Teaching price discrimination: some clarification.

Coates, Dennis

1. Introduction

Economics is useful and important as a tool for the study of policy. Indeed, what interests students most are those topics with direct policy relevance. We think it important that these topics be covered with as little opportunity for confusion as possible, especially in the Principles course, which may be the only exposure students get to many of these issues. Treatment of price discrimination in both Principles and Intermediate texts are often laden with misleading and even incorrect information.

We have reviewed the discussions of price discrimination in several Principles and Intermediate textbooks. Principles texts we have reviewed include: Mansfield (1992), Baumol and Blinder (1994), Miller (1994), Tresch (1994), Gwartney and Stroup (1995), Samuelson and Nordhans (1995), Taylor (1995), Lipsey and Courant (1996), McConnell and Brue (1996), and Parkin (1996). Intermediate texts we have reviewed include Ekelund and Ault (1995), Mansfield (1997), Nicholson (1997), Hirshleifer and Hirshleifer (1998), Landsberg (1998), Pindyck and Rubinfeld (1998), Browning and Zupan (1999), and Perloff (1999). Across these texts, we have found a wide variance in the approach and the issues raised.

In general, the discussions in Principles texts focus on either theory or antitrust policy, but rarely link the two. 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 texts 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 graphical exposition demonstrates first-degree price discrimination, but the examples of real-world price discrimination are of the third-degree variety.

One major problem with these treatments is that the theoretical presentation and the examples are inconsistent. A second problem 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, and 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 is a pure monopoly phenomenon, then proceed to provide examples in which monopoly is dubious at best and ludicrous at worst.

Those texts that focus on the antitrust issues summarize legislation pertaining to regulation of anticompetitive 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 the likely effects of these pricing schemes on economic efficiency and income distribution. In other words, students get little indication that economic theory has anything to contribute in this policy area.

Similar problems with the treatment of price discrimination arise in some Intermediate microeconomics texts. For example, Landsburg (1998, p. 361) defines price discrimination as "the act of charging different prices for identical items"; Nicholson (1997, p. 305) defines price discrimination as "selling identical units of output at different prices"; and both suggest that price discrimination is exclusively a monopoly phenomenon. Pindyck and Rubinfeld (1998) make no mention of cost differences in their treatment of price discrimination, but Ekelund and Ault (1995) do. Mansfield (1997) notes that differences in prices are not sufficient to show price discrimination but makes no mention of efficiency effects. He also indicates that price discrimination can occur whenever a firm has some market power, as do Pindyck and Rubinfeld (1998), Browning and Zupan (1999), and Perloff (1999). Hirshleifer and Hirshleifer (1998) discuss the importance of market segmentation, using the example of differences in the prices of Japanese cars sold in the United States and those sold in Japan. In the context of a chapter on monopoly, as it is presented, the discussion is likely to confuse students who are well aware of the existence of multiple car manufacturers from both the United States and Japan.

This article provides some suggestions for teaching 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: (i) the definition of price discrimination, (ii) situations or conditions in which price discrimination occurs, and (iii) the effects of price discrimination.

2. Definition of Price Discrimination

Popular textbooks on industrial organization define price discrimination as differences in the ratio of price to marginal cost across buyers or units of a good.(1) One form of 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. Another form of price discrimination is the practice of a firm charging the same price for all units of the same good when there are cost variations in supply. This implies that observed identical prices for apparently identical goods may be discriminatory. Cost differences, not simply price differences, must be considered.

Lott and Roberts (1991) make this point forcefully by carefully examining four commonly used "examples" of price discrimination: the spreads in retail gasoline prices, the prices of dinners at restaurants, the price of popcorn at movie theaters, and the variation of airline ticket prices with time between ticket purchase and flight date. They show that cost differences, particularly opportunity cost differences, may explain the price differences. Their examples may not necessarily be convincing, however, because one can reasonably dispute whether the "goods,' sold at different prices are really the same thing. For example, Lott and Roberts (1991) explain why the price of dinner in a restaurant may be higher than the lunch time price of the same food; the time spent at the table is longer for dinner than for lunch, so the higher dinner price represents the greater opportunity cost of tying up the table. Yet eating lunch, with its particular set of accompanying services, is probably not a close substitute for eating dinner, which may have a very different set of accompanying services. The possibility that these two meals may be very differently bundled presents a more complicated pricing situation, along the lines of second-degree price discrimination. In this type of situation, where marginal cost is difficult to determine, the usual definitions of price-marginal cost ratios or differentials may be insufficient to rule out the possibility of price discrimination.(2)

The more standard example of price discrimination at a restaurant is that of senior citizen discounts. In this case, two diners at the same table ordering exactly the same meal will face different prices if one carries an American Association of Retired Persons card but the other does not. Lott and Roberts' opportunity cost explanation for different prices does not work for this example. Nonetheless, Lott and Roberts (1991) have succeeded in showing that there may be subtle cost differences that justify price differences in situations where one may be tempted to claim the existence of price discrimination.

Even though price discrimination occurs when price-marginal cost ratios differ across either units or buyers of a good, not all price discrimination is the same. 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.(3) The most common taxonomy of price discrimination identifies first-, second-, and third-degree price discrimination.

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.(4) The seller is in a position to make a "take-it-or-leave-it" offer to the buyers of the good or to bargain the buyer to his or her reservation price. Sellers are unlikely to have this level of information in many situations. One famous, if controversial, example of first-degree price discrimination is William Niskanen's (1971) 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 of the surplus in the form of budget allocation associated with provision of public services.(5) Another example of individual unit pricing would be a situation where the seller deals individually with each buyer and can "size" him up and price accordingly, such as in auto or insurance sales.

Second-degree price discrimination encompasses a variety of pricing schemes through which the firm is able to induce consumers with high valuations to pay higher prices than consumers with low valuations. Second-degree price discrimination schemes induce consumers to self-select into groups based on their willingness to pay. Firms do not have the consumers' valuation information in this case, as they do under first-degree discrimination, nor do they have information that would enable them to identify high- versus low-demand individuals as under third-degree discrimination. 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, he or she does not know which group any specific buyer is in. One form of second-degree price discrimination is the offer of quantity or volume discounts: the price per unit falls after the purchase of some preset number of units.(6) Another form of second-degree price discrimination is the two-part tariff. Under a two-part tariff, consumers pay a lump sum fee and a per-unit charge.(7) In each of these cases, buyers "self-select" into the pricing arrangement best for them and best for the seller, besides.

Other examples of second-degree price discrimination include tie-in sales and quality choices. In these cases, the firm determines the profit-maximizing prices of multiple products simultaneously. For example, if a firm sells two products that are highly complementary, then it will choose the prices on each to take advantage of that complementarity. Alternatively, the firm might produce the same good in different qualities. By carefully choosing the quality difference, the firm can effectively segment the market into two groups, those whose valuation is high and those whose valuation is low. The firm can then charge a high price to the former and a lower price to the latter, even after accounting for production and delivery cost differences. These may be among the most frequent instances of price discrimination.

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 card; senior citizens by presentation of an American Association of Retired Persons card or a driver'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 until 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.(8) Third-degree price discrimination is clearly "group discrimination."

The distinctions drawn between price discrimination of the varying degrees may seem arbitrary, but in fact these distinctions are important for two reasons. First, they are based on different information requirements for the seller. Second, the distinctions are important because the different types of discrimination have different implications for economic efficiency and income distribution. Principles textbooks frequently describe and show efficiency implications of only one type of discrimination (first degree) then follow with an example of a different type (third degree), as in Gwartney and Stroup (1995), Taylor (1995), Lipsey and Courant (1996), McConnell and Brue (1996), and Parkin (1996). Students are then likely to come away with mistaken impressions of the policy implications of price discrimination. 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.(9) The same texts, however, explain the efficiency effects of (this third-degree) price discrimination only in terms of first-degree (perfect) price discrimination. In addition to the efficiency differences that result from output restrictions that may occur across the different types of price discrimination, there are various inefficiencies that may result because not all consumers pay the same price for the product. Suppose consumer A can purchase additional units of the product at a price discount compared to consumer B. If B's willingness to pay for another unit is higher than that of A, there exist gains to be had from A buying at the low price and selling to B at a price below the price B faces but greater than the price A pays. Because resale is not possible, this represents an additional efficiency loss that occurs when consumers are separated into groups, as in second- and third-degree price discrimination. If the differences between the types of discrimination are not presented, then students may easily be confused into believing that second- and third-degree price discriminations are 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 environment have repercussions for economic efficiency and policy implications. With this as motivation, we now turn to a discussion of the conditions for price discrimination.

3. 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.(10) Even the slightest market power implies that the firm faces a negatively sloped demand curve for its product. Consequently, price discrimination can occur under both oligopoly and monopolistic competition, as well as pure monopoly. The downward sloping demand curve for the firms's 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 can control the sale of its product. 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. If a seller charges a higher per-unit price to large buyers than to small buyers, the firm must prevent multiple purchases at a low price by a single buyer, say, by imposing quantity limitations. 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 or in making multiple purchases.

A third requirement often cited for price discrimination is that consumers have different price elasticities of demand for the good or service. The extent to which the firm knows or correctly infers 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 to some identifiable group characteristic, then it can use third-degree price discrimination to induce the price-insensitive buyers to pay a high price and price-sensitive buyers to pay a low price for the good. This is third-degree price discrimination.

The informational requirements for the three types of price discrimination vary. Under first-degree price discrimination a great deal of information must be known about individual buyers. Second-degree price 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 quantifies of the good differentially or by attaching some other condition to the purchase of the good (tie-ins, for example), second-degree price discrimination induces the individuals to reveal to which class they belong. At the same time, second-degree price 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 sociodemographic trait. This characteristic separates this "group" for differential pricing.

Understanding the differential informational requirements, one can then examine how the differences influence economic efficiency, income distribution, and policy implications. We turn now to efficiency and distribution considerations.

4. Effects of Price Discrimination

Price discrimination affects efficiency and distribution, but the specific effects depend on the type of price discrimination practiced by the firm. Moreover, because the type of discrimination that is possible depends on the availability of information, the efficiency and distribution under price discrimination is linked to this availability of information. Regardless of the type of price discrimination, however, it is profitable for a firm to engage in this practice. This profitability arises from the seller extracting consumer surplus from the buyers that it could not get if it did not have market power and control over sale or resale and if buyers' price elasticities were identical.

The efficiency effects depend on the type of price discrimination practiced by the firm, and this depends on what the firm knows, or can learn, about the buyers' price elasticities. 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). In other words, when the firm has full and perfect information about consumer demands, then price discrimination improves efficiency. This added efficiency comes at the cost of transferring all the gains from trade from consumers to the firm.

Under third-degree price discrimination, the firm knows that identifiable groups have different price elasticities of demand. The firm does not know, however, the maximum willingness to pay of each member within each group. Therefore, the firm must select a single price for each group. Because each group faces a given price, and assuming the group's demand curve is downward sloping, the group members will derive consumer surplus from the purchase of this good that the firm cannot extract. Additionally, because the firm must select a single price for each group, it will select the price by equating marginal revenue to marginal cost. But because marginal revenue is less than price, there is allocative inefficiency. Relative to first-degree price discrimination then, third-degree price discrimination is less efficient but leaves consumers with some consumer surplus.

The exact efficiency effects under third-degree price discrimination depend on the shapes of the cost and demand curves. With straight-line demand curves and constant costs, as are typically found in Principles books, output does not increase over the level of the nondiscriminating firm.(11) Rather, relative to the nondiscriminating firm, the profit maximizing output is simply redistributed among consumers. 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 willingness to pay is lower. In other words, in this case, third-degree price discrimination is not only less efficient than first-degree price discrimination, it is also less efficient than no price discrimination (Schmalensee, 1981; Varian, 1985). However, social welfare may increase under third-degree price discrimination, over nondiscrimination, if output increases. Note that output increasing is a necessary condition for welfare to increase, not a sufficient condition. The intuition of this is straightforward. Inefficiency arises under nondiscrimination because price exceeds marginal cost - output is too low. If output rises under discrimination, then the inefficiency arising from producing too little output is reduced. At the same time, however, price discrimination puts a wedge between the marginal valuations of different consumers, which means that there are uncaptured gains from trade - an efficiency loss. Whether the gain in efficiency from increased output is sufficient to offset the loss in efficiency from the wedge between marginal valuations depends on the precise shapes of the cost and demand curves.

Table 1. Price Discrimination - Numerical Example

 Marginal Marginal
Quantity Revenue 1 Price 1 Revenue 2 Price 2

1 24.5 24.75 46 48
2 24 24.5 42 46
3 23.5 24.25 38 44
4 23 24 34 42
5 22.5 23.75 30 40
6 22 23.5 26 38
7 21.5 23.25 22 36
8 21 23 18 34
9 20.5 22.75 14 32
10 20 22.5 10 30
11 19.5 22.25 6 28
12 19 22 2 26
13 18.5 21.75 -2 24
14 18 21.5 -6 22
15 17.5 21.25 -10 20
16 17 21 -14 18
17 16.5 20.75 -18 16
18 16 20.5 -22 14
19 15.5 20.25 -26 12
20 15 20 -30 10

Demand in market 1: [Q.sub.1] = 100 - 4[P.sub.1]. Demand in market
2: [Q.sub.2] = 25 - 0.5[P.sub.2].

Table 1 provides a numerical example that clarifies the efficiency and distributional differences between first- and third-degree price discrimination, a nondiscriminating monopolist, and competition. The alternative outcomes are illustrated in Figure 1.(12) Assume that the marginal cost is constant at $20. In a perfectly competitive market, output is 35 units and price is $20 per unit - equal in value to marginal cost - each firm earns zero economic profit, and consumer surplus is $275. Consumers of type 1 get $50 of the consumer surplus, consumers of type 2 get $225. The nondiscriminating monopoly model would find a market price of $24, a total quantity of 17.5 units, and profit of $70. Consumer surplus is reduced to about $172.70, with consumers of type 1 getting $2.40 and consumers of type 2 getting $170.30. In this single-price monopoly case, the sum of profit and consumer surplus is $242.70, so the dead weight loss is $32.30.

The first-degree price discriminator would sell the first 12 units produced to buyers in market 2, where buyers are willing to pay more than are buyers from market 1. The firm sells in market 2 at prices starting at $48 for the first unit and declining to $26 for the 12th unit, before selling even the first unit in market 1. This is so because the price at which each of these first 12 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, who prices each unit individually, the market demand curve is the marginal revenue curve. The seller is thus able to extract all of the consumer surplus on each unit sold and earn a total profit of $275. The total sold by the first-degree discriminator is 35:20 to market 1 and 15 to market 2. Note that the price of the last unit sold in each market equals the marginal cost, [P.sub.1] = [P.sub.2] = MC = $20. Hence, the first-degree discriminator sells the efficient (competitive) quantity. Moreover, the price charged on the last unit sold is at or above the maximum any individual is willing to pay for another unit, so there are no uncaptured gains from trade between consumers. The firm captures all of the consumer surplus.

The third-degree price discriminator will sell a total of 17.5 units, just as in the nondiscriminating monopoly model. Because production is the same level as in the nondiscriminating monopoly, there is no reallocation of resources into the production of this good, as occurs with first-degree price discrimination, so allocative inefficiency continues. The third-degree discriminator divides this 17.5 units of output across the two markets, selling 10 units in market 1 at a price of $22.50/unit and 7.5 units in market 2 at a price of $35/unit, for a total profit of $137.50. This profit is less than could be made if the seller was a perfect price discriminator, but more than can be earned with no price discrimination at all. Consumer surplus is $68.75, with type 1 consumers getting $12.50 and type 2 consumers $56.25. The total of consumer surplus and profit in this case is $206.25. Note that the dead weight loss (= $68.75) has risen relative to the single-price monopoly situation. In addition, 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 the firm controls sale of the product, such exchanges do not occur.(13) For this reason, greater inefficiency occurs in the third-degree case than under the nondiscriminating 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, as might occur if marginal cost is upward sloping, efficiency may or may not be increased, depending on the gains from increased output compared to the losses from reallocation of output from low-valued to high-valued consumers (Schmalensee 1981; Varian 1985).(14)

The efficiency of second-degree price discrimination, relative to nondiscrimination, depends on whether output increases and on the losses incurred from introducing different marginal valuations across consumers. This efficiency will also depend on what type of second-degree discrimination is possible. Consider two examples. In the first example, firms allow consumers to select between different two-part tariff schemes. In the second example, firms use quantity discounts.

The first example is similar to memberships in warehouse shopping clubs. The consumer can join with one of two different types of membership. Under the less expensive membership, posted prices are not discounted, whereas under the more expensive membership, posted prices are discounted at 10%. By selecting a membership, consumers reveal information about their demand - information that the firm would not have had otherwise. The membership fees transfer consumer surplus to the firm. The differential pricing induces inefficiency by creating a gap between the marginal valuations of different consumers. Under this scheme, it seems probable that sales are increased. Output will increase if the undiscounted prices are not too much higher and the discounted prices are sufficiently lower than the nondiscriminatory prices. But if the prices faced by those holding low-valued memberships are not lower than the nondiscriminatory prices, which may still be available at other nonwarehouse stores, then it is unclear why anyone would buy these memberships. Therefore, it seems likely that price under either membership plan will be lower than under nondiscrimination and that output will increase. However, output is not likely to rise to the competitive level. If the discounted prices equal marginal cost, then the firm sells to the holders of high-priced memberships the same quantity they would purchase under competition. But the holders of the low-priced memberships face a price higher than marginal cost, so they will purchase fewer units than under competition. Sales fall short of the competitive level. In other words, this type of second-degree price discrimination may be more efficient than nondiscrimination but is certainly less efficient than either competition or first-degree discrimination. This type of discrimination also enables firms to capture a large measure of the consumer surplus - certainly more than under nondiscrimination, although whether more than under third-degree discrimination is not generally determinable.

The second example of second-degree price discrimination is the case of quantity discounts. 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, although it still falls short of the competitive output, unless those facing the higher price would not have purchased any additional units at the lower price. At the same time, because not all consumers pay the same price for the product, there remain uncaptured gains from trade - an efficiency loss. 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. However, under this scheme the firm is unable to capture consumer surplus that consumers derive from purchases at these prices, unlike the two-part tariff example. This type of second-degree price discrimination is, therefore, more akin to third- than to first-degree price discrimination.

Generally then, the efficiency and distributional effects of second-degree price discrimination, relative to the pure monopoly situation, depend on a number of factors. First, the shapes of the cost and demand curves are important. Steeply rising marginal cost, for example, implies smaller dead weight loss in the pure monopoly situation, all other things constant, than in the constant marginal cost case. In this case, the difference between the pure monopoly price and the competitive price is small, so the gap between the willingness of high-value and of low-value consumers to pay is likely to be small. Therefore, price differentials would tend to cause relatively little inefficiency, arising from the lack of resale possibilities. The increased net benefit from increasing output would, therefore, tend to raise overall efficiency.

Second, the effects will vary with the specific second-degree price discrimination strategy the seller employs. Which strategy is appropriate will depend on the nature of the good and the number and closeness of substitutes for it. For example, in the two-part tariff case, the consumer generally has few opportunities to decide to purchase the good, and there are few close substitutes. The permanent seat license (PSL) pricing scheme used by professional sports teams is a good example. Few cities have multiple franchises in any given sport, so there are few substitutes. Season ticket purchases are rare, made only once every year in the absence of PSLs and only once a lifetime with PSLs. Given the lack of substitutes, lumpiness of the good, and infrequent purchases, the firm can use the two-part tariff scheme. Not too many years ago, long distance telephone service would have been a similar example. Consumers generally selected a long distance carrier once. Now, the competition among long distance services can have consumers changing carriers frequently, with the fee portion of the two-part tariff approaching zero for most customers.(15) In effect, the two-part tariff works well when the choice the consumer faces is between being able to purchase the good and not being able to purchase it and there are no close substitutes for the good.

Quantity discounts as a pricing scheme works well when there are close substitutes for the good and consumers make repeated purchases. Frequent flyer plans are a good example. There are several airlines from which to choose, and those who travel by plane often do so several times a year. The consumer has several opportunities to choose, or not choose, any given airline. Quantity discounts provide the consumer an added incentive to choose the same airline each time.

5. Concluding remarks

We began this paper with a criticism of the style and approach of teaching price discrimination found in Principles texts. In this section, we propose a method for presenting price discrimination that would spark student interest in the application of economic theory to policy and, at the same time, create the least confusion possible.

(i) Price discrimination can be defined in a more general way as a variation in the price-cost ratio, or differentials, across units or across groups of buyers. The advantages of this definition are, first, that it is more accurate and, second, that it encompasses alternative forms that price discrimination may take. This definition thus incorporates examples of multiple pricing when costs do not differ (such as selling the identical vehicle to two different buyers at two different prices), and single pricing when costs do differ (such as shipping the same good to two different buyers at different locations and cost but at the same delivered price).

(ii) Provide information about the three necessary conditions for price discrimination to occur.

(iii) Explain that there are three types of price discrimination and that the type of discrimination that occurs depends upon the level of information held by firms.

(iv) Emphasize that the different types of price discrimination have different implications for economic efficiency. One way to do this is through a numerical example in the form of a table or diagram, as presented here. In addition, use of the diagram or table emphasizes the important differences between the competitive outcome, the monopoly outcome, and the outcomes of the different types (degrees) of price discrimination. Moreover, the numerical example can be used to discuss the inefficiency of third-degree discrimination that arises when buyers pay different prices for the marginal unit purchased.

(v) Address issues of distribution, particularly since the price-discriminating firm gains profit by acquiring surplus from consumers. This also can be illustrated through a numerical example, as we have shown here.

(vi) Discuss the practical difficulties of identifying price discrimination. Students should be made aware of the importance of price differences that are not explained by cost differences, the role of opportunity cost, and the important issues of market definition.

Price discrimination is complex. Often, in the attempt to simplify, the.explanation actually provides misleading or incorrect information. We believe, however, that price discrimination can be presented at the introductory and intermediate levels in a way that is correct, yet simpler and less confusing than we currently observe, so that students are not faced with misleading information.

It is clearly inappropriate to attribute the practice of differential pricing to monopoly; price discrimination may arise in any market in which firms are not price takers and they therefore have even a small amount of market power. 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.

The treatment of price discrimination is less misleading if it is presented as both 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 to help students understand the meaning of social efficiency and the distinction between efficiency and distribution.

Examples of price discrimination are pedagogically helpful. Students like them and they have most likely had some experience with many of them. Providing examples classified according to price discrimination by unit (first and second degree), and price discrimination by consumer group (third degree) would be consistent with presentation of theory as we outline above, and clearer to students.

Many students do not fully understand the concept of efficiency as social efficiency. 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. Although this profitable behavior may be "efficient" for the firm (i.e., privately efficient) it is not socially efficient. Discussion of price discrimination is a good opportunity to make this distinction.

Appendix

Note: All results are rounded.

Given: Demand of type 1 buyers: [Q.sub.1] = 100 - 4[P.sub.1]

Demand of type 2 buyers: [Q.sub.2] - 25 - 0.5[P.sub.2]

Long-run supply (S) = marginal cost = $20

1. Perfectly competitive market

Single demand:

[Q.sub.T] = [Q.sub.1] + [Q.sub.2] = (100 - 4[P.sub.1]) + (25 - 0.5[P.sub.2]) = 125 - 4.5P

Therefore, inverted demand (D):

P = 27.8 - 0.224[Q.sub.T] and MR = 27.8 - 0.448[Q.sub.T]

Perfectly competitive equilibrium:

D = S

27.8 - 0.224[Q.sub.T] = 20

[Q.sub.T] = 35

[P.sub.c] = $20

Profit = 0

Consumer surplus = $275

Dead weight loss = 0

Note that, with constant costs, economic profit for each firm is also zero.

2. Nondiscriminating firm with market power

Demand:

[Q.sub.T] = [Q.sub.1] + [Q.sub.2] = (100- 4[P.sub.1] + (25 - 0.5[P.sub.2]) = 125 - 4.5P

Therefore, inverted demand (D):

P = 27.8 - 0.224[Q.sub.T] and MR = 27.8 - 0.448[Q.sub.T]

Nondiscriminating equilibrium:

MR = MC

27.8 - 0.448[Q.sub.T] = 20

[Q.sub.ND] = 17.5

[P.sub.ND] = $24

Profit of nondiscriminating firm = $70

Consumer surplus = $172.70

Dead weight loss = $32.30

3. First-degree (perfect)price discrimination

Demand:

[Q.sub.T] = [Q.sub.T] + [Q.sub.2] = (100 - 4[P.sub.1] + (25 - 0.5[P.sub.2]) = 125 - 4.5P

Therefore, inverted demand (D):

P = 27.8 - 0.224[Q.sub.T] = [MR.sub.1stPD]

Perfect price-discriminating firm equilibrium:

[MR.sub.1stPD] = MC

27.8 - 0.224[Q.sub.T] = 20

[Q.sub.1stPD] = 35

Profit for first-degree price-discriminating firm = $275.25 (= total consumer surplus)

Consumer surplus = 0

Dead weight loss = 0

4. Third-degree price discrimination

Demand of type 1 buyers: [Q.sub.1] = 100 - 4[P.sub.1]

Demand of type 2 buyers: [Q.sub.2] = 25 - 0.5[P.sub.2]

Inverted demand ([D.sub.1]): [P.sub.1] = 25 - 0.25[Q.sub.1][MR.sub.1] = 25 - 0.5[Q.sub.1]

Inverted demand ([D.sub.2]): [P.sub.2] = 50 - 2[Q.sub.2] [MR.sub.2] = 50 - 4[Q.sub.2]

Third-degree price-discriminating equilibrium by buyer type:

[MR.sub.1] = MC [MR.sub.2] = MC

25 - 0.5[Q.sub.1] = 20 50 - 4[Q.sub.2] = 20

[Q.sub.1] = 10 [Q.sub.2] = 7.5

[P.sub.1] = $22.50 [P.sub.2] = $35

Consumer surplus (C[S.sub.1]) = $12.50

Consumer surplus ([CS.sub.2]) = $56.25

Note that [Q.sub.1] + [Q.sub.2] = 17.5 = [Q.sub.M] and that total consumer surplus = $68.75

Profit for third-degree discriminating firm:

[TR.sub.1] = $225 [TR.sub.2] = $262.50

Total cost of all output (TC) = $20(17.5) = $350

[Profit.sub.3rdPD] = [TR.sub.1] + [TR.sub.2] = TC = $225 + $262.50 - $350 = $137.50 [greater than] [Profit.sub.ND] = $70

Dead weight loss ([DWL.sub.3rdPD]) = $68.75 [greater than] ([DWL.sub.ND]) = $32.30

Note also that [Profit.sub.3rdPD] = $137.50 [less than] [Profit.sub.1stPD] = $275.25

The authors thank Michael Bradley, Jonathan Hamilton, and an anonymous referee for helpful comments on an earlier draft of the paper.

1 Scherer and Ross (1990), Shepherd (1997), and Shugart (1997) each use this definition of price discrimination. In addition, Viscusi et al. (1992) define price discrimination this way in their text on regulation and antitrust. An alternative definition of price discrimination compares the difference between the price and the marginal cost of a good across buyers or units of the good. If this difference is measured as a proportion of the sale price, then the resulting value is the Lerner index. Both this definition of price discrimination and the one stated in the text may be overly restrictive. Carlton and Perloff (1994) use the term more broadly to include any pricing scheme in which the firm is able to increase its profit over that earned from a single price. These schemes raise profits because they enable the firm to charge more to consumers who are willing to pay more and charge less to consumers who value the product less.

2 It is in more complex pricing situations such as this that the broader definition of price discrimination suggested by Carlton and Perloff (1994) may be appropriate.

3 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.

4 This situation is much like the "personal discrimination" of Machlup (1952) and Shepherd (1990) because the seller must know or be able to learn very specific information about every consumer to be able to set the highest attainable price on every unit.

5 Many authors have questioned the accuracy of Niskanen's (197 l) assumptions with regard to the power and information available to Congress and the bureaus.

6 It is important to note that some discounts arise because the costs per unit of large-volume transactions are smaller than those from small-volume transactions. Such cases are not instances of price discrimination.

7 Interestingly, Shepherd (1990) includes the case of charging heavy users more for the product as a type of second-degree price discrimination.

8 These examples beg the question of whether the goods are really identical. We defer discussion of this point to section 3.

9 Recall that this is one of the examples in Lott and Roberts (1991). Their argument is that the different prices faced by different travelers may reflect cost differences and, therefore, are not necessarily evidence of price discrimination.

10 In monopolistically competitive markets, firms compete not on price but other concerns such as quality, accessibility, or service. These firms are not price takers, however. Therefore, we describe them as having some market power.

11 Lipsey and Courant (1996, p. 230), after defining price discrimination where a "seller can either distinguish individual units bought by a single buyer or separate buyers into classes . . .," state as a proposition that "output under price discrimination will generally be larger than under single-price monopoly" (p. 231). Students in an introductory course, where straight-line demand curves and constant costs are employed (as in the Lipsey and Courant text) would then believe that all types of price discrimination are efficient.

12 Algebraic solutions to this problem are presented in the appendix.

13 We are indebted to our colleague Mike Bradley for suggesting antiscalping laws as an example in which gains from trade are not captured because resale is impossible. This effect is strengthened when the firm controls sale by limiting quantities to any one original buyer.

14 In our example, where marginal cost is constant, output does not increase with third-degree price discrimination.

15 There are costs associated with switching carriers, although in some cases, these may be avoided. One of the authors recently changed from ATT to MCI and hack to ATT in less than two weeks, getting no monthly fee and 30 minutes of free long distance service per month for six months. The companies even provided vouchers for the switching costs.

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