects the rising MC levels of individual suppliers. For those firms, MC (incremental costs) should not exceed price (incremental revenue) if they are

to maximize profit. When the market price is lower, MC > P for the later units of produc�on. So the firm must reduce its output rate to reduce its MC and avoid making losses on output units produced when MC is higher than the market price. Price will tumble down from P2 to P* because at least some firms will sell their build-up of excess inventories at prices

below P2 and no buyer will be willing to pay a higher price for an undifferen�ated product if a lower price is available somewhere in the market. [return

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#return7) ] 8. The industry supply curve should be drawn as somewhat curved, as in Figure 7.4, to reflect it being the horizontal summa�on of the firms' MC curves which are typically curved.

[return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.1#return8) ]

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The entry of new firms can only occur in the long run. When the barrier to entry is low, new firms will con�nue to sprout up in the industry as long as its profits are superior to those obtainable in other industries.

© Peter Beck/Corbis

7.2 Long-Run Adjustments in Pure Competition

In Table 7.1, we noted that there are many firms in purely compe��ve industries because there are no barriers to entry, which means that other firms can enter the industry if they want to. Of course, they will want to in the case we have just seen—the healthy profits being earned by the representa�ve firm in the above situa�on will surely a�ract the entry of new firms keen to share in the profitability of this industry. Entry of new firms can only happen in the long run which, as we saw in Chapter 5, is the hypothe�cal situa�on in which a firm can change the fixed inputs necessary for produc�on. Some of these new entrant firms will be new firms started by individuals keen to be self-employed rather than work in another firm as an employee, while other new entrant firms will be exis�ng firms star�ng to produce the focal product as a product-line extension or exis�ng firms leaving industries that are unprofitable or less profitable and moving their resources into this more-profitable industry. In the case of entry by start-up firms, these firms must change their fixed resources from zero to some finite plant size, while firms switching into produc�on of this product must acquire at least some new industry- specific fixed resources in order to produce the product that is characteris�c of the industry.

Because the market supply curve is the horizontal summa�on of the individual firms' MC curves, it is evident that the entry of new firms must shi� the industry supply curve to the right, and we know that this will cause excess supply (assuming market demand is unchanged) and, thus, the market price will fall to a new equilibrium level. This will cause each firm to reduce its output level in order to maximize profits under the new condi�ons and the level of profit for the firms will be smaller than before as a direct result of the entry of the new firms. Indeed, if there are no barriers to entry, new firms will con�nue to enter this industry as long as its profits are superior to those obtainable in other industries, such that eventually all profit will be squeezed out of this industry, as we shall see.

Choice of Plant Size in the Long Run

In Chapter 5, we noted that in the long run the firm can switch to any other size of plant and that, in so doing, it might experience economies of plant size, constant returns to plant size, or diseconomies of plant size. That is, a larger plant size might cause the SAC curve to sit lower, or at the same level, or at a higher level than the current plant size. So, if the entry of new firms reduces the profits of exis�ng firms, the exis�ng firms should inves�gate whether a different (larger or smaller) plant size would allow them to be more profitable.

But, in fact, the situa�on facing the firm producing undifferen�ated products in an industry with no barriers to entry is worse than that—there is generally only one plant size that will allow them to even survive, and that is the one we called (in Chapter 5) the op�mum size of plant, which is the SAC that is nested at the lowest point of the long-run average cost curve (LAC). In Figure 7.4, we show an LAC curve and the op�mum size of plant is denoted as SAC*. Imagine that the representa�ve firm is ini�ally opera�ng the smaller plant size shown as SACʹ and the equilibrium market price is ini�ally P* reflec�ng the intersec�on of the ini�al market demand and supply curves D and S. The representa�ve firm's profit-maximizing output level is ini�ally q* where MC = mr under the ini�al market and industry condi�ons.

Figure 7.4: Movement to the op�mum plant size in the long run

At the ini�al market demand (D) and supply (S) situa�on, the representa�ve firm is making a healthy profit, since the market price P* is higher than its average costs (on the SAC' curve) at the profit-maximizing output level q*. But the existence of this profit will a�ract the entry of new firms in the long run. The poten�al for exis�ng firms to make even larger profits by building the op�mum size of plant will result in addi�onal supply of product from these firms, which must shi� the market supply curve to the right, as shown by Sʹ in the le�-hand side of Figure 7.4. If just the right number of new firms enter the market, and all firms adopt the op�mum size of plant, the supply curve will be shi�ed across to Sʹ, which will force the equilibrium price down to P** just equal to the minimum level of the LAC curve. You can see that the only way that the representa�ve firm can survive in this industry is to move to plant sizeProcessing math: 0%

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SAC* since it is inevitable that the market price will fall to the long-run equilibrium price level P**, which just covers average costs at the minimum point of LAC* (where MC* = mr*). If it fails to move to the op�mum plant size before too many new firms enter the industry it will be le� stranded with a higher

cost structure, will take losses, and may be unable to afford to build the op�mum plant size that will allow it to remain in the industry.9

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.2#Ch7footNote9)

Normal Profit in the Long Run

But why would a firm want to stay in an industry if the price is just equal to the level of average costs? Does this mean the firm is making no profit at all? Well, no, it does not, because we are speaking in terms of economic costs (see Chapter 5) meaning that the costs include the opportunity costs of being in this par�cular industry—that is, the cost curves include, as a foregone opportunity cost, the return on investment that could have been obtained in the next-best-alterna�ve investment opportunity. That means there is no incen�ve to shi� from this industry to the next-best-alterna�ve industry because the firm is already earning what it could earn in that alterna�ve industry. When price is just equal to SAC, economists say that the firm is earning normal profit, meaning the profit level is as good as the firm could earn elsewhere. So, suppose the firm could alterna�vely have earned 5% return on investment (ROI) in the next-best-alterna�ve use of its resources (in a different industry); normal profit in the chosen industry represents a 5% rate of return on investment. Conversely, when price exceeds SAC, like in the shaded box in Figure 7.2, economists say the firm is earning pure profit, or excess profit, also known as economic profit, which is a be�er profit rate than it could earn elsewhere (i.e., > 5% ROI in this example).

If the firms in a purely compe��ve market are making losses in the short run, due to too many firms in the industry, they will want to sell up their fixed resources and invest in a different industry as soon as they can—that is, in the long run. Some of these firms will have smaller financial reserves and will be forced to close, or will find a buyer sooner than others, and as they do stop supplying output, the market supply curve will move back to the le�, li�le by li�le, un�l a new market equilibrium is a�ained and all remaining firms can earn normal profit again. Examples of this kind of adjustment are seen in small- farm agriculture and also in the coastal fishing industry: when prices are "bad," some firms cease supplying the market and sell their farm or their fishing boat, reducing total supply. When prices rise again, others buy the assets (farms or boats) and enter the industry, forcing prices down again, and this process con�nues with profits oscilla�ng around the normal profit level.

What we have seen here, in the context of an industry with no barriers to the entry of new firms and where the firms produce undifferen�ated products, is

that while firms may make pure profits in the short run, they can only expect to make normal profits in the long run.10

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.2#Ch7footNote10) In the next sec�on we look at firms producing differen�ated products in other market forms where they are protected by barriers to the entry of new firms, and we will see that such firms can make pure profits in the long run.

9. Note that a late move to the op�mum size plant by an exis�ng firm would shi� the market supply curve to the right and depress market price below the LAC curve. Thus, all firms would take losses and would wish to exit the industry. Some would be able to liquidate their fixed assets sooner than others and would leave, thus causing the market price to rise, such that all remaining firms would no longer be taking losses and would no longer want to exit the industry. Note also that short-run profits may induce a flood of new entrants (ac�ng independently) such that the market price might be forced down below minimum LAC. This would cause some firms to exit the industry un�l exactly the right number of firms remain in the industry, such that market supply and demand intersect at an equilibrium price level that is just equal to the minimum level of the LAC curve. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.2#return9) ]

10. The pure compe��on long-run equilibrium assumes that all pure-profit opportuni�es elsewhere have already been taken; that is, in the absence of barriers to entry, new firms keep being established to exploit pure-profit opportuni�es un�l there are none le�. The long-run equilibrium situa�on (where all firms make only normal profits) is never likely to be observed in prac�ce because market demand and supply curve are con�nually shi�ing back and forth due to exogenous shocks, causing the firms to be con�nually adjus�ng to those changes. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.2#return10) ]

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A farmer's market is an example of monopolis�c compe��on because there are many vendors offering slightly differen�ated products. Some vendors might have friendlier service or be�er looking produce than the compe��on.

© iStockphoto/Thinkstock

7.3 Monopolies and Oligopolies

As we saw in Table 7.1, there are three market forms in which the firms' products are differen�ated, namely monopolis�c compe��on, oligopoly, and monopoly. In the following subsec�ons we shall examine the firm's pricing and output decision for profit maximiza�on in each of these market structures. The common theme is that these firms are price-makers and face downward-sloping demand curves (at the firm level), which means that they can sell more output at lower prices and less at higher prices. Thus, they have a combined price and output decision to make.

Monopolis�c compe��on is characterized by many firms producing slightly differen�ated products in an industry that has no barriers to entry. Thus, it is different from pure compe��on in only one way: the firms' products are differen�ated rather than iden�cal. Because the products are differen�ated, raising price slightly above the price of rivals will not cause sales to fall to zero (as it would in the iden�cal products case). While some customers will switch to another product when the firm raises its price slightly, most customers will remain with the firm, because they believe the firm s�ll offers them the best value proposi�on even at a slightly higher price. You will recall from Chapter 3 that the value proposi�on can be characterized as "quality over price." Different percep�ons of quality underlie the percep�on of product differen�a�on. In monopolis�c compe��on different customers look at the compe�ng products from their own individual perspec�ves and perceive qualita�ve differences that either do appeal to them (or do not), thus inducing them to pay more (or less) for the different products.

An example of monopolis�c compe��on would be a farmer's market, where some of the vendors have more friendly personali�es, and some of the vendor's apples are shinier and less marked than others. You might willingly pay five cents more per apple if the seller was friendlier and the apple was perfect compared with another nearby seller who was grumpy and had blotchy apples. But, if the former seller raised his price by another 10 cents you might change your mind and buy the cheaper less-perfect apple from the less-perfect vendor. Others might s�ck with the friendly seller at the higher price even when the price is raised by an addi�onal 10 cents because in their minds it is s�ll the best value proposi�on. Another example of monopolis�c compe��on might be coffee shops in large ci�es; people will see them as differen�ated on one or more criteria that are important to them (e.g., coffee taste, convenience of loca�on, cheerful vendor) and will prefer one over the others. However, this preference will not be sustained if their preferred seller raises its price by too much—another seller's product then becomes a be�er value proposi�on. A third example might be clothing retailers in large shopping malls. O�en there are dozens of compe�ng clothing stores in a large mall, and the clothes for sale typically differ between the stores, the quality of service may differ, and some stores are closer to the parking lot. Even when two or more stores sell exactly the same dress, the "product" (which includes the a�ributes of service quality, shopping ambiance, and convenience of loca�on) is likely to be seen as slightly differen�ated. Accordingly, some of these firms will have slightly higher prices and others slightly lower prices for their similar but differen�ated products, and all firms could raise their prices slightly without losing all their customers. On the other hand, if they reduced prices slightly, they would gain a significant number of

customers, but many others would ignore the price reduc�ons and s�ck to their current supplier.11

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#Ch7footNote11)

The demand curve for a monopolis�c compe�tor will be downward sloping but rela�vely flat. That is, there will be a rela�vely price–elas�c demand reac�on to price increases or price decreases, meaning that the percentage change in quan�ty demanded would be significantly larger than the percentage change in the firm's price level, as we learned in Chapter 4. Also in Chapter 4 we learned that when the firm's demand curve is downward sloping, total revenue (TR) will rise at first and later fall as price is varied from rela�vely high levels to rela�vely low levels, such that the TR is represented by an inverse U-shaped curve, sloping upwards at first, reaching a maximum, and sloping downwards therea�er as price is reduced s�ll further (see Figure 4.2 in Chapter 4). Since marginal revenue (MR) is the rate of change of TR, we saw that it falls progressively, reaches zero at the midpoint of the demand curve, and is nega�ve therea�er. This rela�onship between the demand curve and the MR curve for a monopolis�c compe�tor is shown in Figure 7.5, but note that because the firm's demand curve is highly elas�c the MR curve does not become nega�ve (i.e., cut the horizontal axis) within the range of outputs relevant to the firm's SAC and MC curves in Figure 7.5. The profit-maximizing rule remains the same: The firm should set price and output such that marginal costs equal marginal revenue, in this case MC = mr. Thus, the firm sets price P and output level q and consequently maximizes profit, which is shown as the rectangle equal to the average profit (i.e., P – SAC) �mes q units.

Figure 7.5: Price and output determina�on for the firm in monopolis�c compe��on

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Long-Run Adjustment in Monopolistic Competition

Because this firm is making pure profit and there are no barriers to entry in monopolis�c compe��on, other firms will be mo�vated to enter this industry producing similar but differen�ated products un�l all the pure profit is squeezed out. As in purely compe��on markets, the exis�ng firms must adjust their plant sizes to ensure that they can make normal profits rather than losses (which would force them to exit the industry). In Figure 7.6 we show the long-run equilibrium outcome for firms opera�ng in a monopolis�cally compe��on market. Their demand curve has shi�ed to the le� as new rivals con�nue to enter and "steal" some of their sales. They can only survive if they build the size of plant (SAC*) that is tangent to the LAC at the point where the LAC is tangent to their demand curve, such that P = SAC = LAC, and separately MC = mr, of course.

Figure 7.6: Long-run equilibrium for the firm in monopolis�c compe��on

Thus, the firm in monopolis�c compe��on faces the same fate as the firm in pure compe��on; that is, other profit-seeking firms will enter the industry and squeeze out all the excess profits. The firms will nonetheless con�nue in business in their chosen industry because their economic cost of produc�on includes the opportunity cost of using their resources in the next-best-alterna�ve industry. The lesson to be learned is that absence of barriers to entry means that while these firms may earn pure profits in the short run they cannot expect to earn pure profits in the long run. We turn now to the remaining market forms that are characterized by barriers to the entry of new firms, and consequently examine situa�ons where the firms can make pure profits in the long run.

Oligopoly

An oligopoly is a market in which there are only a few sellers; the word is derived from the Greek word oligos, meaning few and the La�n word polis, meaning seller. "Few" in this context means a number small enough so that the ac�ons of any one firm have a no�ceable impact on the demand for each of the other firms in the market. Few also means that the firms will each have a significant share of the total sales in the market, and this market share becomes an important yards�ck by which they measure their success in the market. In the real world, the great majority of markets are oligopolies— prominent examples are the aircra�, automobile, steel, chemical, and pharmaceu�cal industries. These are na�onal and in some cases interna�onal oligopolies. In other industries, where there are hundreds or even thousands of firms na�onally or globally, firms will cons�tute oligopolies in the local or regional area due to transporta�on costs or consumer ignorance. For example, your bread would come from one of a few local bakeries, your car would be bought from one of a few local dealerships, ready-mixed cement would be sourced from a few local cement companies, and so on. Looking at this from the customer's viewpoint, an oligopoly exists when a typical customer considers only a few sellers when making a purchase decision, such that the sale made by

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The aircra� industry is an example of an oligopoly because it is a market in which there are only a few sellers.

© iStockphoto/Thinkstock

one seller is in effect a sale missed by another. If one seller conducts a promo�onal campaign or reduces its price, its sales increase substan�ally and the sales of the other firms decrease significantly, unlike monopolis�c compe��on where the gain of sales to one firm were spread as insignificantly small

reduc�ons of demand across many rivals.12 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#Ch7footNote12)

Thus, oligopolists suffer from mutual dependence, meaning the ac�ons of one firm impact upon the others, and vice versa. Restric�ng our discussion to price and output changes for the moment, the focal firm opera�ng in an oligopoly will soon learn that when another firm makes a price reduc�on and gains a substan�al increase in sales, the focal firm suffers a significant decrease in sales. This also works the other way around when the focal firm reduces its price. The firm will also learn that when it increases its price, it loses a substan�al propor�on of its sales while other firms gain significantly, and vice versa. Recogni�on of this mutual dependence will cause oligopolists to predict the reac�ons of rivals to their compe��ve ac�ons. If a firm expects that its rivals will react to its price reduc�on by also reducing price (to avoid loss of market share), the firm may decide that it is not worthwhile cu�ng price. Sales volume would increase only slightly, but there would be a reduced price for all units of output that would have been sold at the original (higher) price. Similarly, if the firm expects that other firms will ignore its price increase (since their sales volumes would increase significantly) it may decide that a price increase is not worthwhile. In the following sec�ons, we shall discuss two scenarios o�en experienced by oligopolists that are based on the firm's predic�on of how rivals

will react to its price changes. The first is the kinked demand curve, which results in prices not being adjusted very frequently despite changes in cost or demand condi�ons, and the second is conscious parallelism, which results in prices being adjusted every �me there is a significant change in cost or demand

condi�ons.13 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#Ch7footNote13)

The Kinked Demand Curve of Oligopoly

Oligopolists face a kinked demand curve when they expect rivals to ignore a price increase (to gain market share) but to match a price decrease (to protect their market share) and this arises because the demand curve for a price increase is highly price elas�c while the demand curve applicable for price

reduc�ons is highly price inelas�c.14 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#Ch7footNote14) That is, for price increases above the current price, quan�ty demand would decrease along a rela�vely flat demand curve, while for price decreases the quan�ty demanded would increase along a rela�vely steep demand curve. Thus, the demand curve faced by the firm is made up of two segments of different slopes that join at the current price level, and thus the firm's demand curve has a kink at the current price level, as shown in Figure 7.7.

Figure 7.7: Price rigidity with a kinked demand curve

Although this figure looks complex, you already have the knowledge to interpret it. The kinked demand curve (shown as the kinked line dadʹ, or the line connec�ng the points d, a, and dʹ) is made up of sec�ons of two different demand curves. The upper sec�on of the kinked demand curve (i.e., the sec�on da) is the demand curve that is appropriate for independent price increases, and the lower sec�on (i.e., adʹ) is the demand curve appropriate for joint price reduc�ons. Similarly, the marginal revenue curve (the disjointed line db-cmr) is made up of two parts of the marginal revenue curves that are associated

with the relevant sec�ons of the demand curve, with a gap (b-c) between the two tangible sec�ons.15

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#Ch7footNote15) Note that each of the marginal revenue curves is located such that it has the same ver�cal intercept and twice the slope of its "parent" demand curve, as we learned in Chapter 4. Now note that I have shown the MC curve passing through the gap in the marginal revenue curve. Thus, if the price were to be raised above price P, the price-quan�ty coordinate would move back along the independent- ac�on demand curve (i.e., sec�on da) and MR would exceed MC, indica�ng that the firm should increase its output rate to maximize profit. Conversely, if the price were to be reduced below P along the joint-ac�on demand curve (i.e., sec�on adʹ), output would increase, MC would exceed MR at any higherProcessing math: 0%

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When the cost of avia�on fuel increases, airlines respond by raising airfares. This is an example of conscious parallelism.

© Comstock/Thinkstock

output rate, so profit would be increased by raising price back to where it was. Thus, the current price level P is indeed the profit-maximizing price, with the magnitude of profit depicted by the rectangle defined by the price–cost margin (P-SACʹ) �mes the number of units sold, q.

Since the MC curve passes through the gap in the marginal revenue curve, costs condi�ons could change substan�ally without causing the price to change. For example, the MC curve could shi� ver�cally up or down a considerable distance yet s�ll remain within the gap in the MR curve. Similarly, with the MC curve unchanged, changes in the customers' incomes or preferences that cause the demand curves to move either to the right or to the le� would shi� the gap in the MR curve (to the right or the le�, within limits) without causing the MC curve to intersect a solid sec�on (either db or cmr) of the MR curve. Thus, the current price would remain the profit-maximizing price (although the magnitude of profit would rise or fall due to the shi�s in the cost or demand curves) and we would see the characteris�c price rigidity of kinked demand curve oligopoly. That is, price levels remain fixed at the current level despite changes in cost or demand condi�ons because of the firms' expecta�ons that price increases would be ignored and price reduc�ons would be followed.

Conscious Parallelism in Oligopoly Markets

In many oligopoly markets the recogni�on of their mutual dependence leads rival firms to adopt an implicit price leadership model, whereby one firm (the price leader) ini�ates a price increase and the other firms (price followers) independently raise price by the same amount or by a similar percentage. Note that an explicit agreement to jointly adjust prices would be quite illegal under collusive pricing provisions of the An�-Combines Act in the United States (or under similar laws against price fixing in other countries). It is not illegal, however, for one firm to raise price independently and take the risk that others will not follow. If rival firms subsequently also raise their prices to a similar extent, all firms will avoid the kink, since quan�ty demanded would move upwards along an extension of the more inelas�c (joint-ac�on) part of the oligopolist's demand curve.

In prac�ce, we o�en see firms in oligopoly markets independently but more or less simultaneously adjus�ng their prices upward (or downward) in response to cost or demand increases (or decreases) that are common to them all. Typically commercial banks all raise (or lower) their interest rates on consumer loans, home mortgages, and business loans over the few days following the central bank (the Federal Reserve in the United States) raising (or lowering) the rate at which it lends money to the banks. Airlines might independently adjust airfares upwards by a similar propor�on when the cost of fuel rises for all airlines. Manufacturers in a par�cular industry might all raise their prices at about the same �me due to the government's implementa�on of a carbon tax applicable to that industry, and so on. This has been called conscious parallelism, defined as firms independently ac�ng in a parallel fashion while conscious that their rivals have the same incen�ves to act in the same way at about the same �me. Given an�-collusion laws it is impera�ve that rival firms do not communicate with each other at all about prices or costs, since evidence of that communica�on might be held as prima facie evidence of collusive price fixing.

In Figure 7.8 we show a firm raising its price in conscious parallelism due to a cost increase that applies more or less equally to all firms in an oligopoly. The firm's ini�al price is P and its demand curve is kinked at point a, causing a ver�cal gap in

the marginal revenue curve through which the ini�al marginal cost curve (shown as MC) passes.16

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#Ch7footNote16) The cost curves then shi� upwards from MC to MCʹ and from SAC and SACʹ. This firm, ac�ng as a price leader, then raises its price from P to Pʹ in the expecta�on that rival firms will do likewise, and if this indeed happens the firm effec�vely moves up the joint-ac�on sec�on of the demand curve from point a to point aʹ where a new kink would be expected, since the firm does not expect rivals to raise their prices by any higher amount.

Figure 7.8: Price leadership through conscious parallelism in oligopoly markets

In Figure 7.8, you will see that we have also shown the market demand curve, D, for the industry, and it is drawn such that the total market demand for the product is four �mes larger than the quan�ty demanded of the focal firm at each of the price levels indicated. This would mean that the focal firm has a 25% share of the market at each price level, and demonstrates that the joint-ac�on sec�on of the demand curve is the firm's constant-share-of-the-market demand curve. In this par�cular case there might be three other firms each also having 25% of the market, or there might be more than, or fewer than, three other firms whose shares of the market sum to the remaining 75% of the market demand at any par�cular price. As men�oned previously, oligopolists

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Due to government prohibi�on, the United States Postal Service has a monopoly on le�er carrying. Monopolies occur when there is only one seller of a par�cular product in a specific market.

© iStockphoto/Thinkstock

are typically very concerned with maintaining their share of the market and will tend to achieve this by ac�ng in conscious parallelism when costs or demand condi�ons change.

Before we leave oligopoly, note that compe�ng firms do not need to set exactly the same price levels, as might seem to be implied by Figures 7.7 and 7.8. Price differen�als between and among firms are common in oligopoly markets and reflect both the differences in the a�ributes contained in the products (i.e., differences in the firms' costs) and differences in customer preferences for those a�ributes (i.e., differences in demand) across compe�ng firms. For example, a par�cular Mercedes Benz model is typically sold at a price that is higher than a similar sized and equipped Ford or Toyota. Such rela�ve prices tend to be the historical outcome of prior profit-maximizing adjustments to price by each firm and tend to be maintained over �me by the prac�ce of

conscious parallelism.17 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#Ch7footNote17)

Monopoly

Monopolies are defined as the only seller of a par�cular product in a par�cular market. This may be because they are the first firm to supply that product to that market (such as an entrepreneurial new venture introducing a new product to a previously unserved market, or an exis�ng firm entering a previously unserved geographical market) or because the entry of other firms into the market is prevented by barriers to entry. As discussed earlier in this chapter, barriers to entry are insurmountable problems that prevent poten�al entrants from assembling the necessary resources to begin producing and selling a compe��ve product. The inability to gain access to the necessary technology (e.g., the monopoly may have a patent on the technology) or to acquire another indispensable resource (e.g., there is only one deep water harbor near a major city and that is controlled by the port authority) will prevent another firm from entering the monopolist's market. Perhaps the major reason for monopoly markets is government prohibi�on of a second supplier. For example, the United States Postal Service is allowed a na�onal monopoly on le�er carrying, and electricity and gas companies are o�en granted regional monopoly status for the provision of these u�lity services.

Since the monopolist firm is the only firm in the market, the market demand curve becomes the firm's demand curve, and the monopolist must choose the profit-maximizing price and output combina�on on that demand curve. The profit-maximizing rule is the same, of course, namely MC = MR. We saw in Chapter 4 that a linear demand curve has an associated marginal revenue curve that shares the same ver�cal intercept with the demand curve and has twice the slope of the demand curve, as we have shown in Figure 7.9. Superimposing the firm's short-run cost curves SAC and MC on the demand and marginal revenue curves, we see that the monopolist should choose price P and sell output level Q to maximize its profit in the short run. Its short-run profit is indicated by the rectangle of height P – SACʹ (the profit margin per unit) and width Q (the number of units of output).

Now considering the long-run average cost curve, LAC, and the associated long-run marginal cost curve, LMC, the monopolist can increase profit in the long run by choosing the output level where LMC = MR, which is shown as Q*, and set the corresponding price P*. The resultant magnitude of profit in the long run is shown by the considerably larger rectangle of height equal to the price–cost margin at output level Q* (i.e., P* – SAC*) and of width equal to Q* units of output. Figure 7.9 is already quite busy, so it does not show the SAC* curve or its related SMC* curve of the plant size that the monopolist would choose in the long run—that is your task! To prove that you understand the analysis, look carefully at Figure 7.9 and tell yourself where in that figure you

would place the SAC* and SMC* curves of the plant that the profit-maximizing monopolist would want to build and operate in the long run.18

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#Ch7footNote18)

Figure 7.9: Monopoly price and output choice in the short and long run

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Natural Monopolies

As men�oned earlier, another reason for the existence and persistence of monopolies is that they may be natural monopolies, meaning that even if another firm did enter the market there would subsequently be a takeover or merger of the two firms and the market would revert to a monopoly again. The inevitable merger of compe�ng firms in a natural monopoly situa�on is due to the rela�onship between the limited size of the market and the economies of plant size available in the industry. If the market demand curve crosses the LAC curve before the lowest point on that curve, the two firms opera�ng smaller plant sizes could make greater profit as a single firm opera�ng a larger but lower-cost plant size. This is illustrated in Figure 7.10, where we show the market demand curve (D) crossing the LAC before its minimum point.

For simplicity of exposi�on, we assume that there are ini�ally two firms, each separately opera�ng a rela�vely small plant size, which we will depict by lowercase le�ers sac and mc for exposi�onal clarity. For further simplicity, we assume the two firms share the market equally, that is, 50% each, and always match the other's price. Accordingly their joint-ac�on or share-of-market demand curve (shown as d) will be coextensive with the MR curve, since both d and MR lie halfway between the ver�cal axis and the market demand curve. The joint-ac�on demand curve, d, will have a marginal revenue curve, shown as mr, associated with it. To maximize profits, each firm would set mc = mr, produce output level qʹ and sell at price Pʹ. The profit of each firm would amount to the rectangle shown by the profit margin (Pʹ – sacʹ) mul�plied by the number of units sold, qʹ.

Figure 7.10: Natural monopoly

Now, the owners/shareholders of these two firms will pre�y soon figure out that if they merged they could make more profit than they could separately as compe�tors in a market that is rela�vely small compared to the available economies of plant size. Opera�ng independently as compe�ng duopolists (i.e., two sellers) they can only make total profit of twice the profit rectangle shown as (Pʹ – sacʹ) �mes qʹ in Figure 7.10. Merging to become a monopolist would allow them to build the plant size SAC* and operate it at the output rate Q* where SMC* = MR = LMC. The profit of the resultant monopoly firm would then be the average profit margin (P* – SACʹ) �mes the output level Q*, which is clearly much larger than the sum of their previous profits opera�ng as compe�ng duopolists.

If you understand Figure 7.10, you should be proud of yourself because it was ge�ng pre�y heavy, wasn't it? Figure 7.10 incorporated a variety of concepts newly introduced in this chapter and also called upon other concepts from earlier chapters, and is probably the most complex figure in this book. Good for you if you understood it all the first �me through. If not, go through the chapter again, maybe when you are not so �red, and I'm sure it will s�ck the next �me through.

Regulated Monopoly

Now for something rela�vely simple to finish the chapter—the situa�on of regulated monopoly. Government regula�ons o�en are imposed on so-called public u�lity "monopolists" to prevent them from making huge profits, o�en from a natural monopoly posi�on, by charging rela�vely high prices for electricity (for example) to ci�zens who have no alterna�ve source of supply. In Figure 7.11, we assume that the regulators have imposed a ceiling price, or maximum allowable price, of Preg on the monopolist (who would prefer set price P* to maximize profits).

Figure 7.11: Price regula�on of monopoly

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If prices above Preg are prohibited, then the demand curve facing the firm is effec�vely the kinked line that is horizontal at the level Preg out to point a and

then con�nuing down the market demand curve, D. As we know, from the oligopoly discussion, a kinked demand curve means that the marginal revenue curve must be the discon�nuous line Preg a– bMR, in this case coextensive with the horizontal sec�on of demand curve (from Preg out to point a), then

falling abruptly to point b and then con�nuing down the MR curve. To maximize profit subject to the regulated price, the monopolist will choose the output level Qreg (where LMC passes equals marginal revenue at point a) and build the size of plant that has its SAC curve (not shown) tangent to the LAC curve at

output level Qreg. The regulators are not likely to be happy with that, however, since the monopolist is s�ll making excess profits, because the regulated

price is above the firm's LAC curve. The regulators are likely to set the regulated price at the lower level Pʹ, where the LAC curve cuts the demand curve, D, such that the supply of the u�lity is increased to Qʹ and the monopoly makes only normal profit where price equals average costs. Note that marginal revenue will not equal marginal costs in this situa�on; the monopolist is prevented from maximizing profits by the regulator who is ac�ng in the public interest to facilitate a lower price and a higher output level for consumers of this product. This form of price regula�on is known as average-cost pricing.

11. No�ce that lack of informa�on, causing the buyer to be unaware of the price difference (or price change), is another reason why some customers do not switch to the lower-priced supplier. Unless customers know all the prices in all the stores all of the �me, they may unwi�ngly pay more on some occasions, being unable to verify if the same or similar item is available elsewhere as a be�er value proposi�on. If buyers must incur search costs of �me and money to find out firms' prices, they might be be�er off simply paying a li�le more for a product when its price is raised and thereby avoid those search costs. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#return11) ]

12. Industries with many firms that look like monopolis�c compe��on when considered na�onally or globally, typically operate as a series of interlinked oligopolies at the local level due to the shopping convenience and informa�on advantages of the local firms, causing poten�al customers to not consider more-distant suppliers. But note that Internet shopping, which offers informa�on, convenience, and lower prices in many cases, tends to offset these advantages of local firms and may make such "many firm" industries operate more like monopolis�c compe��on. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#return12) ]

13. There are many other oligopoly scenarios that might be examined, such as cartel pricing, where the firms act collusively (and illegally) to set the same price, or raise prices by the same percentage to preserve their price differen�als. There are also several price-leadership models of oligopoly, such as low-cost firm price leadership and dominant-firm price leadership. These operate in essen�ally the same manner as conscious parallelism, whereby all firms tend to adjust their prices upward or downward at about the same �mes, following a price adjustment by any one firm, and thus preserve their market shares. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#return13) ]

14. Recall from Chapter 4 that price elas�c means that the percentage change in quan�ty demanded will be higher than the percentage change in price, while price inelas�c means that the percentage change in quan�ty demanded will be less than the percentage change in price. For example, sales might decrease 20% for a 10% price increase, but increase only 2% for a 10% price reduc�on. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#return14) ]

15. We are calling it a "curve" to follow conven�on, even though the MR is not curved when it is derived from a linear demand "curve" and in the case of the kinked demand curve the MR is a series of straight line segments! [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#return15) ]

16. The lower parts of the discon�nuous MR curves are not shown in Fig 7.8, since they would lie below the horizontal axis in this case. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#return16) ]

17. Marketers speak of "price posi�oning" whereby they choose strategically to set price at a premium to (above) or at a discount to (below) the prices of rival firms. Note that unless the quality of the product is simultaneously set at a commensurately higher (or lower) level rela�ve to rivals' quali�es, the price differen�al will not hold up in the market since customers will scru�nize compe�ng products looking for the best value proposi�on, where value equals quality divided by price, as we saw in Chapter 3. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#return17) ]

18. Note that the SAC level at output level Q* must equal the LAC at that output level, and that the short-run marginal cost (SMC*) curve needs to equal the MR at output level Q*. Try to work it out before you look at Figure 7.10! [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec7.3#return18) ]

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Summary

In this chapter, we have been concerned with the opera�on of business firms in markets, and specifically with their choice of price and output levels that will maximize their profits. A�er defining a market as a situa�on in which buyers and sellers communicate for the purpose of exchanging value, the four basic market structures were introduced. These are categorized on the basis of (a) iden�cal or differen�ated products; (b) barriers to entry of new firms, or not; (c) number of compe�ng firms; and (d) expecta�on of rivals' reac�on to strategic changes.

Pure compe��on is characterized by many firms producing iden�cal products, no entry barriers, and no expecta�on of rival reac�ons. Firms in such markets must take the market-determined price as given and simply adjust output to maximize profit in the short run, but can also adjust their plant size to the op�mum plant size in the long run. While they can make excess profits in the short run, they will be reduced to making only normal profit in the long run.

Monopolis�c compe��on is characterized by many firms producing slightly differen�ated products, no entry barriers, and no expecta�on of rival reac�ons. Firms opera�ng in such markets are able to choose their own price and output levels and can also adjust their plant size in the long run but will not adopt the op�mum size of plant because they face a downward-sloping demand curve. While they can make excess profits in the short run, they will be reduced to making only normal profit in the long run, where their demand curve is forced into tangency with the LAC curve on the downward-sloping sec�on of that curve.

Oligopolis�c compe��on is characterized by few firms, due to barriers to entry of new firms. These firms produce differen�ated products, and the firms recognize their mutual dependence and form expecta�ons about whether or not rivals will follow their price increases or price reduc�ons. We considered the kinked demand curve and price leadership via conscious parallelism whereby firms change prices independently but expect rivals to act in the same manner. Oligopolists can make excess profits in both the short and long run, assuming sufficient market demand.

A monopoly market is characterized by a single seller and is typically due to insurmountable barriers to entry. Although a natural monopoly market may allow entry of new firms, they are des�ned to merge with, or be taken over by, the monopoly firm due to the profit incen�ve facing shareholders to consolidate produc�ve capacity within a single business en�ty due to the economies of plant size available to a monopoly firm. Because monopolies can make excess profits in both the short run and the long run, governments o�en regulate a maximum price that the monopoly may charge, and the monopoly then selects the output level that is profit maximizing, given this constraint.

In the following chapter, we will u�lize the conceptual material from this and from preceding chapters to address pricing by business firms in real-world situa�ons when the managers do not have the data they need to simply draw the cost and demand curves and find the intersec�on of the MC and MR curves. Instead they must u�lize es�mated demand and cost func�ons or u�lize rules-of-thumb pricing procedures that avoid or minimize data search costs and provide acceptably correct solu�ons to their profit- maximizing problem.

Ques�ons for Review and Discussion

Click on each ques�on to reveal the answer.

1. Define "market." Explain how people can enter a market without actually being there. (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 market is a place or a situa�on where poten�al buyers and sellers can meet in person or by proxy to exchange items of value (including money). People can enter markets without being there by using a purchasing or sales agent, by using an electronic intermediary (e.g., buying and selling online) or paper-based statement of willingness to buy or sell at a par�cular price.

2. What are "barriers to entry"? Does a monopoly or oligopoly market necessarily have insurmountable barriers to entry? (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

Barriers to entry are reasons why new firms cannot enter some markets. They are either legislated by governments or are due to the prospec�ve entrants' inability to purchase or gain control of resources that are necessary to become established and to compete in the market. A monopoly or oligopoly market may not have insurmountable barriers to entry, but could be a "natural" monopoly or oligopoly in the sense that although other firms can enter the market they would soon be absorbed by merger or takeover. This would occur because shareholder value would be maximized by a smaller number of firms in markets that are small rela�ve to the scale of plant at which diseconomies of plant size begin.

3. Define product differen�a�on in terms of the a�ributes of the firm's products or services. (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

Product differen�a�on can be defined as the design of products within a product category such that the products contain different product a�ributes, and/or different combina�ons of product a�ributes, and/or different quan��es of the same product a�ributes.

4. In what way(s) does a monopolis�cally compe��ve market differ from a purely compe��ve market? (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

Monopolis�cally-compe��ve markets differ from purely-compe��ve markets in that the former supply differen�ated products whereas the la�er supply iden�cal or undifferen�ated products. They share the characteris�cs of many firms, due to no barriers to entry, and firms having no expecta�on of rival reac�ons.

5. Under what circumstances would an industry that has many firms opera�ng na�onally be perceived by customers to be an oligopoly? (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/booProcessing math: 0%

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If customers only consider a few local suppliers, those customers effec�vely face an oligopoly market situa�on. The suppliers are likely to monitor each other's prices and quali�es if they realize that their loss of a sale is another firm's gain, especially if the products have rela�vely large value and are purchased infrequently (that is, "lumpy" sales).

6. Characterize the following market situa�ons in terms of the four market structures introduced in this chapter: (a) automobile dealerships in a large city; (b) colleges and universi�es marke�ng their degree programs to poten�al students; (c) an art dealer who wants to sell a unique pain�ng, such as the Mona Lisa; (d) a grain farmer selling wheat to one of 40 different flour-milling companies. (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) Auto dealerships in a large city are most likely to be oligopolists; (b) colleges and universi�es are also likely to be oligopolists for most students due to their loca�on and/or their focus on par�cular disciplines of study. For some students, such as an interna�onal student simply wishing to study anything anywhere in the United States, the market structure might be regarded as monopolis�cally compe��ve. (c) Although there are many other pain�ngs, the Mona Lisa is treated by art aficionados as unique, and thus the dealer selling it is the monopoly supplier of a product with no close subs�tutes. (d) The grain farmer is one of perhaps hundreds of such sellers of an essen�ally undifferen�ated product, with many buyers, and is thus in a purely compe��ve market situa�on.

7. Explain why you think people would want to become self-employed and establish firms to compete in monopolis�cally compe��ve markets when all they can hope for in the long run is normal profit. (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

Normal profit means as much profit as they could earn in the next-best-alterna�ve use of their resources. In the context of employment, people work for income and other non-monetary benefits associated with the workplace. Thus people might be happy to start their own business and earn only normal profits (what they could earn working for someone else) but gain be�er working condi�ons and job sa�sfac�on. Indeed, a self-employed person might earn less money but greater non-monetary rewards such that overall he or she prefers the self-employment alterna�ve.

8. Explain why the entry of new firms in the long run might depress the market price below the minimum level of long-run average cost (LAC) and immediately cause firms to want to exit the industry? Then explain why ALL the firms don't immediately exit and thus cause price to rise drama�cally, followed by a rush of new firms immediately entering the market, followed by endless repeats of this 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/boo

Since entry of new firms is an uncoordinated ac�vity across firms, dozens (maybe hundreds) of would-be firms might simultaneously react to the news of pure profits in an industry and start the entry process, resul�ng in too many firms entering the industry causing supply of the product to exceed demand, which forces price to fall and all firms to incur losses. At that point, all firms would see that they could make more profit elsewhere and be inclined to leave the industry, which they would all do together if they were alike in all respects. But in reality they are not exactly alike – some are slower to realize that prices have fallen; some take more �me to consider their op�ons and decide; some are unable to sell their assets as quickly as others; some are wise to the poten�al fluctua�on between profits and losses due to free entry and free exit of firms and so borrow to stay in business un�l profitability returns, and so on. Thus only some firms leave the industry and it returns to normal profitability in due course.

9. Why would you expect a firm opera�ng in an oligopoly to be more likely to absorb a cost increase (i.e., not increase price) when the cost increase only occurs for that firm, as compared to pass on a cost increase (i.e., increase price) when the cost increase applies to all or most firms in the industry. (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 oligopoly firm might absorb a cost increase that is specific to it because it knows that no other firm would be mo�vated to raise price but instead would be mo�vated to hold price constant and expand its market share if the focal firm raises price. Conversely if all firms suffer a common cost increase (such as a new tax, a mandated wage increase, or a price increase for a common raw material) the firm would expect all firms to raise price in conscious parallelism.

10. Why is it considered fair to regulate monopolies, such as public u�li�es? Why is the welfare of consumers (who want lower prices) put above the welfare of stockholders (who want higher profit)? (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

It is considered equitable to regulate monopolies because all people are consumers whereas not all are stockholders in firms (since many people cannot afford to make investments in the stock of business firms). Secondly, the holding of shares in a firm is typically concentrated in the hands of a few major stockholders rather than being spread equally among all stockholders. All consumers have to pay (directly or indirectly) u�li�es costs whereas only a smaller and more privileged group would benefit from higher profits due to un-regulated monopoly pricing.

Decision Problems

1. Show graphically what happens to price and output levels when the price of a par�cular agricultural commodity (e.g., corn) is ini�ally stable but then rises as a result of an announcement that crop failures are higher than expected. Explain why individual farmers (whose crops did not fail) increase the quan�ty of corn they are willing to sell, while food manufacturers decrease the quan�ty of corn they are willing to buy.

2. Suppose that medical scien�sts find that coffee causes cancer. Show graphically what would happen in the long run to the price and output levels of coffee in a representa�ve coffee shop. (Hint: a�er this announcement, the demand for coffee is likely to become more inelas�c for those who con�nue to want to buy coffee, such as those who are hooked on caffeine.)

3. Suppose that a par�cular airline is confronted with a 20% increase in SAC due to a wage se�lement with the union represen�ng their cabin crew fuel, but that other airlines have not suffered this cost increase.

a. From an assumed ini�al situa�on of airfares and costs (P, MC, AVC, SAC), show graphically (with careful measurement) why in one scenario a profit- maximizing airline would not raise its airfares, while in another scenario it would raise its airfares but by somewhat less than 20%. Explain why this happens. (Hint: the scenarios relate to the placement of the MC curve in the gap of the MR curve.)Processing math: 0%

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b. Now suppose that the 20% increase in costs is due to the increased cost of avia�on fuel, which impacts all airlines. Explain why it would most likely be profit maximizing for an individual airline to raise prices by the full 20% in this situa�on.

4. An entrepreneur has established a new firm that has a monopoly (secured by a patent) in the market for a new machine that changes chrome pla�ng to gold pla�ng in a simple and economical two-step process; that is, remove the chrome pla�ng and then apply the gold pla�ng using a series of chemical baths within the machine. A market survey has es�mated that the market demand curve for this machine is Q = 5,013.824 – 0.25P where Q is thousands of machines per year and P is in dollars. Cost es�ma�on processes have determined that the firm's cost func�on is represented by TC = 20,000 + 3600Q +

500Q2. a. Advise the entrepreneur as to the profit-maximizing price and output level. (If you cannot solve this algebraically, plot the MC, D, and MR curves and

es�mate the profit-maximizing price and output levels from your graphs.) b. What profit do you expect the firm will make in the first year? c. Do you expect this profit level to con�nue in subsequent years? Why or why not?

5. A public u�lity monopolist has es�mated its long-run total cost curve to be LTC = 1000Q – 150Q2+ 30Q3 where Q is thousands of units. Demand es�ma�on has indicated that the u�lity's demand curve is P = 9.9847 – 1.29Q where P is in dollars and Q is in thousands of units.

a. What price and output level would the u�lity prefer if it wanted to maximize profit? b. What price would the regulator force the u�lity to set if the regulator wanted the u�lity to earn only normal profit?

Key Terms

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

barriers to entry (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 things that prevent new firms from entering a given market, including their inability to gain supplies of essen�al resources, or very high costs required to set up a firm or build a credible reputa�on, or government prohibi�on of more than one firm opera�ng in a par�cular market.

conscious parallelism (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 whereby rival firms adjust price (or any other strategic variable) in the expecta�on that their rivals are likely to do the same, following a significant change in cost or demand condi�ons.

constant-share-of-the-market 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

A demand curve that preserves the firm's market share when rival oligopolists change their prices at the same �me and to the same extent (also known as the joint-ac�on sec�on of a kinked demand curve).

excess 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

Excess of the quan�ty demanded of a good or service, at a given price, over its aggregate supply at that price. Excess demand causes price to rise as sellers are able to gain higher prices for their output.

excess profit (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

Also known as pure profit, or economic profit, it occurs when price exceeds average costs.

excess supply (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 excess of the quan�ty supplied over the quan�ty demanded at a given price in a par�cular market. When there is excess supply, the price for the product is likely to fall, as sellers try to rid themselves of their surplus, or extra supply.

individual firm's supply 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

For firms in pure compe��on, an MC curve that shows what output level the individual firm will supply at various price levels.

kinked 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

A demand curve made up of two parts—one part is applicable for the oligopoly firm's independent price increases and the other part is applicable for joint- ac�on price changes where all rivals increase or decrease price at the same �me.

long-run equilibrium price level (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 price that would prevail a�er firms have entered or exited the industry and all firms have made profit-maximizing adjustments to their plant size, such that price equals the minimum point of the long-run average cost curve (LAC).

market (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 real or virtual loca�on that allows for buyers to interact with sellers to exchange goods for money or for other goods.

market 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

The line depic�ng quan�ty demanded at various prices in the market for a par�cular product. It is the aggregate of the demand curves for individual buyers of that product.

market forces (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 forces that are triggered by excess demand or excess supply that serve to raise or reduce the market price level for a par�cular product, as opposed to any government regulatory force.

market supply 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

A line depic�ng the aggregate quan�ty supplied by the individual suppliers of a par�cular product at various price levels.

monopolies (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

Firms that are the only supplier of a par�cular product in the market for a given good or service. Monopolies thus have no close subs�tutes and are able to set their prices to maximize profit, unless they are regulated by a government agency.

monopolis�c 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 market structure in which many firms with slightly differen�ated products compete with each other. These firms independently set prices for their products without expec�ng any reac�on from rivals because their output is a rela�vely small share of the total market.

natural monopolies (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 market situa�on in which mergers or takeovers of rival firms would occur un�l only one firm remains in the market, due to the small size of the market rela�ve to the economies of scale that are possible for a single firm.

normal profit (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 profit level sufficient to induce a firm to remain in business since it includes the economic cost of all resources u�lized by the firm—its costs therefore include as an opportunity cost the rate of return the firm could earn in the next best use of its resources.

oligopoly (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 market structure where rela�vely few firms compete with each other and each should expect rivals to react to their price reduc�ons and other strategic ini�a�ves.

price differen�als (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

Price differences that exist between firms in differen�ated product oligopoly markets that reflect differences in the a�ributes contained in the products and different costs of produc�on.

price rigidity (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 where the current price remains constant despite changes in cost or demand condi�ons, due to the firm's reluctance to raise prices independently, since this would cause them to lose market share, as in kinked demand curve oligopoly.

price–cost 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 difference between price (P) and short-run average costs (SAC), at any output level, also known as the profit margin.

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price–elas�c 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 reac�on to price increases or price decreases where the percentage change in the quan�ty demanded is significantly larger than the (absolute) percentage change in the firm's price level.

product differen�a�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 difference between rival products in terms of the a�ributes (or characteris�cs) of the products that are perceived by poten�al customers.

profit 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 profit per unit of output, also known as the price–cost margin.

profit-maximizing rule (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

To maximize profit firms should set price where marginal cost is equal to marginal revenue.

pure 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

Markets in which there are many sellers supplying iden�cal products, such as farmers selling milk, eggs or corn, or individuals selling shares on the Stock Exchange.

pure profit (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 profit that occurs when total revenue exceeds total costs and the la�er include the opportunity costs of all resources, and thus the firm is earning more profit than it could earn elsewhere.

rela�ve prices (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 price of a given good or service rela�ve to the prices of other goods or services.

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8

© Glow Images/SuperStock

Pricing Decisions in Practice

Learning Objectives

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

Explain how managers can u�lize es�mates of cost and revenue data, and es�mates of price elas�city, to determine the profit-maximizing price. Explain how markup pricing can be the profit-maximizing means of price se�ng when search cost for data is significant. Reconcile markup pricing with marginal pricing, and understand that markup pricing can remain profit- maximizing despite shi�s of the demand and cost curves. Iden�fy ways that price discrimina�on can increase the profitability of the firm. Recognize when bundle pricing can increase the firm's profitability.

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Search costs are the costs associated with finding informa�on. Profit-maximizing firms only incur these costs if doing so improves the profit of the decision.

© Stockbyte/Thinkstock

Introduction

In this chapter, we u�lize the theore�cal concepts introduced in prior chapters to help the manager make profit- maximizing decisions in the real world where cost and demand data is not available without incurring significant informa�on search costs. Informa�on search costs, defined previously as the costs of obtaining reasonably accurate data or knowledge pertaining to the issue at hand, are discre�onary costs that may be avoided. In all cases, the profit-maximizing firm should incur search costs only if doing so would increase profit by enough to cover the cost of obtaining the data necessary to make the decision. In some cases, search costs will be rela�vely low, such as is possible by u�lizing data that is internal to the firm and that has been rou�nely collected in past produc�on periods. In other cases search costs to obtain data from customers or suppliers might be so large that the manager's educated guess will be profit-maximizing as long as it misses the mark by less than the search costs that were avoided.

Accordingly, this chapter is organized on the basis of the "search versus don't search" dichotomy. In the next sec�on, we start with marginalist pricing—se�ng price using the marginal cost equals marginal revenue rule using es�mated cost, revenue, and price elas�city data that can be obtained from informa�on search ac�vity by firms from prior produc�on and market experience. We then turn to the use of simple (search-cost avoiding) pricing rules that allow a sufficiently accurate price and output decision such that the firm might maximize profits by avoiding expenditures on search costs and choosing a price that is "near enough" to that which would maximize profits with full informa�on. We introduce markup pricing—whereby price is determined as a percentage markup over the firm's average costs—and examine the condi�ons under which it is likely to be, and to remain, profit maximizing despite shi�s in the cost and demand condi�ons facing the firm. Finally, we examine two specific pricing topics, namely price discrimina�on and bundle pricing, which can allow the firm to make larger profit from the same number of customers.

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8.1 Marginalist Pricing Using Estimated Revenue and Cost Data

First, a quick review of what we learned in Chapter 4 about es�ma�ng the demand func�on. We saw that a manager can es�mate the firm's demand func�on by collec�ng data on both the firm's sales volume and the main variables that influence sales, and then using mul�ple regression analysis to es�mate the coefficients in the demand func�on for each of those determinants of the firm's demand. The equa�on we used for the demand func�on in Chapter 4 was

Qx = α + β1Px + β2Py + β3Ax + β4Ay + β5GNI (8-1)

where Qx represents quan�ty demanded of product X (in physical units); α (alpha) represents the influence of variables not included in the regression

analysis; and the βs (betas) are the coefficients to the independent variables used in the regression equa�on, with each one showing the marginal impact on Qx of a change in each of the independent variables, for example β1 = δQx/δPx. The independent variables included in this regression equa�on were the

prices of product X and product Y; the adver�sing expenditures of product X and product Y; and the level of gross na�onal income (GNI), the la�er being a proxy variable represen�ng the income of customers for product X. In Chapter 4 we found the constant term and the coefficients to the independent variables as follows:

Qx = 5,030 − 3,806.2Px + 1,458.5Py + 256.6Ax − 32.3Ay + 0.18GNI (8-2)

The es�mated demand func�on must be evaluated for its predic�ve reliability by considering the regression sta�s�cs that are provided by the regression analysis so�ware. First, the level of significance of each of the independent variables is checked by observing whether its P-value is 0.05 or smaller for each variable—the P-values indicate the probability that the dependent variable (Qx) really does not depend on each independent variable (e.g., Ay). For example,

a P-value of 0.05 indicates that we can be confident at the 95% level of significance that the independent variable is indeed a significant determinant of demand.

Second, we consider the coefficient of determina�on (R2), which indicates the propor�on of the variance in the dependent variable that is explained by

varia�ons in the independent variables that were included in the regression equa�on. For example R2 = 0.65 indicates that 65% of the varia�on in demand is explained by the independent variables on the right-hand side of the regression equa�on (and thus 35% of the variance in Qx demanded must be

explained by missing variables). The es�mated demand func�on is the best measure of central tendency within the data, but predic�ons of sales (for any

price level, for example) will be surrounded by a range of possible outcomes above and below the predicted value of sales, and as R2 becomes smaller, this

range of outcomes becomes larger. Note that the value of R2 might range from a minimum of zero, indica�ng no correla�on at all, to a maximum of 1.0, indica�ng perfect correla�on.

The standard error of es�mate (Se) sta�s�c provides a measure of the range of possible outcomes around the predicted value of sales. We can be confident

at the 95% confidence level that the actual value of demand will lie within plus or minus 2Se of the es�mated value (for any level of price, for example). The

standard error of the coefficient, Sβ, (for each independent variable) provides a range of values around the es�mated value of each β coefficient in the

regression equa�on within which the true value might fall.1 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt1) Again, we can be confident at the 95% level of confidence that the true value of the coefficient lies within a range that is plus or minus 2Sβ from the es�mated value of the β. Thus, managers

can use these regression sta�s�cs to conduct sensi�vity analysis on their predic�ons of sales for any level of price (or other independent variable) selected.

On the cost side, in Chapter 6, we considered several methods for the es�ma�on of cost func�ons u�lizing known data points. We demonstrated that we could es�mate the loca�on and shape of a par�cular cost curve (e.g., TVC) by interpola�ng between the known data points using gradient analysis, and then calculate the value of related cost measures (e.g., AVC and MC). With a greater number of known data points, we can achieve a more accurate es�ma�on of the TVC func�on by fi�ng a "line of best fit" to the data using regression analysis and, subsequently, calculate the AVC and MC values for any output level. The line of best fit may be a linear, quadra�c, or cubic func�on of output, the choice being made on the basis of which func�onal form best fits the data.

This will be the form that exhibits the highest coefficient of determina�on (R2) while maintaining 95% confidence levels of significance (P-values less than 0.05) for the independent variables included in the equa�on.

If your understanding of the terms and concepts in the above two paragraphs is a li�le rusty, you should go back and quickly review the relevant parts of Chapters 4 and 6 to refresh your memory.

Using Estimated Lines of Best Fit

Given the es�ma�on of the demand and cost func�ons, we can find the profit-maximizing output level either by solving for Q using a pair of simultaneous equa�ons, or by deriving and plo�ng the relevant curves (i.e., MC and MR) on a graph and observing the intersec�on point of these curves. The first method starts with deriving equa�ons for the MR and MC curves. Considering first the MR curve, we know it has the same slope and twice the slope of the demand curve, so we need to first derive the demand curve from the demand func�on, as we did in Chapter 4. To do this we need to collapse equa�on 8-2 into the reduced form equa�on Qx = AOV + βPx (where AOV represents the influence of all other variables except the price of X). In Chapter 4, using the

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values Py = $6; Ax = 168 (in thousands of dollars); Ay = 182 (in thousands of dollars); and GNI = 12,875 (in billions of dollars), we evaluated AOV to find the

reduced form of the demand func�on shown as follows:

Qx = 53,328.7 − 3,806.2Px (8-3)

Next we inverted the demand func�on equa�on to find an expression for the firm's demand curve:

Px = 14.011 − 0.00026273Qx (8-4)

As we noted in Chapter 4, this very small coefficient to the variable Qx is hard to comprehend, so we define Qx in thousands of units and mul�ply the

coefficient to Qx by 1000, to express the demand curve equivalently as:

Px = 14.011 − 0.26273Qx (8-5)

Because the marginal revenue (MR) curve has the same intercept and twice the slope of the demand curve, it must be represented by:

MR = 14.011 − 0.52546Qx (8-6)

Now on the cost side, suppose (as we found in Chapter 6) that our most reliable es�mate of the TVC func�on is a straight line of best fit in the form TVC = α + βQ, namely:

TVC = 2.2873 + 5.9639Qx (8-7)

where TVC is in thousands of dollars and Qx is in thousands of units. We know from Chapter 6 that MC is the first deriva�ve of TVC, so:

MC = 5.9639 (8-8)

In this case, TVC was es�mated as a linear func�on of output over the range of output levels represented by the sample data. Note that the first term (2.2873) on the right-hand side of equa�on 8-7 is the residual, or the amount of TVC that is not explained by the varia�on in Qx. The first term serves as

the ver�cal intercept value of the es�mated TVC line and operates to raise the TVC line to the appropriate height to best represent the rela�onship between TVC and Qx in the relevant range of the data observa�ons. We illustrate this in Figure 8.1 where the do�ed line indicates the unobserved TVC curve for all

values of Qx, and the straight line with intercept 2.2873 and slope 5.9639 for each thousand units of Qx represents the es�mated TVC that best fits the data

in the range of data observa�ons actually observed.2 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt2)

Figure 8.1: Es�mated TVC func�on that best fits the data in the observed range

Now, se�ng the expression for MR, which is equa�on (8-5), equal to the expression for MC, which is equa�on (8-7), we have:

14.011 − 0.52546Qx = 5.9639 (8-9)

This is a single equa�on with one unknown variable, so we can solve3 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt3) for the value of Qx by

subtrac�ng 14.011 from both sides, and then dividing both sides by –0.52546, to find Qx = 15.314. This is the profit-maximizing output (in thousands of

units), so inser�ng this value of Qx into the demand curve, equa�on 8-5, and solving for Px we find the profit-maximizing price level to be $9.99. 4

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt4) Total revenue (TR, in thousands of dollars) is calculated as PxQx = 152.9869 and total variable

cost (TVC, in thousands of dollars) can be calculated (from equa�on 8-6) as TVC = 2.2873 + 5.9639(15.314) = 93.6185. The contribu�on to total fixed cost and profit is equal to TR − TVC = 152.9869 − 93.61185 = 59.3684, or $59,368.40. Thus, if total fixed cost is less than $59,368.40 then the firm would be making a profit.Processing math: 0%

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Now let's find the same result using graphical analysis. In Figure 8.2, we show the demand curve having an intercept value at 14.011, as per equa�on 8-5. To plot the demand curve we need to find a second point on the (straight line) demand curve. We do this by solving equa�on 8-5 to find a value for Px at

any par�cular value of Qx, for example 15. When Qx = 15, we solve for Px = 10.07 from equa�on 8-5, which provides the coordinates for a second point on

the demand curve. A straight line drawn from the intercept point (where Px = 14.011 and Qx = 0) that also passes through the point where Px = 10.07 and

Qx = 15, thus represents the demand curve. To plot the MR curve we know the MR curve has the same intercept and twice the slope of the demand curve,

so we know that the MR curve must also intercept the ver�cal axis at 14.011 and then slope down toward the horizontal axis at twice the rate that the demand curve does. Since we found that Px = 10.07 when Qx was 15, we can conclude that when MR = 10.7, the Qx coordinate of the MR curve must be

7.5 (i.e., half of 15), so we can sketch in the MR curve as shown in Figure 8.2.5 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt5)

Figure 8.2: Graphical representa�on of the price and output decision

For the marginal cost curve, we know from the regression equa�on that TVC = 2.2873 + 5.9639Qx and that MC = 5.9639, because marginal cost is the first

deriva�ve of the TVC func�on. Thus, MC is constant at $5.96 per thousand units regardless of output level, in this par�cular case. Plo�ng MC as the horizontal line at $5.96 we see that the MR curve crosses the MC curve at approximately Qx = 15.314 units of output, and following that up ver�cally to the

demand curve we find the profit-maximizing price level is $9.99. These graphical results confirm the accuracy of our earlier algebraic results, or vice versa!

Using Estimates of Price Elasticity

Now, let's suppose that a manager knows the current price is $7 and the output level is 25,000 units and has es�mated the price elas�city of demand (ε) to be –2.5. As we saw in Chapter 4, price elas�city can be expressed as the percentage change in quan�ty demanded over the percentage change in the price level. For example, if ε = –2.5 this implies that the quan�ty demanded would increase by 2.5% if price was reduced by 1%. Since a 1% price change might not be no�ced by consumers we would usually expect a more substan�al price adjustment; for example, the manager would expect that a 10% price reduc�on would cause a 25% increase in quan�ty demanded (or conversely a 25% reduc�on in demand for a 10% price increase). Price elas�city of demand, as we saw in Chapter 4, can also be expressed as:

ε = ΔQ/ΔP • P/Q (8-10)

We can subs�tute the known or es�mated values of ε, P, and Q from above into this equa�on to say –2.5 = ΔQ/ΔP • 7/25 and solve this equa�on to find ΔQ/ΔP = –8.9286 (where Q is in thousands). Note that ΔQ/ΔP is the reciprocal of the slope of the demand curve, so 1/–8.9286 = –0.112 must be the slope of the demand curve. To find the intercept of the demand curve, we know that P = a − 0.112Q, where a is the intercept term, and since we know P = 7 when Q = 25, we can subs�tute these values into the equa�on to solve for the intercept term a = 9.8. Thus, the es�mated expression for the demand curve is P = 9.8 − 0.112Q, and the marginal revenue curve must be MR = 9.8 − 0.224Q (having the same intercept and twice the slope).

Now, supposing that the manager does regression analysis of TVC data and finds that the line of best fit is TVC = 2Q + 0.2Q2, and (taking the first deriva�ve) finds that MC = 2 + 0.4Q. Having an expression for both MC and MR we can now solve for the profit-maximizing output and price, either mathema�cally or graphically. The former will be faster, so let's set MC = MR and solve for Q as follows:

2 + 0.4Q = 9.8 − 0.224Q (8-11)

By adding 0.224Q to both sides and subtrac�ng 2 from both sides we find 0.264Q = 7.8. From this we find Q = 7.8/0.264 = 29.545 (thousands). Subs�tu�ng this profit-maximizing output level into the demand curve expression we find P = 9.8 − 0.112(29.545) = 6.49. Thus, the profit-maximizing price is $6.49, so the manager should reduce price from the current level of $7 in order to maximize profit. Doing so would soon verify or disprove the ini�al es�mate of price elas�city that formed the basis of the es�ma�on of the demand curve, as quan�ty demanded should increase to about 29,545 units and profit should increase from the ini�al level. If profit does not increase as expected, then the resultant Q observa�on at the new price level ($6.49) provides a second known point on the demand curve, which allows the slope and intercept to be calculated (assuming no changes in the other determinants of demand) and, thus, the manager can proceed to find the profit-maximizing price and output level.

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1. The "true" value is the value we would find if the en�re popula�on of observa�ons is used in the regression analysis. Typically, we select a sample that we expect to be representa�ve of the popula�on and thereby keep informa�on search costs to a tolerable level. The standard errors of the coefficients indicate the extent to which sampling error might have occurred. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return1) ]

2. As in Chapter 6, we choose the func�onal form of the line of best fit on the basis of which form (e.g., linear, quadra�c, or cubic) that best fits the observed data points, and we judge

"best fit" by the highest R2 value when all of the independent variables that are included in the regression equa�on (e.g., Q, Q2, and Q3) are significant at the 95% confidence level. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return2) ]

3. To do this step by step, we start with 14.011 − 0.52546Qx = 5.9639. By subtrac�ng 14.011 from both sides we have –8.0471 = –0.52546Qx. Then, by dividing both sides of this equa�on

by –0.52546 we find Qx = 15.314. Subs�tu�ng 15.314 for Qx in the demand curve expression Px = 14.011 − 0.26273Qx we have Px = 14.011 − 0.26273(15.314) which evaluates to be Px = $9.99. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return3) ]

4. When the profit-maximizing price turns out to be an odd number, such as $9.52, it may require a cosme�c adjustment to let's say $9.49, to be more suitable for marke�ng purposes. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return3) ]

5. Alterna�vely, we could find the horizontal-axis intercept of the demand curve by se�ng Px = 0 and solving for Qx in the demand curve, and then halve this Qx value to find where the

MR curve must cut the horizontal axis. We found earlier (see Figure 4.1 in Chapter 4) that this demand curve intercepts the horizontal axis at Qx = 53.328, so the MR curve must

intercept that axis at 26.664 (thousand units). [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return5) ]

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When implemen�ng markup pricing, firms must take into account the price elas�city of demand, since higher markups translate to higher prices which reduce demand by an amount that depends on the price elas�city of demand.

© BananaStock/Thinkstock

8.2 Markup (or Cost-Plus) Pricing

In prac�ce, many firms use markup pricing, whereby average variable costs, AVC (also known as direct costs per unit), are marked up by a percentage of AVC to arrive at the price level. Thus:

P = AVC + X(AVC) (8-12)

where X is the markup percentage and X(AVC) is the contribu�on margin, which as we saw previously is equal to P − AVC and represents the contribu�on that the price makes to the overhead costs and profit of the firm. Markup pricing is o�en called "cost-based pricing," but it is clear that the markup percentage must also take into account the price elas�city of demand, since higher markups mean higher prices and these will cause demand to be reduced by an amount that depends on the price elas�city of demand. In fact, markup pricing can be reconciled with the marginalist pricing rule (i.e., MC = MR) in the case where AVC is constant (and therefore AVC = MC), which we shall do in the next sec�on.

Reconciliation With Marginalist Pricing

In Figure 8.3, we show two graphs—on the le�-hand side, we show the $7.50 price as determined by a 50% markup over direct costs of $5 per unit, and, subsequently, the firm's customers demand Q units, thus revealing one known point on the demand curve (depicted by the star). On the right-hand side of Figure 8.3, we show the complete demand and MR curves that are unknown to the firm. In this carefully drawn case, it is clear that the 50% markup is indeed profit-maximizing, since MC = MR at that price and output level.

Figure 8.3: Markup pricing and marginalist pricing reconciled

By observing the graph on the right-hand side, you can see that if the markup had been set instead at, say, 60% (for an $8 price with a $3 contribu�on margin), the consequent level of quan�ty demanded would be less than Q units and MC would be less than MR at that higher price and lower output combina�on, and thus that price and output combina�on would not be profit maximizing. Similarly, if the markup rate had been only 40% the price would be $7, quan�ty demanded would be more than Q, and, again, profit would not maximized because MC > MR at that price and quan�ty combina�on.

So, to be profit-maximizing the markup rate must reflect the height and slope of the demand curve, rela�ve to the MC curve. As we have seen, the price elas�city of demand is related to the height and slope of the demand curve, and, indeed, there is a special rela�onship between price elas�city and the profit-maximizing markup rate over AVC, which is evident in the following expression:

(8-13)

This expression shows that the profit-maximizing markup rate (the term in brackets in equa�on 8-13) is inversely related to the price elas�city of demand

and is derived to include the requirement that MC = MR.6 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#ch08txt6) Note that this formula is only correct for the case where direct costs (AVC) are constant and, thus, AVC = MC in the relevant output range.

In Table 8.1 we show the profit-maximizing markup rates for a selec�on of price-elas�city values. It is evident that the higher (in absolute terms) is the price elas�city the lower the markup rate must be if the price is to be profit-maximizing. From Chapter 4, we know that price elas�city has an extremely high nega�ve value near the ver�cal intercept with the price axis, with these values increasing as we move towards the midpoint of the demand curve, where ε = −1. We also know that MR falls to zero at the midpoint of the demand curve, and, therefore, any price below the midpoint cannot be profit-maximizing

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because we want MR = MC (and MC cannot be nega�ve). Closer to the midpoint of the demand curve, where MR is quite low, MC must also be quite low if MR is to be equal to MC, and, hence, the higher will be the markup rate. Conversely, at points higher on the demand curve the MR is also higher, so for MR to be equal to MC, the MC must also be rela�vely high and, thus, the markup rate must be rela�vely low.

Table 8.1: Profit-maximizing markup rate (X) given price elas�city of demand (ε) ε –9 –8 –7 –6 –5 –4 –3 –2 –1.5

X 12.5% 14.3% 16.7% 20% 25% 33.3% 50% 100% 200%

This is illustrated by the examples in Figure 8.4 (where the same demand situa�on is depicted with two different cost situa�ons), and in Figure 8.5 (where the cost situa�ons are the same but the demand situa�ons differ). Fundamentally, the markup percentages are different because the price elas�city of demand is different at the profit-maximizing-price levels, and these differ because of the differences in the cost levels (see Figure 8.4) or because of the differences in the demand situa�on (see Figure 8.5). Thus it is clearly important for managers to have in their minds an es�mate of price elas�city before se�ng prices via markups over direct costs in situa�ons where they do not know much about the height and slope of the demand curve.

Figure 8.4: Low markup rates versus high markup rates with different cost condi�ons

Figure 8.5: Low markup rates versus high markup rates with different demand condi�ons

As discussed in Chapter 4, managers should understand that price elas�city depends on two main drivers—namely, the subs�tu�on effect and the income

effect.7 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#ch08txt7) The subs�tu�on effect is greater if the number and closeness of subs�tutes is greater; thus a 10% price increase, for example, might be expected to cause the loss of, say, 40% of sales when there are many close subs�tutes (as in monopolis�c compe��on). Conversely, a 10% price increase would expect to cause the loss of only, say, 15% of sales if there are not many close subs�tutes (as in a highly-differen�ated-products oligopoly) for example. The income effect is about affordability—if the price is rela�vely high compared to the customer's income, a price increase is more likely to cause the customer to stop purchasing that product, compared to a product where the price is small rela�ve to customers' incomes. These are things that managers should know about their product and their customers, and so managers should be able to make a rough es�mate of the value of price elas�city for that product.

How would managers use this informa�on? They might either calculate (from equa�on 8-13) the profit-maximizing markup rate based on their best es�mate of price elas�city, or conversely work from their preferred markup rate to find the implied price elas�city if that markup is to be profit-maximizing. Having arrived at an implied markup rate, managers must then ask themselves the ques�on: Does that seem right? Is it congruent with what I know about the number and closeness of subs�tutes for my product and the general affordability of my product? For example, if a manager wants to maximize profit and intends to apply a 25% markup on direct costs to determine its price, this implies that the price elas�city of demand is –5, which infers that quan�ty demanded would drop by 50% if price were to be raised by 10%. The manager must ask the ques�on "Does it seem reasonable that fully half the firm's demand would disappear if the firm raised price by 10%?" This implies either that the product has very close subs�tutes or that it is rela�vely expensive in rela�on to customers' incomes. If the implied price elas�city seems too high this means the chosen markup rate is probably too low and should be increased to increase profit. Oppositely, if the implied price elas�city seems too low, given the availability of subs�tutes and the ra�o of price to customer

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Managers must strategically set a markup rate. If the implied price elas�city seems too high, the markup rate is probably too high and should be reduced to increase profit.

© Fuse/Thinkstock

incomes, the markup rate is probably too high and profits will increase if a lower markup (and price) is used. A simple test is possible, of course—the manager could go ahead and reduce the price slightly and see what happens to volume and profit, and then make a subsequent adjustment one way or the other.

Search Costs and the Range of Acceptable Markup Rates

Search costs, as you know, are the costs associated with finding informa�on. The search costs of es�ma�ng price elas�city and/or the demand and TVC func�ons can be avoided by using simple pricing rules like markup pricing. If search costs are avoided the markup rate can be "wrong" (i.e., not profit-maximizing) to some extent yet s�ll allow the firm to make greater profit as compared to first undertaking informa�on search ac�vity and later se�ng the profit-maximizing price (but having higher overhead costs due to the expenditures on search ac�vity). We show the extent to which the markup can be wrong in Figure 8.6 for a presumed case where search ac�vity, if

undertaken, would increase the firm's total fixed costs (TFC) by a substan�al amount.8

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#ch08txt8) We exaggerate the size of the search costs in Figure 8.5 to allow a clear explana�on of the effect.

In Figure 8.5, the curve labeled TC shows the total costs including the search costs, while the curve labeled TCʹ represents total costs when search costs are avoided. You will note that these total cost curves emanate from the

ver�cal axis at the level of total fixed costs and rise at a constant rate (equal to MC) reflec�ng a linear TVC curve. The ver�cal difference between the total revenue curve, TR, and the TC curve is mapped as the profit curve Π (the Greek le�er pi) while the ver�cal difference between the TR and the TCʹ curve is mapped as the profit curve Πʹ. No�ce that the "no-search-costs" profit curve Πʹ lies above the "search-cost-included" profit curve Π for a considerable range of outputs, this range being shown as Q1 to Q2 in the lower graph.

Figure 8.6: The range of acceptable markup rates for the firm avoiding search costs

The profit-maximizing price and output levels, with or without search costs, are shown as P* and Q* where MR = MC. But note that price could be anywhere between P1 and P2 if search costs are avoided and yet allow profit (on Πʹ) to exceed the profit available a�er incurring search costs (on Π). In

terms of markup rates, while the profit-maximizing markup rate in this example looks to be about 50% (at P*), the markup rate could range anywhere between about 80% at P1 to about 20% at P2 and s�ll earn more profit (if search costs are avoided) compared to first spending the search costs and then

se�ng price at the profit-maximizing level P*. So you can see there is a lot of room for error in choosing the markup rate! But, be cau�oned that this example shows extraordinarily high search costs as a propor�on of total costs; in most cases the range for error in the markup rate will be somewhatProcessing math: 0%

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Infla�on is caused by an excess of aggregate demand over aggregate supply of all goods and services resul�ng in

© Photodisc/Thinkstock

smaller than in this "teaching example." Note also that the range of acceptable markup rates will be smaller if price elas�city in the relevant range of outputs is higher (causing the demand curve to be less steeply sloping). If the demand curve is not as steep (as in Figure 8.6), the range of "wrong" markup rates that nonetheless allow greater profit, will be smaller, other things being equal. So, managers must first ask themselves the ques�on: "What is the likely magnitude of search costs that would need to be spent to gain suitably reliable es�mates of the cost and revenue curves?" Then, they must couple this es�mate with their best es�mate of the price elas�city of demand to complete an analysis of whether their chosen markup rate is likely to be profit- maximizing if they avoid search costs.

Markup Pricing and Demand Shifts

When the demand curve shi�s (due to a change in one of the "shi� variables" such as customer incomes or adver�sing) the profit-maximizing price (and hence the profit-maximizing markup rate) would generally need to change because the price elas�city of demand will be different at the new price level associated with each quan�ty level. But in the case of iso-elas�c demand shi�s, where the price elas�city stays the same at each output level when the demand curve shi�s, the same markup rate remains profit-maximizing despite the shi� of the demand curve. In Figure 8.7, we show an iso-elas�c demand shi� from D to Dʹ that involves a rota�on of the demand curve while maintaining the same price axis intercept value, shown as P. Since the demand curve rotates from the same intercept point, the marginal revenue curve must also rotate to maintain its "same intercept, twice the slope" rela�onship with the demand curve. But, as you can see in Figure 8.7, the shi�ing demand curve does not require a change in the profit-maximizing price, because MR = MC at the same price level (P*) as before. Quan�ty demanded increases from Q to Qʹ units per period due to the shi� in demand but the same price (P*) and

markup rate (100%) remain appropriate because the price elas�city remains the same (ε = –2) at both price-quan�ty combina�ons.9

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#ch08txt9)

Figure 8.7: Constant markup rate despite an iso-elas�c shi� of the demand curve

It is probably unlikely that a demand shi� would be precisely iso-elas�c, but we have seen in the preceding sec�on that it does not need to be so for a con�nua�on of the same markup rate to remain the profit-maximizing policy if significant search costs must be expended to find the exact intercept and slope of the demand curve. What we have demonstrated here is that iso-elas�c demand shi�s mean that the firm does not have to change its price level. Thus, the demand shi�s that are somewhere close to being iso-elas�c will make it likely that the exis�ng markup rate remains profit-maximizing. This reduces the financial incen�ve to incur search costs to iden�fy the precise loca�on of the demand and costs func�ons.

Markup Pricing and Cost Shifts due to Inflation

Infla�on is the con�nuing increase in cost and price levels due to the decrease in the value of the na�onal monetary unit (i.e., the dollar). At the firm level, management may find that their AVC has risen, for example, by 10% over the past year and that this has reduced their profit. They may wonder whether they should simply raise their price level by 10% to restore their profit margin and overall profit level, or whether they should increase prices by more or less. The answer depends on how much more their customers can afford to pay. If customers' incomes have also risen by 10%, this product will require the same propor�on of their incomes as it did before the period of infla�on. In Figure 8.8, we show a situa�on where each point on the ini�al demand curve (D) has shi�ed ver�cally by a constant propor�on—10% in this case—to the new demand curve Dʹ. This reflects each customer's ability to pay 10% more for each unit of quan�ty demanded. Similarly, the AVC = MC curve has shi�ed ver�cally by 10% due to infla�onary increases in the cost of direct materials, direct labor, and variable overheads. Note that the new marginal cost and revenue curves (MCʹ and MRʹ) cross at the same output level (Q*) as the pre-infla�on MC and MR curves. Also note that the profit-maximizing markup remains the same, at 40% in this case. Thus, in the case where customers' incomes and the firm's AVC rise by the same percentage due to infla�on (or, indeed for reasons that apply only to this firm and its customers) it is profit-maximizing to con�nue to use the same markup rate as before.

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increased costs and a decrease in the value of the na�onal monetary unit.

Figure 8.8: Constant markup rate with infla�onary shi�s of both demand and costs

Note that Figure 8.8 is drawn in nominal-dollar terms, that is, using the nominal values for costs and prices. In real terms—constant purchasing power terms —neither the demand curve nor the costs curves would have shi�ed at all. But, people generally think (and make purchases) in nominal dollar terms. Managers must be aware of their customers' percep�ons of the firm's price increases and ensure that they are not perceived to be passing on more than is jus�fied by their cost increases. In this case, AVC increased by 60 cents and, yet, the price was increased by 84 cents, which, although not an increase in real terms, might be perceived as such by customers. In most cases, of course, the customer is not privy to the magnitude of cost increase suffered by the firm. But in some cases the magnitude of cost increase is known to the public; for example, when the Federal Reserve Bank raises the rate at which it lends money to the commercial banks, by, say, 50 basis points (e.g., from 3.5% to 4%), home-mortgage holders typically complain loudly if the commercial banks subsequently raise their mortgage rates by more than 50 basis points—from 5% to more than 5.5%. Yet as we have seen above, the profit-maximizing home mortgage rate may well be higher than 5.5% if the commercial banks' other direct costs and variable overheads have also increased. Managers in this case must argue to their customers that their other costs have gone up, while, at the same �me, assuring their shareholders that they are trying to maximize shareholder return on investment.

We should note in this context that fixed costs, comprising deprecia�on charges against revenue for capital costs incurred in preceding periods plus unavoidable present period costs such as managers' salaries, lease costs, and so on, may not have increased at the rate of infla�on in the current produc�on period (due to lags in salary increases, longer term agreements on lease costs, and so on). Thus, the increase in the firm's contribu�on to overheads and costs due to the applica�on of a constant markup rate during infla�onary �mes might actually increase profit, rather than simply restoring the profit rate to the prior level. Thus, those customers (and the business press) who cri�cize the commercial banks who "pass on more than their cost increase" may have a valid point. On the other hand, their managers would argue that salaries and lease costs must be adjusted upwards in subsequent periods (to retain the use of resources and to maintain produc�on efficiency) and that the "leads and lags" roughly offset each other in the longer term.

Markup Pricing as a Coordinating Device

Finally, in jus�fica�on of markup pricing, we note that it provides a simple and effec�ve means for firms who compete in oligopolis�c markets, where mutual dependence must be recognized, to coordinate their price increases in infla�onary �mes or in response to other cost increases that apply specifically to firms in that industry. By all firms independently using a markup pricing rule, the firms each raise their prices in "conscious parallelism" (see Chapter 7), and, thus, avoid raising their price independently and suffering a highly-elas�c demand reac�on along the upper half of the kinked demand curve. Coordina�on of price increases by oligopolists allows their market shares to remain the same, other things remaining equal. Retaining market share is important to firms because it avoids fluctua�ons in output levels and the consequent need for fluctua�ons in the purchases of variable inputs and the hiring of direct labor.

6. To express X in terms of the MC = MR rule, we start by finding an alterna�ve expression for MR. Since MR = dTR/dQ, and TR = P • Q, and since P also depends on Q, we use the chain rule of deriva�on to express marginal revenue as MR = P + Q(dP/dQ). Now mul�ply and divide the last term in equa�on 8-11 by P to find MR = P + QP/P • dP/dQ. Factoring out P we obtain MR = P {1 Q/P • dP/dQ}. Now note that the term in the brackets is equivalent to one plus the reciprocal of the price elas�city of demand (since ε = dQ/dP • P/Q). Hence, MR = P (1 + 1/ε). Se�ng MC = MR and invoking the special case where MC = AVC we have AVC = P (1 + 1/ε), which can be rewri�en as P = AVC + [–1/(ε + 1)] AVC. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#return6) ]

7. Recall that the subs�tu�on effect is the change in quan�ty demanded due to a change in the price of a product rela�ve to the unchanged prices of its subs�tute (rival) products, with a no�onal compensa�on for the change in real income (the purchasing power of money income) caused by the price change. The income effect is the change in the quan�ty demanded due to the change in real income due to the changed price of the focal product, holding rela�ve prices constant. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#return7) ]

8. Search costs are a fixed (or overhead) cost because they are unrelated to output levels (and thus are not a variable cost). Search costs would be expended and then become a sunk cost that the firm hopes will be paid for later by the contribu�on margins of units sold. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#return8) ]

9. Note that although price elas�city stays the same for any given price level despite shi�s in the demand curve, the price elas�city changes as we move along each demand curve. A different concept is the iso-elas�c demand curve, where price elas�city is the same at all points along a given demand curve—such curves must be rectangular hyperbolas where the rectangular areas under all points on the curve, where the area is defined by each price (height) �mes its associated quan�ty (width), are the same. Looking back at the price elas�city formula you will appreciate that for elas�city to remain at the same level at different prices, the changes in the slope of the curvilinear demand curve (ΔP/ΔQ) must be exactly offset by the change in the ra�o of P/Q as we "move down" the demand curve. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#return9) ]Processing math: 0%

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Auc�ons are o�en used to establish the price of highly differen�ated items. Auc�ons can occur in person or through websites such as eBay, which allow poten�al buyers to bid on a wide variety of items online.

© ASSOCIATED PRESS/AP Images

Market Price

8.3 Pricing Topics

In this final sec�on, we examine some varia�ons on the theme of profit-maximizing prices. We shall consider price discrimina�on, in which different customers are charged different prices, and bundle pricing, where the prices of products that are complementary in consump�on are adjusted to increase the firm's overall profits.

Price Discrimination

Price discrimina�on, for our purposes here, is defined as the prac�ce of charging different prices to different buyers (or groups of buyers) for essen�ally the same product, where customer differences mean they are more or less willing to pay higher prices. Note that under the United States' Robinson-Patman Act, price discrimina�on is defined as systema�cally charging different prices to different people for iden�cal products sold under the same circumstances and is illegal. However, here we are considering products sold under different circumstances where those circumstances effec�vely produce different a�ributes of the product, such as the convenience of immediate versus delayed delivery. We shall consider three types of price discrimina�on. You will likely recognize that it is happening all around us in the business world and that customers willingly pay higher prices in some circumstances.

Auc�ons

Auc�ons are examples of first-degree price discrimina�on, defined as the seller forcing the buyer to pay the maximum or close to the maximum that the buyer is willing to pay. An auc�on discriminates against customers who are willing to pay more by requiring them to pay higher prices, and ul�mately allows only the person who was willing to pay the most to actually purchase the product. There are two styles of auc�on. In a so-called English auc�on, prices are bid upwards sequen�ally by compe�ng buyers un�l the last bid made is the highest price that anyone is prepared to bid, and thus, the sale is made to the last bidder. English auc�ons are rou�nely used to establish the price of highly differen�ated or unique items such as racehorses, pain�ngs, the bric-a-brac of celebri�es, and private homes or apartments. The winning bidder is charged a rela�vely high price, and that price is determined by the maximum price that the second-highest bidder was prepared to pay plus the small increment included in the last bid by the winning bidder. Note that the winning bidder may have been prepared to pay even more, but only had to offer slightly more than the second-most-keen buyer. English auc�ons are now prevalent online—you can buy (or sell) a wide variety of items in an auc�on procedure on eBay or similar auc�on-based websites.

Auc�ons are typically used where it is difficult to decide what is the appropriate price for the item that the seller wishes to sell, and the auc�on mechanism allows the best price (on the day, given the a�endance of all interested poten�al buyers) for the seller to be achieved. Alterna�vely, it allows the buyer to get a bargain if no one else is interested in bidding the price higher. All poten�al buyers have a reserva�on price, which is the maximum price they would be willing to pay for the item. As the bid price moves above their reserva�on prices the poten�al buyers drop out of the bidding un�l only one is le�. As long as the highest bid exceeds the seller's reserve price, which is the minimum that the seller is prepared to accept for the item, then a sale is made.

A Dutch auc�on sees the price level offered by the seller move downward from an unrealis�cally high level un�l a point where one of the poten�al buyers jumps in and accepts the latest price offered by the seller. This is how flowers are sold by the Dutch at the flower auc�ons in Holland, hence the name. Other large markets, such as fish markets, also use the Dutch auc�on method since it is an efficient way to sell large quan��es of product in the shortest possible �me. But how does it work? Again, all buyers need to form a personal view, before the bidding starts, as to the highest price they would pay (their reserva�on price). This, in turn, is based on how much the item is worth to them in revenue or in intrinsic terms. For example, suppose a New York flower merchant knows that he or she can sell 40 dozen roses at $30 each and that buying them at $15 per dozen in Amsterdam would provide an acceptable profit margin a�er airfreight and other costs. The New Yorker is thus unwilling to jump in as the price �cks down from $20 to $19, $18, $17, and $16, but jumps in when the price �cks down to $15. If that buyer were to wait any longer, someone for whom $14 is a sa�sfactory price would jump in, and the New York

merchant would miss out on the opportunity to make profit.10

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In ordinary markets where the market clearing price (i.e., the one that causes supply to equal demand) is received by all sellers and paid by all buyers, this price is less than the reserva�on price for all except the marginal buyer—who is the buyer willing to pay no more than the market price. All other buyers were willing to pay more than the market price but did not have to (assuming a downward- sloping demand curve, i.e., differen�ated products). Note that a demand curve is, a�er all, simply a line joining the reserva�on prices of all the buyers in the market.Processing math: 0%

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Prices Based on Urgency of Demand

Second-degree price discrimina�on involves discrimina�ng among groups of buyers on a �me or urgency basis. Those who want to buy the product soonest pay a higher price than those who are willing to wait un�l later. The sale of innova�ve new electronic and so�ware products typically involve higher prices at first for the pioneer's product, with lower prices subsequently as the pioneer's AVC curves shi� downwards due to the learning curve and as new rivals enter the market with compe��ve prices for their own version of the new product. Another example is the pricing of �ckets for new movie releases. First runs in city theaters are priced substan�ally above the second runs in suburban and rural theaters. Later, the movie is typically shown on cable television (for a subscrip�on fee) and, finally, it is shown on free-to-air television (supported by adver�sing revenue). Another common example is provided by passenger airfares—business users usually book flights at rela�vely short no�ce whereas tourists and people visi�ng family members can plan ahead— hence, airlines discriminate on the basis of how urgently you want to fly.

Some rural and suburban moviegoers certainly do go to the city to see first-run movies. They do this because their reserva�on price to see a par�cular movie is above the price asked by the city movie theater. But, city markets are rela�vely thick markets, while suburban and rural markets are rela�vely thin markets, meaning that there is a rela�vely large number of buyers willing to pay the first-run price in the city compared to a rela�vely small number of buyers willing to pay the first-run price in suburban and rural markets. Accordingly, it is profit-maximizing for the movie producer to show a new movie first in larger city theaters for a higher price and later in smaller suburban and rural theaters for a lesser price.

Figure 8.9: Pricing based on urgency of demand

Figure 8.9 demonstrates the circumstance in which the demand for the new product in period 1 (e.g., first-run movies), shown as D1, is rela�vely strong, and

the profit-maximizing price and sales, P1 and Q1 respec�vely, are found where MC = MR1.The demand for the product in period 2 is less strong, shown as

D2. The buyers represented here include those who did not buy the product in period 1 (those whose reserva�on prices are less than P1) plus new buyers

who have entered the market as a result of reading favorable reviews or listening to word-of-mouth endorsements for the new movie or new product in general. The profit-maximizing price in period 2 is thus P2. Similarly in period 3, the demand curve D3 is made up of those who did not purchase in period 1

or 2 because their reserva�on price is below P2, as well as new buyers who have now entered the market a�er learning about the new product and the

benefits it offers. Thus, the price level is reduced period by period as the seller discriminates among buyers based on their reserva�on prices which reflect their urgency to purchase the new product.

Prices Based on Differing Elas�ci�es of Demand

Third-degree price discrimina�on is a situa�on whereby a seller can simultaneously charge two or more different prices to customers who have differing price elas�ci�es of demand for the same product or service. Examples of third-degree price discrimina�on are the telephone and electricity price differen�als between household users and business users of these services. Telephone companies may also charge different amounts for long-distance calls according to whether they are made during business hours or in the evenings and on weekends. When signing up for these services in the first instance, the seller wants to know whether it is a business account or a private (household) account. Sellers charge businesses a higher price because their demand is less elas�c—the business must use the phone and use electricity in the normal conduct of their business, and employees will be less interested in saving electricity or in shortening their phone calls than will householders who, a�er all, have to pay their own bills. Also, businesses need to make calls in business hours because people may resent receiving business calls a�er hours, or because they only have a work phone number and want to reach the other personProcessing math: 0%

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Telephone service is an example of third-degree price discrimina�on. Telephone companies o�en charge different rates for long-distance calls according to the �me and day of the week they are placed.

© Monkey Business/Thinkstock

at their desk. Householders can wait un�l the evening or weekends to call friends or family at their homes (or on their cell phones).

Another common situa�on is that the firm has both a domes�c market and an export market for its output (see Figure 8.10). Its domes�c price can be somewhat higher than its export price because the price elas�city of demand in the export market is typically much higher, due to the greater presence of subs�tutes and rival suppliers, and also customer income levels in export markets may be lower than domes�c customers' incomes. In Figure 8.10, we demonstrate how the firm should choose two different prices for two different groups of customers such that it maximizes its overall profit.

Figure 8.10: Third degree pricing discrimina�on

Note in Figure 8.10 that demand is shown to be rela�vely more inelas�c in market 1 and rela�vely more elas�c in market 2. The manager's task is to choose the total output level and then allocate it between markets 1 and 2 such that MC = MR in both markets. To do this we need to find an aggregate measure of marginal revenue; we do this by the horizontal addi�on of the MR1 and MR2 curves. In the third panel of Figure 8.10 we show the ΣMR curve (Σ is the

Greek le�er sigma) which connotes the horizontal sum of the two MR curves. Note that it follows MR1 un�l MR2 "kicks in" at which point it kinks and

represents the sum of both MR1 and MR2. The ΣMR curve falls to intersect the MC curve at the total output level shown as ΣQ in the right-hand part of

Figure 8.10, where ΣQ is necessarily the sum of Q1 and Q2. Thus, the firm should set price P1 in market 1 and price P2 in market 2 to maximize its profit. 11

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While a firm may suspect that the price elas�city of demand differs significantly between two main groups of customers that demand its product, it will typically require significant expenditure on search ac�vity to es�mate those price elas�ci�es with any great accuracy. We have seen that if managers do know the firm's AVC = MC level, or, more generally, the shape of the MC curve, they can make "informed guesses" about the price elas�ci�es based on their knowledge of the customers from previous market experience. Given these es�mates managers can derive the demand and marginal revenue curves that are needed to find the profit-maximizing price and output levels. While these es�mates may contain substan�al errors, we know that there is scope for error due to the avoidance of more expensive search processes that are not invoked by making educated guesses. Managers who believe that one group of their customers is substan�ally more price elas�c than the rest might find a way to isolate these two groups of customers and tenta�vely raise the price against the more inelas�c group and lower the price faced by the more elas�c market. Before too long the result of this market experiment would be clear —sales in the more elas�c market would expand more than the sales in the less elas�c market fell and profits would increase, or not. If it seems to be working the manager might push the experiment a li�le further to see if profit can be increased s�ll further. If the experiment fails, the manager could revert to the former pricing strategy.

Simple rules o�en suffice; for example, airlines simply charge less for airfares if the dura�on of the return trip involves a Saturday night. They reason that most business travelers want to be home for the weekend and, thus, charge more for flights between any par�cular two ci�es if the trip does not include a Saturday night stopover. Similarly, textbook publishing companies charge more for textbooks sold in the wealthier U.S. market than they do for the same textbooks sold in less-wealthy foreign countries, with the price being different according to the shipping address. Cheaper U.S. textbooks sold in Asia are o�en labeled: "Not for resale in the U.S.," and legal ac�on is threatened if a bookseller were to buy books at export prices and a�empt to resell them in the United States at domes�c prices. Given the knowledge managers should have about the firms' markets, they should be able to devise a decision rule that effec�vely separates their customers into two or more discrete groups based on differing price elas�city of demand, and then set different prices for different subgroups of customers.Processing math: 0%

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"Buy one get one free" and "25% off your next purchase" are examples of bundle pricing, which is used to en�ce consumers to spend more than they ini�ally intended and thus increase overall revenue for the business.

© Mar�n Poole/Thinkstock

Bundle Pricing

Bundle pricing is the prac�ce of combining two or more products and selling them at a single "package" price that is less than the combined prices of the products if sold separately. The purpose of bundle pricing is to induce the buyer to spend more than they would have if they had only bought one unit of the product, and thus increase the overall revenue of the firm. You have likely seen many examples of bundle pricing. A coffee shop might offer coffee for $3 and a croissant for $1.50 if sold separately, or offer both for $3.95 as a package deal. Computer so�ware is typically bundled with computer hardware at a single price. Restaurants offer fixed-price menus that include, for example, soup, main course, and dessert for a single price that is less than the a-la-carte menu prices of these items added together. Retailers offer free parking if you buy something at their store. Professional sports teams and symphony orchestras offer season �ckets that are less than the total price of �ckets to all the individual performances.

Bundling Complementary Goods

As long as the incremental revenue accruing to the firm from the bundle price exceeds the incremental costs of producing and selling the two or more products, the firm will increase its profits by prac�cing bundle pricing. Let's consider the example of the offer of a pair of complementary goods, such as coffee and a croissant, for $3.95. Assume that the average variable cost of each is constant and, thus, equal to marginal costs, and that there are no incremental fixed costs, so that the marginal cost of each is equal to the incremental cost of each, as shown in Table 8.2.

Table 8.2: Bundle pricing example—coffee and croissant for $3.95 Coffee sold separately Croissant sold separately Coffee and croissant bundle

Incremental revenue $3.00 Incremental costs Direct materials $0.30 Direct labor 0.50 Variable overhead 0.20 Total incremental costs $1.00 Contribu�on margin = $2.00 Units sold before were 50 Total contribu�on before = $100 Units sold a�er will be 30 Total contribu�on a�er = $60

Incremental revenue $1.50 Incremental costs Direct materials $0.40 Direct labor 0.15 Variable overhead 0.05 Total incremental costs $0.60 Contribu�on margin = $0.90 Units sold before were 20 Total contribu�on before = $18 Units sold a�er will be 10 Total contribu�on a�er = $9

Incremental revenue $3.95 Incremental costs Direct materials $0.70 Direct labor 0.65 Variable overhead 0.25 Total incremental costs $1.60 Contribu�on margin = $2.35 Units sold before were 0 Total contribu�on before = $0 Units sold a�er will be 60 Total contribu�on a�er = $141

In this case, we can see that the coffee and croissant bundle makes a lesser contribu�on margin (i.e., $2.35) than the sum of the two component items (i.e., $2.90) but offering them in combina�on sells more coffees and croissants than before, such the total contribu�on rises from $118 before the introduc�on of bundle pricing to $210 a�er the introduc�on of bundle pricing. This happens because some customers who previously bought only coffee or only a croissant now see the bundle as a superior value proposi�on, and in addi�on some new buyers are a�racted into the coffee shop because the bundle offers them a superior value proposi�on. No�ce also that some buyers con�nue to buy just coffee or just a croissant at the a-la-carte prices. These extra 30 coffees contribute an addi�onal $60 and the extra 10 croissants contribute an extra $9 to the $141 contributed by the bundle to make the total contribu�on from coffee and croissants $210.

From the customer's perspec�ve, the bundle price offers an addi�onal item for an addi�onal amount of money that may be less than the customer's reserva�on price for that addi�onal item. In this case if a customer who regularly buys coffee has a reserva�on price for a croissant of, say $1.25, that customer would not buy a croissant at the a-la- carte price of $1.50, but would buy one when it is included in the bundle price because it costs only an addi�onal $0.95 over the cost of a coffee alone. Oppositely, a regular customer who buys only croissants and has a reserva�on price for coffee of say, $2.50, would not buy a coffee at the a-la-carte price of $3.00 but would buy one in the bundle because the addi�onal cost of the coffee is effec�vely only $2.45 more than the croissant alone. Similarly, people whose reserva�on price for coffee is below $3 (say $2.75) and for a croissant is below $1.50 (say $1.25) would not be customers of this coffee shop at the a-la-carte prices but would now find the "coffee plus croissant" bundle price an a�rac�ve proposi�on because the bundle price of $3.95 is less than their combined reserva�on price of $4.00. Finally, some customers who currently buy both coffee and croissants at other coffee shops would be a�racted to this par�cular coffee shop because it has effec�vely reduced its price for this combina�on of products.

Discounts for Larger Volumes

It may surprise you that discounts for larger volumes are another form of bundle pricing. Many firms offer a product in different sized packages and rather than mul�plying the unit price by the number of units, o�en say things like "20% off the second meal"; or "three for the price of two"; or "pay for 4 nights, get the 5th night free" and so on. Similarly, Coca-Cola prac�ces bundle pricing by offering its product in containers of various sizes—note that bo�les that hold twice as much cola cost less than twice as much as the smaller bo�le, for example. The larger sizes can be viewed as bundles, or mul�ples, of the smallest size offered for sale and the buyer is effec�vely given a discount per unit (per fluid ounce) for purchasing larger quan��es.

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Again, the customer will choose to buy the larger size container, or the greater number of units in the bundle, if the incremental cost to the buyer is less than the sum of his or her reserva�on prices for the extra volume or units provided. We illustrate this in Table 8.3 where we show the results of a market experiment where several different sizes of liquid detergent are offered at the prices indicated, as well as the reserva�on prices of three different buyers.

Table 8.3: Quan�ty discounts and reserva�on prices for three customers Size of container (fluid ounces)

Seller's price for each size

Customer A's reserva�on prices

Customer B's reserva�on prices

Customer C's reserva�on prices

10 $2.00 $2.80 $2.50 $1.80

20 $3.50 $3.60 $3.30 $3.40

30 $5.00 $4.80 $4.20 $4.90

40 $6.25 $6.00 $5.00 $6.20

50 $7.50 $7.00 $5.50 $7.55

The shaded prices show where the customer's reserva�on price is greater than the seller's asking price. We see that customer A would buy either of the first two sizes because the bundle price is less than this customer's reserva�on price for each of these sizes. Customer B would only buy the smallest size because the bundle price of larger sizes exceeds his or her reserva�on price. Customer C would not buy any of the smaller sizes but would enter the market and buy the 50-ounce container if it is available at the price of $7.55 or less. If these three customers are representa�ve of the market as a whole, this seller might decide to offer the product in the 10-, 20-, and 50-ounce sizes since it would sell a total of 90 ounces of detergent (rather than only 20 ounces if offering only the smallest size) for every three customers like these.

Whether the detergent firm will want to do that depends on the incremental costs of producing the larger-sized containers and filling them with detergent, of course. The rule, as you know, is that if the incremental revenue is greater than the incremental cost, then the firm should do it. In the simple example here with only three buyers, the incremental revenue of selling an addi�onal 20-ounce container and a 50-ounce container is $11. If the market is made up of 100,000 buyers like these three, the incremental revenues would be $1.1 million, all other things being equal. So, if the incremental fixed costs of se�ng up addi�onal filling lines, plus the incremental costs of the direct materials, labor, and variable overhead costs, are less than $1.1 million, it would appear to be a profit-making decision to go ahead with the three different sized containers of detergent.

10. "Ticks down" is the appropriate wording because Dutch auc�ons typically use a large clock-like dial and the single hand is first ratcheted around to start �cking down from a very high price. Each �ck is followed by a very short pause (like a cheaper watch) or in some cases (like a Rolex) the hand slides smoothly around the dial. The buyers either yell when they reach their reserva�on price, or to avoid arguments about who was slightly faster, the auc�on house provides bu�ons to push so that the buyer might win by milliseconds. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.3#return10) ]

11. In the case where MC is an upward sloping curve, this curve should be superimposed on the ΣMR curve in the third panel of Figure 8.10, and at the MC level where it intercepts the ΣMR curve, a horizontal line would be drawn back across the other two panels to find the output levels at which the MR curves (MR1 and MR2, respec�vely) fall to meet that MC level

in each of the two markets. To demonstrate that you understand this, visualize the upward sloping MC curve in the right-hand panel of Figure 8.10 that would cause the prices and outputs shown to be profit maximizing. Hint: it needs to cut the ΣMR curve at output level ΣQ. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.3#return11) ]

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Summary

In this chapter, we have applied theore�cal concepts learned in the preceding chapters to the pricing decisions of the firm in prac�cal situa�ons where

1. the cost of informa�on about the cost and revenue func�ons might be low enough to allow es�mates to be made of the cost and revenue func�ons such that the manager can proceed to use the "marginalist pricing" rule of MC = MR and

2. the informa�on search costs is expected to be higher such that the managers make the business decision to forego any further informa�on search ac�vity and use a markup pricing rule whereby a percentage markup over average variable costs is used to arrive at the price level to be charged.

Instead of obtaining es�mates of the underlying demand func�on, we saw that an es�mate of the price elas�city of demand provides enough informa�on, given current price and quan�ty demanded data, to derive expressions for the firm's demand and marginal revenue curves. Par�cularly, if average variable costs are expected to be constant at the current observed level, it then becomes a simple ma�er to apply the marginalist pricing rule to find the profit- maximizing price and output level.

We saw that the marginalist pricing rule and the markup pricing rule can be reconciled—that for every price obtained by the MC = MR rule there is a corresponding markup rate that would arrive at the same price. We found that the profit-maximizing markup rate is determined by the price elas�city of demand, and that the size of the profit-maximizing markup is inversely propor�onal to the (absolute) value of the price elas�city; that is, the higher the price elas�city in absolute terms, the lower is the profit-maximizing markup rate. Thus, products with more and closer subs�tutes and for which price is a larger propor�on of customers' incomes should be expected to carry smaller markup rates than products with few close subs�tutes and which are rela�vely inexpensive compared to customers' incomes.

Next, we showed that the avoidance of search cost provides a margin for error for the markup rate. This margin for error is wider the larger are the expected costs of informa�on search necessary to gain reliable es�mates of the cost and revenue curves. Thus, the actual markup rate u�lized can diverge significantly from the true (but unknown) profit-maximizing rate, such that the actual price and quan�ty demanded are quite different from the profit- maximizing levels. Despite this, the firm can make a larger profit as compared to first incurring the search costs and then se�ng the profit-maximizing price and output. Further, demand shi�s that are iso-elas�c, or roughly so, will poten�ally leave the current markup rate as the profit-maximizing one and not require a recalibra�on of the markup rate. Also, shi�s of the cost and demand curves due to infla�on are also likely to leave the current markup rate as op�mal if the curves are equally affected by infla�on.

Finally, in this chapter we considered ways to increase profits by se�ng different prices for different customers, discrimina�ng against those with higher reserva�on prices, more urgent demand, and less elas�c demand. We also considered bundle pricing, which allows the firm to extract more revenue from customers and increase profits as long as the incremental revenue exceeds the incremental costs associated with this pricing strategy.

In the following two chapters, we con�nue to examine the pricing decision of business firms in the context of new products (Chapter 9) and compe��ve bidding and price tendering (Chapter 10).

Ques�ons for Review and Discussion

Click on each ques�on to reveal the answer.

1. If the regression equa�on that best fits the TVC data collected for a firm is a linear equa�on, does that mean that the diminishing returns to the variable factors of produc�on is not applicable to that par�cular firm? Why or why not? (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 regression analysis of a limited range of output levels may show constant returns to variable inputs over that range of output levels without meaning that diminishing returns would not be observed at higher output levels. A linear line of best fit is compa�ble with a situa�on in which there are ini�ally increasing returns and later diminishing returns, but the data has been collected only from output levels around the point of inflec�on in the TP (or TVC) curve.

2. Explain in words (and some symbolic nota�on) how knowledge of the current price and quan�ty demand levels, combined with an es�mate of the price elas�city of demand at that price and quan�ty combina�on, can be used to derive an equa�on for the 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/boo

The demand curve can be expressed as P = a + bQ, so if we already know the current values of P and Q we would need to find only the values of a and b. We can deduce the values of a and b if we know the price elas�city at the current price. Since ε = (1/b) . (P/Q) and we know ε, P, and Q, we can solve for b and subsequently solve for a in the demand curve since it is now reduced to one equa�on with only one unknown value.

3. Suppose a firm chooses the price of its product by applying a 50% markup to its average variable costs, which are constant over the relevant range. Suppose also that top management agree that a 10% price increase would cause sales to fall by about 15%. What should they do now (if they want to maximize short-run profits)? (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

For the 50% mark-up to be profit maximizing, that would imply the price elas�city is −3.0, using the formula for the profit-maximizing mark-up, X = [−1/(ε +1)]. But top management agree that price elas�city is −15%/10% = −1.5. Subs�tu�ng for ε in the mark-up equa�on, we would find X = [−1/(−1.5 +1)] = −1/−0.5 = 2, which implies that a 200% mark-up over AVC would be profit maximizing. Management should raise prices to confirm their elas�city data and subsequently their mark-up rate.

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4. Explain why the demand for some products is more elas�c than it is for other products. (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

Price elas�city is higher if there are more and closer subs�tutes, and/or if the price is rela�vely high and represents a larger propor�on of consumers' incomes. The closer the subs�tutes are the more likely it is that the consumer will switch to a subs�tute if the price of X rises, and the more income it takes to purchase the product, the more likely the consumer is to switch to a cheaper subs�tute.

5. Explain in your own words why the magnitude of search costs (that would be required to ascertain the demand and costs curves) is posi�vely related to the range of prices (and markup rates) that allow the firm to make more profit than it could if it first incurred search costs and then set the price where MC = 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/boo

The higher the search costs are the more wrong you can be about the mark-up rate. Search cost avoided is opportunity revenue that can be added to the sales revenue at the current price. If search was undertaken and revealed that the price should be changed, the contribu�on from sales would need to rise by more than the search costs incurred before the "search then change price" strategy would be worthwhile.

6. Explain why an outward shi� of the demand curve that causes the value of price elas�city to be more or less unchanged at the current price level would not cause managers to want to raise the price. (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 iso-elas�c demand shi� that leaves the price elas�city at about the same level would cause managers to leave price at the same level if they are happy that the current price level was previously profit maximizing (given the prospect of large search costs). Unless search costs are small the managers are unlikely to want to re-examine price elas�ci�es or demand curve es�ma�on, since the search costs would be expected to outweigh any subsequent improvement in profits.

7. If infla�on causes the firm's costs to rise by a higher percentage than it causes customers' incomes to rise, explain whether the firm should raise or lower its markup rate to maximize its profit. (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

If infla�on impacts the firm's costs more than it does the consumers' incomes, managers would want to raise prices to maximize profits because the intersec�on of the MC and MR curves would occur at a lower output level, and demand curves are downward sloping. Thus they would want to increase their mark-up rate. In a kinked-demand-curve oligopoly situa�on they would expect their rivals to also raise prices since the cost increase is likely to be suffered by all firms.

8. Suppose I own a valuable oil pain�ng (e.g., the Mona Lisa) and wish to sell it. For a given group of poten�al buyers, which auc�on method, English or Dutch, would deliver the highest price, and why? (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

In theory, the Dutch auc�on would garner the higher price, equal to the reserve price of the person or organiza�on that values the pain�ng most highly (whereas the English auc�on price might be only $1 above the reserve price of the person or organiza�on that values it second-most highly). This assumes that all poten�al bidders are present at the auc�on, that they have a clear idea of their reserva�on price, and that they all understand that in the Dutch auc�on they will lose the item if they are not the first to bid and stop the clock.

9. What is the difference between first-degree, second-degree, and third-degree price discrimina�on? On what bases does the discrimina�on occur? (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

First-degree price discrimina�on (PD) discriminates against buyers on the basis of their willingness to pay, inducing the person who is willing to pay the most to bid the highest. Second-degree PD discriminates against buyers based on their urgency of demand—those who want the product sooner pay more than others who are willing to wait longer. Third-degree PD discriminates against buyers based on their price elas�city of demand—those whose demand is more inelas�c pay more than others whose demand is more price elas�c.

10. Describe several ways that the firm might u�lize bundle pricing to increase its profit from the same group of poten�al customers. (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

Bundle pricing can be prac�ced by offering the product in different sized containers where larger containers cost less than propor�onally more. Another bundling method is to offer 2 for the price of 1, or 11 for the price of 10, or frequent-buyer programs. A third method is to combine unlike but usually complementary products into a package deal that is priced at less than the simple sum of the prices of the products when sold separately.

Decision Problems

1. You have been called in as a consultant to the manager of Smith's Bookstore who is wondering if the present price of $9.95 for paperback novels is profit maximizing. The firm has experimented with prices every week for the past six months and collected data on prices and quan��es demanded for paperback novels sold each week. You conduct regression analysis of the data and obtain the following results (where P is in dollars and Q represents thousands of books sold per week):

Regression equa�on Q = 49.147 − 2.941P

Coefficient of determina�on R

2 = 0.96

Standard error of es�mate Se = 0.128

Standard error of the coefficient

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Regression analysis of the firm's weekly total variable cost and sales levels over the same period provide the following informa�on:

Regression equa�on TVC = 102.35 + 0.025Q2

Coefficient of determina�on R

2 = 0.92

Standard error of es�mate Se = 0.232

Standard error of the coefficient

Sβ = 0.003

a. What is the profit-maximizing price for the paperback novels sold by this bookstore? b. What is your predic�on for the level of sales at that price, and what is your 95% confidence interval for sales at that price? c. What is the price elas�city of demand at the price you are recommending?

2. The Laura Ann Bou�que purchases a line of inexpensive dresses from an importer and pays $30 per dress regardless of volume. These dresses are marked up by about one-third to sell at $39.95 each and quan�ty demanded averages 300 dresses per week.

a. What would the price elas�city of demand have to be for that markup rate to be profit maximizing? b. Laura Ann wants to maximize profit and is wondering if she is using the appropriate markup rate. Suppose she pays $500 for a marke�ng student to

conduct a survey of customers and this results in an es�mate of price elas�city of ε = –3.5. What price is profit maximizing if this es�mate can be regarded as being reliable?

c. Was it worthwhile for Laura Ann to spend the $500 on search costs?

3. Archibald Tires buys car �res at an average price of $600 per set of four, applies a 25% markup, and sells them for an average price of $750 per set, regardless of volume. Archibald typically sells about 60 sets of �res per week at that price. Joe Archibald has conducted an informal survey of his customers and has es�mated that if he raised his price by 10% he would lose 1 out of every 9 customers.

a. Derive an expression for the demand curve for these �res. b. What is the profit-maximizing price and quan�ty demanded, based on Joe's es�mate of price elas�city? c. What do you advise Joe Archibald to do, and why?

4. The Thomas Tent Company has two markets for its mid-size tent, the domes�c market and the export market. The demand curve for the domes�c market is characterized by P = 100 − 15Q, while the demand curve for the export market is P = 60 − 2.5Q, where P is the price in U.S. dollars and Q represents thousands of tents. The firm has one produc�on facility that manufactures the tents, which has a total cost func�on characterized by TC = 10,800 + 20Q +

0.1Q2 in the relevant range of outputs. a. What is the profit-maximizing level of mid-size tent produc�on for the firm? b. How should Thomas Tent divide this output between the two markets? c. What price should be set in the domes�c market? d. What price should be set for the export market?

5. Greener Grass Company (GGC) competes with its main rival, Be�er Lawns and Gardens (BLG), in the supply and installa�on of in-ground lawn watering systems in the wealthy western suburbs of a major east-coast city. Last year, GGC's price for the typical lawn system was $1,995 compared with BLG's price of $2,100. GGC installed 9,130 systems, or about 55% of total sales, and BLG installed the rest. (No doubt many addi�onal systems were installed by do-it- yourself homeowners since the parts are readily available at hardware stores.) GGC has substan�al excess capacity—it could easily install 25,000 systems annually, as it has all the necessary equipment and can easily hire and train installers. Accordingly, GGC is considering expansion into the eastern suburbs, where the homeowners are less wealthy. In past years, both GGC and BLG have installed several hundred systems in the eastern suburbs but generally their sales efforts are met with the response that the systems are too expensive. GGC has hired you to recommend a pricing strategy for both the western and eastern suburb markets for this coming season. You have es�mated two dis�nct demand func�ons, as follows:

Qw = 1,035.548 − 6.07164Pgw + 2.83Pbw + 2,100Ag − 1,500Ab + 0.2348Yw

for the western market and

Qe = 49,714.29 − 30.7692Pge + 6.984Pbe + 1,180Ag − 950Ab + 0.0825Ye

for the eastern market, where Q refers to the number of units sold; P refers to price level; A refers to adver�sing budgets of the firms (in millions); Y refers to average disposable income levels of the poten�al customers; the subscripts w and e refer to the western and eastern markets, respec�vely; and the subscripts g and b refer to GGC and BLG, respec�vely. GGC expects to spend $1.5 million on adver�sing this coming year and expects BLG to spend $1.2 million on adver�sing. The average household disposable income is $55,000 in the western suburbs and $25,000 in the eastern suburbs. GGC does not expect BLG to change its price from last year, since it has already distributed its glossy brochures (with the $2,100 price stated) in both suburbs, and its TV

commercial has already been produced. GGC's cost structure has been es�mated as TVC = 755.363Q + 0.005Q2 where Q represents single lawn watering systems.

a. Derive the demand curves for GGC's product in each market.Processing math: 0%

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b. Plot graphically the demand and MR curves for each market, and also show GGC's combined marginal revenue curve (ΣMR) and its MC curve. Show graphically the quan��es that should be produced and sold, and the prices that should be charged, in each market.

c. Confirm your quan�ty and price results algebraically. d. Calculate the price elas�ci�es of demand in each market and discuss these in rela�on to the prices to be charged in each market. e. Add a short note to GGC management outlining any reserva�ons and qualifica�ons you may have concerning your price recommenda�ons.

Key Terms

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

bundle pricing (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 prac�ce of combining two or more products and selling them at a "package" price that is less than the combined prices of the products if sold separately. The purpose of bundle pricing is to induce the buyer to spend more and thus increase the overall revenue of the firm.

Dutch auc�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 "reverse" auc�on where the seller's bidding begins at an unrealis�cally high price then drops down progressively un�l somebody accepts the asking price, and thereby wins the item.

English auc�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

An auc�on where the ar�cle's ini�al cost is set at a rela�vely low level, and then the poten�al buyers compete with each other, bidding the price higher un�l only one buyer with the highest bid price is le�, who then wins the item.

first-degree price discrimina�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 system of pricing whereby the seller induces the winning buyer to pay at or near the maximum that the buyer is willing to pay for an item. Auc�ons are examples of first-degree price discrimina�on.

infla�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 process by which the prices of goods and services in a given country con�nue to rise over a period of �me, which means that people can buy fewer goods and services with any given amount of money due to the deprecia�on of the monetary unit (dollar).

iso-elas�c demand shi�s (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

Shi�s of the demand curve where price elas�city stays the same at any given price level. Thus, if marginal costs are constant, the same markup rate con�nues to be the profit-maximizing rate, despite shi�s of the demand curve.

level of significance (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 degree of confidence we can have that the regression analysis of data from a sample indicates the true rela�onship that exists between the variables in the whole popula�on.

marginalist pricing (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 form of pricing where the firm sets price using the "marginal cost equals marginal revenue" rule, by using data obtained by firms based on their prior produc�on and market experience.

markup pricing (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 prac�ce of se�ng price by adding an amount, calculated as a percentage of direct costs per unit (AVC), to the AVC, to determine the asking price of a product.

price discrimina�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 pricing prac�ce where a firm (legally) charges its customers different prices for what is basically the same product (e.g., air travel) because that base product is delivered at different �mes or in different circumstances that contribute addi�onal value to some consumers who are prepared to pay a higher price.

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real 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 assessment of the monetary value of an asset or other item that is expressed in constant-purchasing power dollars, as dis�nct from nominal (or monetary) terms where price is expressed in terms of the face value of a currency that is deprecia�ng due to infla�on.

reserva�on price (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 maximum price that a buyer is willing to pay for a given item, or in the case of sellers, the minimum price for which they will sell an item.

second-degree price discrimina�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 pricing prac�ce that involves charging higher prices to those whose demand is more urgent, and lower prices to those whose demand is less urgent, such as short-no�ce airfares cos�ng more than advance-purchase airfares.

seller's reserve price (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 minimum price that the seller is prepared to accept for a given item in order for a sale to be made.

thick markets (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

Markets that are rela�vely dense with many poten�al buyers of a par�cular item within a given radius of the seller(s), such as exists for most products in large ci�es.

thin markets (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

Markets in which there are rela�vely few buyers in a given area, such as in rural and remote areas, or for products in dense areas of popula�on that very few buyers need or can afford. Examples are the market for hip replacements or uncut diamonds.

third-degree price discrimina�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 pricing prac�ce that involves charging higher prices to those whose demand is less price elas�c, and lower prices to those whose demand is more price elas�c, such as business class airfares cos�ng more than economy class airfares.

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