Teaching Price Discrimination:
Some Clarification
Kathleen Carroll
Dennis Coates
Department of Economics
UMBC
1000 Hilltop Circle
Baltimore, MD 21250
Draft: Aug. 19, 1996
Economics is useful and important as a tool for the study of policy. Indeed, what interests students most in Principles of Economics courses are those topics with direct policy relevance. Since the discussion in Principles may be the only exposure students get to many of these issues, we think it important that these topics be covered with as little opportunity for confusion as possible. The typical textbook treatment of multipart pricing, or price discrimination, is especially laden with pitfalls.
In fact, even to say that there is a typical treatment of price discrimination is misleading. We have reviewed the discussions of price discrimination in several principles textbooks: Lipsey and Courant (1996); McConnell and Bruce (1996); Parkin (1996); Gwartney and Stroup (1995); Samuelson and Nordhaus (1995); Taylor (1996); Baumol and Blinder (1994); Miller (1994); Tresch (1994); and Mansfield (1992). Across these texts we have found a wide variance in the approach and the issues raised. In general, however, the discussions focus on either theory or antitrust policy.
Those that focus on theory scarcely mention the regulatory issues and legislation. These discussions usually are part of the chapter on monopoly. Most of these indicate that a downward sloping demand curve and market segmentation are required. Some mention that prohibition of resale is a requirement. Most texts in this group define price discrimination as a situation in which the same good is sold at different prices unrelated to cost differences, but there are exceptions. Almost exclusively, the examples of real world price discrimination are of the third degree variety. A major problem with these treatments is that it is very hard to justify the examples as coming from monopolized industries. For example, common textbook cases of price discrimination are: senior citizen discounts offered by restaurants, child prices for movie theaters, differential pricing for business and vacation travelers on airlines. Few people would argue that restaurants, theaters or airlines are monopolies. Hence, texts suggest that price discrimination requires monopoly or market power, then proceed to provide examples in which monopoly is dubious at best and ludicrous atworst.
Those texts that focus on the antitrust issues summarize legislation pertaining to regulation of anti-competitive behaviors and defenses that business can use if charged with illegal price discrimination. Students reading from this group of texts get little information on the conditions under which price discrimination may occur, that there are several varieties of price discrimination, or multipart pricing more generally, or the likely effects of these pricing schemes on economic efficiency. In other words, students get little indication that economic theory has anything to contribute in this policy area.
This article provides some suggestions for organizing textbook treatments of price discrimination and for providing examples that should avoid confusion and give students a better understanding of the important issues. Our discussion of price discrimination focuses on three areas: (1) theoretical treatment of price discrimination; (2) policy implications of price discrimination; and (3) the existence and practice of price discrimination.
1. Theory of price discrimination
The theoretical treatment of price discrimination concerns three issues: (1) the definition of price discrimination; (2) situations or conditions in which price discrimination occurs; and (3) the effects of price discrimination.
Definition of price discrimination
Price discrimination is the practice of a firm charging multiple prices for the same good where the difference in price is not attributable to a corresponding difference in cost. This definition implies that different observed prices for apparently identical goods need not be discriminatory. Costdifferences, not simply price differences, must be considered. Moreover, different types of price discrimination have been identified, each with different implications and distinct characteristics. In fact, two distinct, but related, taxonomies of price discrimination exist.
The first taxonomy, by Fritz Machlup (1952), listed several different types of price discrimination, summarized by Shepherd (1990). The three types described by Machlup are: personal discrimination in which the firm tailors price to the specific buyer, group discrimination wherein identifiable groups are charged different prices, and product differentiation which involves different prices charged for identical goods over time, say through end-of-season sales. The second taxonomy of price discrimination identifies first, second and third degree price discrimination. There are similarities between the two taxonomies, some of which we will point out as we define these three types of price discrimination by degree. Table 1 summarizes the relationship between the first and second taxonomies.
[Table 1 about here]
First degree price discrimination occurs when a different price is charged for each and every unit offered for sale. The seller is able to set price on each unit at the maximum that some buyer is willing and able to pay. This situation is much like the "personal discrimination" of Machlup and Shepherd because the seller must know very specific information about every consumer to be able to set the highest attainable price on every unit. The seller is in position to make a "take-it-or-leave-it" offer to the buyers of the good. Sellers are unlikely to have this level of information in many situations. One famous, if controversial, example of first degree price discrimination is WilliamNiskanen's model of the relationship between bureaus and Congress. Niskanen gives bureaucrats the ability and the desire to make "take-it-or-leave-it" offers to Congress. Niskanen's bureaucrats then capture all the surplus, in the form of budget allocation, associated with provision of public services.
Second degree price discrimination results if the seller cannot set the correct price on every unit. Simply put, second degree discrimination allows firms to set prices only for groups of units because the seller only has general information about maximum willingness to pay. For example, the firm might know that there are two groups of buyers of its product. The first group will buy a great deal of the good if the price for the marginal unit is low enough; the second group will buy only a small amount of the good no matter what the price. Unfortunately for the seller, it does not know which group any specific buyer is in. Consequently, the seller may offer quantity or volume discounts: the price per unit falls after the purchase of some pre-set number of units. Buyers reveal to which group they belong through their consumption behavior and are charged a price that corresponds to their marginal willingness to pay for the good. Shepherd includes volume discounts in the group discrimination category.
Third degree price discrimination is based on characteristics of the consumer or group of consumers. Firms recognize that some consumers are more sensitive to price than are others. Moreover, firms can separate consumers into either group through some easily or costlessly identifiable trait of the consumer. For example, students may be identified by asking for a student identification; senior citizens by presentation of an American Association of Retired Persons card ordriver's license. Those whose demand for movies is insensitive to price may show up to see first run movies at their premiers; individuals with more sensitive demand may wait till later to see the film in low cost venues or on video. Prices in each of these instances may well differ for different consumers even after accounting for cost differences. Third degree price discrimination is clearly "group discrimination."
The distinctions drawn between price discrimination of the varying degrees may seem arbitrary. Nonetheless, the distinctions are important because the different types of discrimination have different implications for economic efficiency. Moreover, if textbooks describe only one type of discrimination then follow that up with the efficiency implications of a second type, as in McConnell and Bruce (1996), Parkin (1996), Gwartney and Stroup (1995), and Taylor (1995), students are likely to come away with very mistaken impressions of the policy implications of price discrimination analyses. We noted earlier that a common textbook application of price discrimination is the difference in prices charged to business travelers and vacation travelers who use airline services. This is clearly an example of price discrimination by consumer group (third degree), if it is price discrimination at all. The same texts, however, explain the efficiency effects of price discrimination only in terms of perfect price discrimination. If students have not been told of the differences between these two types of discrimination they may easily be confused into believing that third degree price discrimination is efficient.
We believe that a fruitful and less confusing approach is to give greater emphasis to the conditions required for price discrimination to be possible. Because the conditions vary slightly between types, students can be shown how slight differences in the economic or business environmentcan have dramatic repercussions for economic efficiency and policy implications. With this as motivation, we now turn to a discussion of the conditions for price discrimination.
Conditions for price discrimination
For a firm to practice price discrimination, three conditions are necessary. First, the firm must not be a price taker, it must have some market power. Even the slightest market power implies that the firm faces a negatively sloped demand curve for its product. The downward sloping demand curve for its product means that there is consumer surplus arising from the transactions. Price discrimination is the firm's attempt to capture some of this surplus for itself.
Price discrimination also requires that the firm is able to prevent resale. If arbitrage is possible, the law of one price holds. That is, those who face the low price can purchase the product and sell it at a profit to those facing the higher price. Resale may be prevented by the nature of the commodity or via licensing agreements, copyrights, or other legal impediments to resale. Services such as haircuts, physical examinations, or legal advice, are likely examples of goods for which price discrimination is possible because of the obvious difficulty in reselling them.
A third requirement often cited for price discrimination is that consumers have different elasticities for the good or service. The extent to which the firm knows the demand behavior of buyers largely determines which degree of price discrimination is possible. For example, if the firm knows each and every individual buyer's demand curve perfectly, then the firm can set price on each unit to entice that buyer with the highest willingness to pay into a purchase. This is, clearly, first degree price discrimination. If the firm knows only of the existence of buyers with high willingness to pay and buyers with low willingness to pay then it can offer quantity discounts or use tie-in sales to capture some of the consumer surplus created by the transactions. These are instances of second degree price discrimination or nonlinear pricing. Finally, if the firm knows that elasticity is related tosome identifiable group characteristic then it can use third degree price discrimination to induce the price insensitive buyers to pay a high price for the good and price sensitive buyers to pay a low price. This is, of course, third degree price discrimination.
The informational requirements for the three types of price discrimination vary. Under first degree discrimination a great deal of information must be known about individual buyers. Second degree discrimination relaxes that assumption substantially, allowing firms only to know that some buyers have high willingness and others low willingness to pay. By pricing specific quantities of the good differentially or attaching some other condition to the purchase of the good (coupons, tie-ins, etc), second degree discrimination forces the individuals to further reveal to which class they belong. At the same time, second degree discrimination does not require the seller to have sufficient information prior to the transaction to guess which people belong in which category. Under third degree discrimination the seller does have that kind of information; to wit, the seller can identify those with unresponsive demand based on some readily observable characteristic, such as some socio-demographic trait. This characteristic separates this "group" for differential pricing.
Understanding the differential informational requirements, one can then examine how the differences influence economic efficiency and policy implications. We turn now to the efficiency considerations.
Effects of price discrimination
Price discrimination affects efficiency and distribution, but the specific efficiency effects depend on the type of price discrimination practiced by the firm. Regardless of the type of price discrimination, however, it is profitable for a firm to engage in this practice. In any case of price discrimination, some buyers face a lower price than others. The act of price discrimination can be thought of as offering a high price to those who willingly pay it and a low price to those who wouldnot pay the higher price, holding marginal cost constant. Because resale is impossible, the seller extracts consumer surplus from the buyers that it would not get if it sold the same number of units all at the lower price. The firm gains profit from redistribution of surplus rather than through increased efficiency of production.
The efficiency effects depend on the type of price discrimination practiced by the firm. When a firm practices first degree price discrimination, it is profitable to expand output to the point where price equals marginal cost. The firm, recall, knows the maximum willingness to pay of every individual buyer. Consequently, it offers a unit for sale only if the most anyone will pay for it is at least the marginal cost of producing that unit. On every unit for which the maximum willingness to pay exceeds marginal cost the firm captures the entire difference as its own. On the last unit offered for sale the firm makes no profit because marginal cost equals price. But marginal cost equal to price is precisely the condition for maximizing net social gain from this market (that is, in partial equilibrium).
When a firm practices third degree price discrimination, the efficiency effects depend on the shapes of the demand and cost curves. With straight-line demand curves and constant costs, output does not increase over the level of the nondiscriminating firm. Rather, the firm's profit maximizing output is simply divided among its separate groups of consumers and priced differentially, inversely related to each group's elasticity. In this situation, any deadweight loss that had existed with no discrimination still exists, by which we mean that the gap between marginal willingness to pay for one more unit and marginal cost of producing one more unit is the same. There is, however, an additional welfare cost caused by the allocation of the good from those whose willingness to pay is higher to those whose is lower which results from the price discrimination. The firm has made profit by reallocating its sales among the buyers.
Table 2 provides a numerical example which clarifies the efficiency differences between firstand second degree price discrimination, a non-discriminating monopolist and competition. Assume that the marginal cost is constant at 20. The non-discriminating monopoly model would find a market price of 22.50 and a total quantity of 17.5. How many units will go to market 1 and how many to market 2 is indeterminate, however. The first degree price discriminator would sell the first 12 units produced to the second market, at prices starting at 48 for the first unit and declining to 26 for the twelfth, before selling even the first unit in market 1. This is so because the price at which each of these first twelve units can sell in market 2 is higher than the price the monopolist can get for even the first unit in market 1. Indeed, for the first degree discriminator, the market demand curve is the marginal revenue curve. The total sold by the first degree discriminator is 35, 20 to market 1 and 15 to market 2. Note that the price in each market equals the marginal cost, P1=P2=MC=20. Hence, the first degree discriminator sells the efficient quantity. Moreover, the price charged to each consumer for the last unit sold is the same which means that there are no uncaptured gains from trade between consumers.
[Table 2 about here]
The third degree discriminator will sell a total of 17.5 units, just as in the non-discriminating monopoly model. However, the third degree discriminator will sell 10 in market 1 at a price of 22.50 per unit and 7.5 in market 2 at a price of 35 per unit. Consequently, there exist uncaptured gains from trade as buyers from market 2 would gladly pay buyers from market 1 more than 22.50 to acquire another unit of the good. Because resale is impossible, however, such exchanges do not occur. For this reason greater inefficiency occurs in the third degree case beyond that under the non-discriminating monopoly model despite the fact that the same quantity of the good is sold in both situations. If the cost and demand curves result in an expansion of output beyond that offered in the pure monopoly model, efficiency may or may not be increased, depending on the effect on totaldeadweight loss.
Second degree discrimination has unknown efficiency effects. The more like the first degree case the situation is, the more likely efficiency is enhanced by price discrimination. Take the case of quantity discounts, for example. The second degree price discriminator could set the higher price at the monopoly price and the lower price at the competitive price. Net social welfare rises because output rises, relative to the pure monopoly situation. The deadweight loss of this situation is zero. Yet because not all consumers pay the same price for the product there remain uncaptured gains from trade, an efficiency loss. Suppose consumer A purchased the product in sufficient quantity that the volume discount applied on the last unit. Suppose that consumer B paid the higher price on the last unit she bought. Since B's willingness to pay for another unit is higher than that of A, there exist gains to be had from trading. Hence, second degree discrimination is not efficient. Moreover, it is uncertain whether the lost welfare from these misallocations of the good away from high value consumers to low value consumers is greater than or less than the welfare loss from the simple monopoly case. Generally, then, whether efficiency improves or declines depends upon the shapes of the supply and demand curves.
2. Policy implications of price discrimination
From the discussion above it is clear that price discrimination occurs when a firm with some, perhaps quite small, market power sets prices such that identical units of a given good or service sell for different prices. It is also clear that whether this is purely redistributive or both redistributive and inefficient depends upon the information available to the firm and the shapes of the supply and demand functions. Consequently, policy with regard to price discrimination must address both efficiency and/or equity concerns. Price discrimination figures prominently in both antitrust policy and regulation of natural monopoly. This section describes current policy, focusing on legislative andjudicial interpretations regarding antitrust issues and how these relate to the theoretical issues outlined above. We also discuss, though much more briefly, the use of third degree price discrimination in regulating natural monopoly.
The Robinson-Patman Act, which in 1936 amended Section 2 of the 1914 Clayton Act, outlaws price discrimination. Sections 2a and 2b of the Act make it unlawful for firms to set different prices for "goods of like grade and quality" sold to different buyers when the effect of doing so "may be substantially to lessen competition or tend to create a monopoly in any line of commerce." Moreover, such pricing is also illegal if it tends "to injure, destroy, or prevent competition with any person who either grants or knowingly receives the benefit of such discrimination, or with customers of either of them."
The Act provides the accused price discriminator with three defenses. First, differential prices may be justified as part of a plan to dispose of perishable or obsolete items or as part of a close-out or bankruptcy sale. A second justification of the price differentials is differences in "the cost of manufacture, sale, or delivery resulting from differing methods or quantities" sold or delivered. Finally, price differentials are lawful if they were implemented "in good faith to meet an equally low price of a competitor."
The language of the Robinson-Patman Act defines price discrimination consistently with the economic definition. Both definitions make it clear that price differentials must be related to cost differences. Moreover, the law clearly recognizes that the cost differences may be in either the production or the distribution/delivery of the good. Consequently, situations such as those described by Lott and Richard (1991) can easily be defended as lawful variations in price.
A primary concern of this law is the harmful effects on competition that price discriminationmay induce. Recall that charging different prices for like quality goods is unlawful if those prices harm competition. However, the legislative history of the Robinson-Patman Act reveals that the intent was really to weaken competition. Indeed, Scherer and Ross (1990) state, "There is virtual unanimity among students of the act that, in sharp contrast to other antitrust laws, its motivation was mainly a desire to limit competition, not to enhance it." Specifically, the law was a response to the growth of chain stores who, because of purchasing in large volumes, could obtain lower prices from suppliers than could the neighborhood locally owned stores. The chain stores could, therefore, offer lower prices to the consumer and were in a position to drive small operations out of the market. The Robinson-Patman Act makes it more difficult for chain stores to obtain lawful price breaks and, therefore, to undercut small firms at the retail level. Thus, implicit in the law is the notion that the protection and promotion of small firms is desirable, presumably on grounds of increased social efficiency.
An additional circumstance in which price discrimination may be lawful occurs when it is allowed by regulators to enable a natural monopoly to operate profitably at the efficient level of output. Price discrimination enables the natural monopolist to produce the efficient level of output, on which it takes a loss, but to earn enough on the non-marginal units to earn a normal rate of return, and to make up the loss that it incurs with a policy of marginal cost pricing. This represents an alternative to the less efficient pricing policy of average cost pricing where some deadweight loss results. Of course, one implication of this is that some consumers subsidize the firm's ability to provide output to more consumers than it otherwise could.
3. Existence and practice of price discrimination
As noted earlier, price discrimination occurs where a firm charges multiple prices for the same good, and the price differential does not correspond to differential cost. The existence of pricediscrimination therefore depends first, on market definition, and second, on the relationship of the differential prices to the difference in costs.
Market definition is important to the theoretical and practical concept of price discrimination. The commodities which are differentially priced must be in the same market; indeed, they must be essentially the same product. Of immediate concern is the notion of product discrimination. This clearly requires some variance in the characteristics of the goods that are differentially priced. The question is: to what extent does the variance in characteristics define a different good? If the goods are really different goods, can this be price discrimination?
One specific characteristic is quality. If a lower quality good is not a substitute for a higher quality version of the same good, then differential pricing may not be a situation of price discrimination. The low-quality good and the high-quality good are not the same good. That is, the goods are themselves not comparable so that price comparisons are not meaningful.
One example of this is the comparison of a Cadillac with a Chevrolet. As an example of third degree price discrimination, the usual approach is to consider that all buyers are in a single market ("car") but they can be separated out into subgroups of that market ("high-quality car" and "low-quality car"). Whether this approach is appropriate is an empirical question. One could test whether these, or any two, goods are best considered as part of the same market by measuring the cross price elasticity of demand between them. If the goods are close substitutes then the assumption of them belonging to the same market is more tenable than if they are not close substitutes even though they are very similar in outward appearance and in use.
Another example of similar goods that may not truly belong to the same market are goods defined by a time dimension, such as for clear-the-stock or peak-and-off-peak pricing. Off-season goods or time-dependent use may indicate that the goods are not the same and that they are not in the same market. If this is the case, then comparisons of time-related prices to determine pricediscrimination are not meaningful. Note also that if peak-load pricing is properly employed where price in each period equals marginal cost in that period, then this practice is clearly not discriminatory.
If we are defining separate markets in which the goods are sold, then it is unclear whether price discrimination exists. The separation of markets may again reflect differences in goods, particularly in the perception of the buyers, as with potential subscribers and continuing subscribers. Going to a single concert or buying a magazine or newspaper at a newsstand may be a different commodity than buying a subscription package of concerts or delivered magazines or newspapers.
Market definition is also important to the issue of market power. We have previously indicated that market power is a necessary but not sufficient condition for the existence of price discrimination. In many cases of personal and group price discrimination discussed above, such as with bazaars, new and used cars, geographic price discrimination, and price discrimination related to customer tenure, market power may be questionable. Often the situations in which the price discrimination is said to occur are situations of considerable competition among the firms in the market.
In a number of the pricing practices listed in Table 1 above there may be no clear connection to market power. Rather, the likely market imperfection in these cases is asymmetric information rather than market power. The superior information of the seller may provide some "power" in the market, but this is not market power in the usual sense described earlier, as a lack of competition or price-taking behavior. Asymmetric information where the seller has the advantage may apply to: Haggle-every-time; give-in-if-you-must; all-or-nothing-package; absorb-the-freight; and dump-the-surplus. Asymmetric information favorable to the buyer may apply to: Size-up-buyer-income and measure-the-use.
The misalignment of prices to costs is an important aspect of price discrimination. Economists define cost as opportunity cost. Opportunity cost includes implicit as well as explicit cost. Indeed, this is the point of Lott and Richard (1991). The risk of holding inventories in order to obtain the in-season price would represent a cost to the firm; lowering price to clear inventories may reflect this lower opportunity cost of risk. Selling goods by subscription lowers risk, thereby lowering opportunity cost. The practice of offering lower prices to entice new subscribers or to develop customer loyalty may reflect the expected lower risk associated with a given subscriber base, even though production costs are the same for the two goods.
4. Concluding remarks
We began this paper with a criticism of the style and approach to teaching about price discrimination found in principles texts. In this section we summarize how we think price discrimination ought to be covered to create the least confusion possible.
First, any discussion should contain information about the three necessary conditions for price discrimination to occur. Second, the discussion should explain that there are three types of price discrimination and that the type of discrimination which occurs depends upon the level of information held by firms. Third, the discussion should emphasize that the different types of price discrimination have different implications for economic efficiency. A table like that presented here may be useful in this regard. In addition, use of such a table emphasizes the differences between the competitive outcome, the monopoly outcome and the first and third degree price discrimination outcomes. Therefore, the table is a helpful review of important points for each of these models. Moreover, such a table can be used to discuss the inefficiency of second degree discrimination which arises from buyers paying different prices for the marginal unit purchased. Fourth, distribution issues should be discussed, particularly since the price discriminating firm gains profit by acquiring surplus fromconsumers. Finally, the discussion should reflect upon the practical difficulties of identifying price discrimination. Students should be made aware of the importance of price differences which are not explained by cost differences and the issues of market definition.
The issue of price discrimination is complex. We believe, however, that it can be presented at the introductory level in a way that is simpler and less confusing than we currently observe, so that students are not presented with misleading information.
First, it is clearly inappropriate to attribute the practice of price discrimination to market power, and monopoly. Situations of multiple pricing may reflect any number of economic situations other than price discrimination, such as problems in market definition, the existence of opportunity costs not accounted for explicitly by the firm, a situation of competitive behavior indicating the absence of market power, or the presence of an alternative market imperfection, such as asymmetric information.
Second, examples of price discrimination are pedagogically helpful. Students like them and they have most likely had some experience with many of them. We believe that providing examples classified according to price discrimination by unit (first and second degree), and price discrimination by consumer group (third degree) is more useful than either a classification based on personal, group, and product discrimination, or a presentation of examples that are not clearly associated with the analysis of this pricing practice.
Third, we believe that the treatment of price discrimination is less misleading if it is presented as a theoretical issue and a policy issue. The theoretical issue is concerned with the behavior that leads to the efficiency and distributional effects of price discrimination. This requires distinguishing between the two basic types (price discrimination by unit and by consumer group) and clearly stating the conditions required in each case, so that students know what the practice is and when it can occur. The policy issue involves both antitrust and regulatory policy. Either or both can be examined tohelp students understand the meaning of social efficiency and the distinction between efficiency and distribution.
Often students believe that if a firm increases profit it is doing better, so it must be efficient. This is the case if a firm is able to lower its cost and thereby increase its profit; it is not necessarily the case when profit is increased by other circumstances. Witness the increase in a firm's profit with a collusive agreement that replaces interfirm competition, or with third degree price discrimination with no corresponding increase in output. While this profitable behavior may be "efficient" for the firm, i.e., privately efficient, it is not socially efficient. Many students do not fully understand the concept of efficiency as social efficiency. Discussion of price discrimination is a good opportunity to make this distinction.
Table 1: Price Discrimination Practices
_________________________________________________________
Pricing Practice Machlup Category Degree
Haggle-every-timePersonal First
Give-in-if-you-mustPersonal First
Size-up-buyer-incomePersonal Third
Measure-the-usePersonal Third
All-or-nothing-package --- First
Absorb-the-freightGroup Third
Kill-the-rivalGroup Third
Dump-the-surplusGroup Third
Get-the-most-from-each-regionGroup Third
Promote-new-customersGroup Third
Keep-old-customers-loyalGroup Third
Favor-the-big-onesGroup Third
Sort-buyers-by-time-valueGroup Third
Divide-buyers-by-elasticityGroup Third
Appeal-to-the-classesProduct Third
Pay-for-the-labelProduct Second
Clear-the-stockProduct Second
Peak-and-off-peakProduct Second
Quantity/volume-discountsProduct Second
_________________________________________________________
Table 2:QuantityMarginal Revenue 1Price 1Marginal Revenue 2Price 2124.524.75464822424.54246323.524.253844423243442522.523.75304062223.52638721.523.252236821231834920.522.751432102022.510301119.522.256281219222261318.521.75-224141821.5-6221517.521.25-1020161721-14181716.520.75-1816181620.5-22141915.520.25-2612201520-3010
Demand in market 1: Q1=100-4P1
Demand in market 2: Q2=25-.5P2
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