Price discrimination and efficient distribution.

Beard, T. Randolph ; Blair, Roger D. ; Kaserman, David L. 等

1. Introduction

Economists have long warned of the danger that, on occasion, antitrust enforcement might be used perversely to protect competitors at the expense of competition. (1) Moreover, one of the most likely suspects for this charge has traditionally been Section 2 of the Clayton Act, as amended by the Robinson-Patman Act--namely the law on price discrimination. (2) Specifically, while the language of the Act proscribes discriminatory prices only "... where the effect ... may be substantially to lessen competition or tend to create a monopoly," judicial interpretation of the Act, as well as some other language contained in it, have resulted in a substantial weakening of that requirement. (3) As a result, there have been a number of cases in which the law appears to have been used to protect firms from aggressive but selective price cutting by either input suppliers or rival producers. Accordingly, many antitrust scholars have been particularly critical of both the law and enforcement practices in this area. (4)

We believe that an important reason for this flawed public policy is the paucity of applicable economic theories involving price discrimination by intermediate product suppliers. As Katz (1987, pp. 154-5) points out, the bulk of the theoretical work on price discrimination has focused upon final product markets, while the vast majority of antitrust cases have involved intermediate goods. In fact, to our knowledge, only a handful of formal models have been introduced that treat discriminatory pricing by an input supplier, most notably those of Perry (1978), Katz (1987), and DeGraba (1990). These models either incorporate incentives for vertical integration or find price discrimination in favor of inefficient downstream firms, both of which tend to limit their relevancy in many real-word cases. (5)

Also, while some economists instinctively believe that some (perhaps most) price discrimination is motivated by procompetitive efficiency considerations, none of the existing theories provide an unambiguous efficiency-based explanation for the practice. All models introduced to date--that apply to either intermediate or final product markets--indicate either a negative or an a priori indeterminate welfare effect. As a result, policymakers and the courts are left with an uneasy suspicion of the practice. And that suspicion is magnified by the lack of a better overall understanding of the observed behavior. As both Coase (1972) and Williamson (1979) note, incomplete understanding of a business practice often results in antagonism toward that practice in antitrust circles. (6)

Here, we offer a theory of upstream price discrimination that potentially yields relatively strong conclusions regarding the likely impact on efficiency at the downstream (distribution) stage. Specifically, under the assumed conditions, price discrimination is shown to be both profitable upstream and efficiency improving downstream. Thus, such discrimination has an unambiguously positive effect on social welfare. Moreover, our theory appears to be consistent with the facts in several important secondary-line cases in which price discrimination has been alleged against an input supplier and, we believe, incorrectly judged to have significant anticompetitive effects.

The article is organized as follows. Section 2 lays out the model and establishes the central welfare results. Section 3 briefly discusses our results and draws some policy implications. Section 4 provides a brief review of some antitrust cases to which our model seems to apply, and section 5 concludes.

2. The Model

The basic economic process we seek to model here is the following. An upstream firm (manufacturer or wholesaler) with some, perhaps limited, market power sells its output to a set of downstream firms (distributors or retailers) that compete in the final product market. (7) Production at the downstream stage involves a fixed, one-to-one input-output ratio. That is, the downstream firms merely distribute or resell the upstream firm's product. (8)

Two types of firms are assumed to be present in the downstream market: relatively efficient and relatively inefficient firms. We will generally use a subscript of "e" to denote the efficient firms and a subscript of "i" to denote the inefficient firms. By "efficient" we simply mean that the firms so labeled experience a comparatively lower cost of transforming the upstream, intermediate product into the final good. As a result of these cost differences, there exist corresponding final output price differences at the downstream stage. These downstream prices will be denoted by [P.sub.e] and [P.sub.i].

We imagine a downstream retail sector in which some degree of price variation between efficient and inefficient retailers is possible because search or switching by consumers is costly. At this stage, we will leave unspecified the effects of wholesale prices ([w.sub.e] and [w.sub.i]) on the degree of consumer search or switching and on the (equilibrium) numbers and frequencies of efficient versus inefficient firms. These issues are important, and we will have more to say about them later. For now, we assume that some fraction ([pi]) of buyers patronizes the efficient retailers, and the remaining fraction of buyers (1--[pi]) patronizes the inefficient retailers.

The retail stage is assumed to be competitive, so that the final output prices of retailers are equal to marginal costs. We normalize the marginal cost of efficient retailers to zero and denote the marginal cost of inefficient retailers using "c." The downstream prices faced by consumers are [P.sub.e] = [w.sub.e] in the efficient markets and [P.sub.i] = [w.sub.i] + c in the inefficient markets. The consumer demand for the good, denoted by D(P), is generally assumed to depend only on the relevant final price. Hence, the consumer demand faced by the efficient retailers is [pi]D(Pe), and the demand faced by the inefficient retailers is (1--[pi])D([P.sub.i]).

We will also make the simplifying assumption that the demand function is linear. The assumption of linearity will make the presentation very concise and will also allow us to relate some of the results to the notable findings of Robinson (1933), and later Schmalensee (1981), Varian (1985), and Layson (1988). (9) However, it should be noted that for small price changes, all smooth demand curves are well approximated by a linear function. The case of small efficiency differentials could, therefore, lean quite heavily on the analysis of linear functions. In order to ensure positive demand at key price levels in our analysis, we also generally assume that demand is still positive at the sum of the efficient monopoly price and the marginal cost of the inefficient retailers. (10)

We begin the analysis with a benchmark case roughly corresponding to that described in Katz (1987). Suppose initially that [pi] (the fraction of buyers in the efficient market) is invariant to the retail prices. Normalizing the marginal costs of the upstream firm to zero, the optimal wholesale prices

[w.sup.*.sub.e], [w.sup.*.sub.i] are defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

The first-order conditions and the linear demand curve immediately yield the following result:

[w.sup.*.sub.i] = [w.sup.*.sub.i] - c/2 (2)

In other words, the efficient retailer is charged more than the inefficient retailer; although, the difference must be less than the amount of the cost inefficiency (e). Another implication is that the retail price at inefficient stores ([P.sup.*.sub.i] = [w.sup.*.sub.i] + c) must exceed the price at the efficient vendors. This price discrimination in favor of the inefficient firm mirrors Katz (1987, Proposition 4) and DeGraba (1990) and generally corresponds to the conventional wisdom concerning price discriminating intermediate good monopolists.

We next define the profit-maximizing uniform (non-discriminatory) wholesale price, [w.sup.*]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII](3)

Combining the first-order conditions associated with Equations 1 and 3 together with the convex properties of linear functions will quickly lead one to the following characterization (11) of the optimal uniform wholesale price:

LEMMA 1. [w.sup.*]([pi])=[pi][w.sup.*.sub.e] + (1- [pi])[w.sup.*.sub.i], for any [pi] [member of] [0, 1].

Lemma 1 immediately yields the famous result attributed to Pigou (1920) that with linear demands, third-degree price discrimination produces no change in output compared to uniform monopoly pricing.(12) In turn, this result also illustrates that legal restrictions that impose uniform wholesale prices (for example, the Robinson-Patman Act) are welfare improving, given our current set of assumptions. To see this, define social welfare, SS([w.sub.e], [w.sub.i], [pi]), as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

THEOREM 1. SS([w.sup.*],[w.sup.*], [pi])> SS([w.sup.*],[w.sup.*],[pi]), for any [pi] [member of] (0, 1).

Proof Combining Lemma 1 and the properties of a linear function, note that

[pi]D([w.sup.*]) + (1 - [pi])D([w.sup.*] + c) = [pi]D([w.sup.*.sub.e]) + (1 -- [pi])D([w.sup.*sub.i] + c).

Using this fact, SS([w.sup.*], [w.sup.*], [pi]) - SS([w.sup.*], [w.sup.*.sub.i], [pi]) equals

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Since the demand function is decreasing, both integrals must be positive. Hence, we have that SS([[w.sup.*],[w.sup.*],[pi]) - SS([w.sup.*.sub.e], [w.sup.*.sub.i], [pi]) > O.

Theorem 1 establishes the desirable welfare credentials of the Robinson-Patman Act when [pi], the frequency of consumer patronage of efficient sellers, is invariant to prices. (13) This conclusion depends crucially on the assumption of an invariant distribution of customers across retail firm types. As we will argue, if the distribution of customers is allowed to vary in relation to the prices set by the downstream firms, then the imposition of uniform wholesale pricing can instead diminish social welfare. To demonstrate this result, we define the efficient firms' market share, [pi], to be an (increasing) function of the price differential between the inefficient and the efficient downstream firms.

A1. [pi]: R [right arrow] [0, 1] and there exists s > c such that [pi]([P.sub.i] - [P.sub.e]) = 1 if and only if([P.sub.i]- [P.sub.e]) [greater than or equal to] S. This assumption holds that when the price difference between inefficient and efficient retailers is sufficiently large, then the frequency of buyers patronizing the inefficient retailer will fall to zero. Assumption A1 is somewhat stronger than we require, but it allows the primary welfare result to be obtained in a very straightforward fashion. Given that the distribution of consumers is now endogenous, the upstream firm's optimal pricing vector ([[??].sup.*.sub.e], [[??].sup.*.sub.i]) is defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

We note that, under A1, the upstream firm's optimal pricing vector, ([[??].sup.*.sub.e], [[??].sup.*.sub.i]), will clearly equal ([w.sup.*], [w.sup.*.sub.e] + (s-c)). (14) In other words, the upstream firm will mark up the wholesale price to the inefficient firms sufficiently to shift all consumers to the efficient vendors. (15) The upstream firm can then charge its optimal monopoly price ([w.sup.*.sub.e]) to the entire consumer population via the efficient vendors. This is clearly an ideal situation for the upstream firm, and the firm would necessarily suffer reduced profits if a uniform pricing restriction were imposed. The welfare implications of uniform pricing on consumers and society as a whole, however, are slightly more complicated questions, which we now address.

If a uniform wholesale pricing rule were imposed on the upstream firm, then the final product price gap between the efficient and inefficient firms would be constrained to the cost inefficiency: that is, ([P.sub.i] - [P.sub.e]) = c. The distribution of consumers would therefore equal [pi](c), which we denote by [[pi].sub.c].

The optimal uniform wholesale price would be defined by Equation 3 with [pi] = [[pi].sub.c]. We denote this optimal uniform wholesale price by [w.sup.*.sub.c] = [w.sup.*] (no). Imposing uniform wholesale prices would lower the price in the efficient market and thus increase consumer surplus. However, the increase in retail prices for consumers in the inefficient market will result in a decrease in consumer surplus. We will argue in Theorem 2 that the decrease in surplus for consumers in the inefficient market is greater in magnitude than the gain for consumers in the efficient market. Hence, uniform pricing will not only reduce producer surplus, it will also reduce consumer surplus. Social surplus (as defined in Eqn. 4) would, therefore, unambiguously decline as a result of uniform wholesale pricing.

THEOREM 2. If assumption A1 holds, then SS([[??].sup.*.sub.e], [[??].sup.*.sub.i],1)>SS([w.sup.*.sub.c],[w.sup.*.sub.c]], [[pi].sub.c]).

PROOF. Start by noting the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The bracketed term on the left is just a weighted average of profits, both of which are less Than [w.sup.*.sub.c]D([w.sup.*.sub.e), Firm profits will clearly be higher if the consumers are shifted into the efficient marketplace. We will now argue that consumer surplus also increases.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Note that the linear structure of demand implies [[integral].sup.b.sub.a] D(w)dw = (b-a) 1/2 + D(a)+D(b)]. Thus,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Combining Lemma 1 and Equation 2 with [pi] = [[pi].sub.c] yields

[w.sup.*.sub.e] - [w.sup.*.sub.c] = (1 - [[pi].sub.c]) c/2

Hence,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Note that the linear demand structure implies [D([w.sup.*])+D([w.sup.*.sub.c]] + c)] = [D([w.sup.*.sub.e]] + c)+D([w.sup.*.sub.c])]. We are left with

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

By assumption in footnote 10, D([w.sup.*.sub.e]+c)>O, and since [w.sup.*.sub.c]] < [w.sup.*.sub.e], we also have that [D([w.sup.*]) - [[pi].sub.c]D([w.sup.*.sub.e]) > 0. Consumer surplus is therefore greater with wholesale price discrimination. We are left with the conclusion that SS([[??].sup.*.sub.e], [[??].sup.*.sub.i], 1)>SS([w.sup.*.sub.c],[w.sup.*.sub.c][[pi].sub.c]).

3. Discussion

Theorem 2 establishes our main welfare finding: Legal restrictions, such as the RobinsonPatman Act and state-level variants of it, that require uniform wholesale prices when retailers vary in efficiency can reduce social welfare. Such restrictions preclude the upstream manufacturer from engaging in useful strategies of price discrimination against inefficient downstream retailers. The beneficial aspects of the discriminatory prices in this model arise entirely from the impact that such prices have on the structure (and thereby the efficiency) of the downstream market. Discrimination against the inefficient vendors causes the market share of the efficient firms to increase. In turn, that shift in market shares improves the overall efficiency of the downstream stage, thereby increasing social surplus.

One potential weakness in our analysis is the absence of explicit switching costs experienced by consumers. We assumed that if the price difference were sufficiently large, then all of the customers of the inefficient retailer would switch to the efficient retailers without experiencing any sort of cost or loss of utility. This assumption allowed us to make a very clean and strong point regarding the potential negative welfare implications of uniform wholesale pricing. If there were literally no switching costs, however, one would expect consumers in the inefficient market to switch to the efficient retailers given any retail price differential, including the price differential arising from uniform wholesale pricing. We will address this important point and illustrate the results of the prior section by means of an example.

The combined gain in surplus outlined in Theorem 2 can be sufficiently large that explicit switching costs can be imposed on consumers that are large enough to deter switching for a price differential equal to the retail cost differential but that still yield an increase in social surplus when wholesalers are allowed to discriminate against inefficient retailers (inducing consumer switching). Consider a simple linear (aggregate) demand curve, given by D(p) = 50 -p, and assume that the marketplace is currently split evenly (50-50) between efficient and inefficient retailers. Let marginal costs equal zero for the efficient retailers and c = 4 for the inefficient retailers. The consumers currently in the inefficient market experience a switching cost of $124 (per unit of mass) because they prefer the overall shopping experience provided by the inefficient retailers. (17)

The optimal uniform wholesale price (defined in Eqn. 3 with [pi] = 0.5) for our example is [w.sup.*] = $24. Hence, the efficient price is $24, the inefficient price is $28, the efficient quantity is 26 (per unit of mass), and the inefficient quantity is 22 (per unit of mass). The wholesale firm profit is $576, the consumer surplus is $290, and the social surplus is $866. Notice that the 50% of consumers in the inefficient market will not switch because the utility gain would be only $96 (per unit of mass), while the cost is assumed to be $124 (per unit of mass). (18) If the wholesale firm is allowed to price discriminate, then it will charge $25 to the efficient firms and (approximately) $27 to the inefficient firms. The resulting $6 retail price differential will induce switching ($132 gain vs. $124 cost), and 100% of consumers will purchase from the efficient retailers. This results in a firm profit of $625, consumer surplus (net of switching costs) (19) of $250.50, and an aggregate surplus of $875.50. The aggregate social surplus is clearly higher when wholesale price discrimination is allowed.

It should be noted that the pattern of price differences exhibited here--with the efficient downstream firms receiving the lower price--is the opposite of the ordering obtained in Lemma 1 and under the frameworks of Katz (1987) and DeGraba (1990). (20) This point is critical because several important cases, most notably the Morton Salt and the Hasbrouck cases, which are discussed in the next section, have involved secondary-line price discrimination in favor of the efficient downstream firms. Yet, both of these cases were decided in favor of the plaintiffs. The Robinson-Patman Act contains a cost justification defense. If a price differential reflects the difference in the costs of dealing with the disfavored party, there is no liability for the seller. This defense would not work here, however, because the cost differences that we have analyzed arise at the retail stage, rather than at the wholesale stage.

A few theoretical notes concerning our results should also be mentioned. First, differences in demands for buyers patronizing different types of retailers could certainly affect the conclusions, but the impacts will depend on whether the demands are inherently larger or smaller (or more or less elastic) between vendor types. Second, note that the linearity of the underlying demands is not absolutely necessary, although it certainly simplifies the presentation. Our results could potentially extend to the use of nonlinear base demand functions (D) for a relatively small efficiency differential. The parameterization of the degree of asymmetry by the efficiency differential (c) allows the welfare analysis to be localized. The linear properties of the underlying demand structure are not, in fact, utilized in the proof of Theorem 2 until the welfare integrals have been reduced to the interval ([w.sup.*.sub.c], [w.sup.*.sub.c] + c) Hence, nonlinearities outside this interval are of little concern, and if this interval is small, then the demand function's properties are approximately linear. There is not, however, likely to be any generalization of the overall analysis to arbitrarily large differentials and nonlinearities. (21)

Next, we have largely ignored the issue of the connection between [pi] and the number of retailers of different types. This is acceptable in the limited sense that we have already ignored retailer profits entirely by asserting that they are always competed away to zero. Thus, the change in market structure at the retail stage is assumed to have no (long-run) welfare consequences. Certainly it would be difficult to maintain that losses incurred by inefficient vendors upon exit should deter society from allowing their demise. But it is not inconceivable that in some broader analytic framework such an effect could matter. That complication, though, would take us far away from the tradition of Robinson (1933), Schmalensee (1981), Varian (1985), Katz (1987), Layson (1988), DeGraba (1990), and Kaftal and Pal (2008).

While our model focuses on a strategy of simple third-degree price discrimination, it would appear that equivalent results could be obtained through a variety of alternative vertical control mechanisms. For example, discriminatory promotional allowances, rebate programs, quantity discounts, or a simple refusal to deal could all be used to favor the relatively efficient downstream firms, with broadly equivalent efficiency consequences. To the extent that antitrust enforcement policies fail to treat these alternative strategies equally, manufacturers' choices among them will be biased. (22)

Congress recognized that there was "more than one way to skin a cat." As a result, various provisions of the Robinson-Patman Act deal with efforts to disguise price discrimination. (23) Promotional allowances and rebate programs clearly influence the net price paid without affecting the nominal list price. In order to avoid charges of price discrimination, allowances and rebates must be made available to all customers on proportionately equal terms. For example, suppose Firm A buys 10,000 cases per month and receives a promotional allowance of $1000. If Finn B buys 1000 cases per month, it must receive a $100 promotional allowance for the seller to avoid liability. Even quantity discounts are vulnerable if they are not realistically available to all customers.

As a general proposition, a manufacturer has a fight to deal or to refuse to deal with whomever it chooses. In the context of our model, the manufacturer might refuse to deal with inefficient retailers by simply refusing to fill orders from those customers. No doubt these firms will complain because this refusal diminishes their business. They might file suit under the Sherman Act. (24) Success depends upon the plaintiff being able to prove that the refusal to deal was anticompetitive. Under the assumed conditions in our model, however, no anticompetitive effect could be shown since a shift in volume toward the more efficient distributors would result in lower prices and higher quantities. This is obviously procompetitive. In other words, there is a valid business justification for the refusal, and therefore, there will in principle be no antitrust liability.

Another way of enhancing efficiency at the retail stage is to impose maximum resale prices. The manufacturer could set the maximum resale price equal to the price that an efficient retailer would charge in a competitive environment. The inefficient firms will not be able to stay in business at the prescribed maximum price. Although the inefficient firms may stay in business during the short run, they will not survive in the long run. This vertical price control is now unlikely to violate the antitrust laws; although, that was not always true.

In its Albrecht decision, the Supreme Court in 1968 made maximum resale price fixingper se illegal under the Sherman Act. (25) Such vertical price restraints arise almost invariably under successive monopoly conditions as a means of preventing double marginalization. This, of course, leads to lower prices and higher outputs, which clearly improve social welfare. For nearly 20 years, Albrecht's per se prohibition received unrelenting criticism. Finally, in its Khan decision, the Supreme Court specifically overruled Albrecht. (26) Now, maximum resale price restraints are accorded rule-of-reason treatment. A successful plaintiff must therefore prove that the maximum resale price restraint reduced competition. This is virtually impossible, and therefore, such restraints should not be vulnerable under the antitrust laws.

Finally, it is clear that the classic alternative to vertical control, the merging of the upstream and downstream retailers, is a feasible, if unattractive, solution. Such an approach is likely to be extremely costly, and it is difficult to see such a combination as a socially or privately efficient solution to inefficient retailing. In particular, the source of the inefficiency is not obviously eliminated by a mere change in ownership.

It is also worth noting that the welfare-improving effects we have shown arise entirely within the market for the single upstream firm's product. To the extent that the final product market consists of a number of competing but differentiated brands of the same good, these positive effects could be magnified. That is, where the final good market encompasses multiple brands that are viewed as imperfect substitutes by consumers, the resulting increase in the efficiency of one brand's distribution system appears likely to intensify competition among the competing brands. Consequently, the traditional tradeoff between intrabrand and interbrand competition may not exist here. Rather, both are enhanced by the manufacturer's price discrimination against the less efficient retailers.

Turning to policy issues, the U.S. law on price discrimination provides an exemption for observed price differences that are fully accounted for by differences in the upstream firm's costs of supplying its different customers. (27) Our results here indicate the need for a complementary principle--that is, price discrimination should be permitted when there exist cost differences at the downstream stage. In particular, where such discrimination is undertaken in order to improve the efficiency of the retail stage, antitrust exemption is warranted.

4. From Morton Salt to Volvo--The Law on Secondary-Line Competitive Injury

Under the conditions analyzed above, price discrimination promotes efficiency and, therefore, should be applauded by the antitrust authorities. The Robinson-Patman Act, however, has often led to the opposite response. Specifically, when a supplier sells the same good to two different buyers at different prices, the resultant price difference is viewed as prima facie evidence of illegal price discrimination. Moreover, this presumptive interpretation has evolved despite the Act's explicit requirement that plaintiffs demonstrate the likelihood of a substantial lessening of competition. That is, the language of the statute requires proof of competitive injury or at least a reasonable probability of such injury. (28) level, it is said to be "secondary-line" injury. In primary-line cases, plaintiffs must now prove that the discriminatory price was predatory. See Brooke Group Ltd. v. Brown & Williamson Tobacco Corp., 509 U.S. 209 (1993). Our analysis, however, applies to secondary-line cases.

As a result of judicial interpretations of the statute over time, it has become alarmingly easy to prove "competitive injury," which is, in fact, a misnomer, since the injury in question may have nothing to do with competition. Specifically, in secondary-line cases, a successful plaintiff need only show that a price difference existed and that it competed for sales with the favored buyer. (29) Assuming that the disfavored buyer can meet these prerequisite requirements, competitive injury can then be proved with evidence of actual lost sales. Thus, in this area, the judiciary has confused injury to competition with injury to a competitor. (30)

Perhaps more alarming is the fact that, under existing law, competitive injury may be inferred from the mere existence of persistent, substantial price discrimination. This view is generally attributed to the Morton Salt case. (31) There, the Federal Trade Commission complained about the quantity discount schedule that Morton Salt had made available to its customers. Under that schedule, wholesale prices fell from $1.60 to $1.35 per case, depending upon the volume purchased. The Court was concerned about the fact that, under this schedule, only five customers ever qualified for the lowest price. These five customers, of course, were large chain-store retailers. In its Opinion, the Court observed that "[a]s a result of this low price, these five companies have been able to sell Blue Label salt at retail cheaper than wholesale purchasers from [Morton Salt] could reasonably sell the same brand of salt to independently operated retail stores, many of whom competed with the local outlets of the five chain stores."32 The Court then went on to say that the government did not have to prove actual competitive injury. Instead, competitive injury could be inferred from the mere presence of discriminatory prices. (33)

In Morton Salt, the five largest customers were supermarket chains: A&P, Kroger, Safeway, American, and National. There is little doubt that these large chains were more efficient than their smaller rivals. The Robinson-Patman Act clearly protected the inefficient distributors at the expense of both the more efficient firms and consumers. As a result, the transition to a more efficient distribution system was hindered but obviously not derailed.34

Unfortunately, the Morton Salt inference regarding secondary-line competitive injury has persisted over the years. For example, in the Falls City decision, the Supreme Court applied this inference in a case in which the favored buyer was not extraordinarily large. (35) More recently, the same inference was applied in a case involving gasoline distribution, an industry that has undergone a dramatic transformation over the past few decades. (36) To the extent that the Hasbrouck ruling slowed the transition to a more efficient distribution system, consumers again paid the price.

Despite these prior cases, however, there are some more promising developments in Robinson-Patman litigation. Specifically, the Volvo decision contains some passages that suggest a serious change in the Court's attitude toward secondary-line price discrimination.

There, the Court advised that

 Interbrand competition, our opinions affirm, is the "primary
 concern of antitrust law." The Robinson-Patman Act signals no large
 departure from that main concern. ... we would resist
 interpretation geared more to the protection of existing
 competitors than to the stimulation of competition. In the case
 before us .... the supplier's selective price discounting fosters
 competition among suppliers of different brands. By declining to
 extend Robinson-Patman's governance to such cases, we continue to
 construe the Act "consistently with broader policies of
 the antitrust laws." (37)

Despite the Court's assertions to the contrary, this is a major departure from earlier cases. Moreover, it flies in the face of the conventional wisdom that the Robinson-Patman Act was intended to be protectionist in nature. If the Court really means what it said in Volvo, the sort of price discrimination that our model elaborates should now pass muster. Of course, only time (and new cases) will tell.

5. Conclusion

It is not uncommon for retail markets to undergo dynamic transformations that alter, in fundamental ways, the principal means through which final goods are delivered to consumers. For example, small, single-outlet grocery stores that provided home delivery were supplanted by much larger chain stores that, essentially, warehouse food and other household items. Small service stations that once offered pumped gasoline and washed windshields and that sold tires, batteries, and tune-ups evolved into convenience stores with much larger gasoline storage facilities, self service, and virtually no other automotive products. In general, these and many other retail-stage transitions have resulted in improved efficiency of distribution and, ultimately, lower prices for consumers.

Realization of those efficiencies, however, inevitably requires the exit of the older, less efficient retail outlets. That exit, in turn, may occur naturally over time from the attrition that arises through the normal course of competition. We have shown here, however, that upstream firms may have a profit incentive to accelerate that transition process through price discrimination in favor of the more efficient distributors. Thus, under these circumstances, wholesale-stage price discrimination facilitates the movement to more efficient (and often more competitive) modes of distribution. Historically, the injured (inefficient) retailers have been able to enlist the Robinson-Patman Act to thwart (or at least slow) such efforts. However, the exemption to Robinson-Patman liability currently afforded through wholesale cost differences should be extended to retail-level differences. Thus, the law on price discrimination must evolve as well to recognize this important, efficiency-enhancing role of discriminatory pricing.

Received November 2007; accepted January 2009.

References

Baumol, William J., and Janusz A. Ordover. 1985. Use of antitrust to subvert competition. Journal of Law and Economics 28:247-66.

Blair, Roger D., and David L. Kaserman. 2009. Antitrust economics. New York: Oxford University Press.

Blair, Roger D., and John E. Lopatka. 1998. Albrecht overruled--At last. Antitrust Law Journal 66:537-56.

Coase, Ronald H. 1972. Industrial organization: A proposal for research. In Policy issues and research opportunities in industrial organization, edited by Victor R. Fuchs. Cambridge, MA: National Bureau of Economic Research, pp. 59-73.

DeGraba, Patrick. 1990. Input market price discrimination and the choice of technology. American Economic Review 80:124653.

Easterbrook, Frank H. 1986. On identifying exclusionary conduct. Notre Dame Law Review 61:972-80.

Kaftal, Victor, and Debashis Pal. 2008. Third degree price discrimination in linear-demand markets: Effects on number of markets served and social welfare. Southern Economic Journal 75:558-73.

Katz, Michael L. 1987. The welfare effects of third degree price discrimination in intermediate good markets. American Economic Review 77:154-67.

Layson, Stephen. 1988. Third degree price discrimination, welfare and profits: A geometrical analysis. American Economic Review 78:1131-2.

Perry, Martin K. 1978. Price discrimination and forward integration. Bell Journal of Economics 9:209-17.

Pigou, Arthur C. 1920. Economics of welfare. London: Macmillan.

Posner, Richard A. 1976. Antitrust law: An economic perspective. Chicago: The University of Chicago Press.

Robinson, Joan. 1933. Economics of imperfect competition. London: Macmillan. Scherer, Frederic M., and David Ross. 1990. Industrial market structure and economic performance. Boston: Houghton Mifflin Company.

Schmalensee, Richard. 1981. Output and welfare implications of monopolistic third degree price discrimination. American Economic Review 71:242-7.

Varian, Hal R. 1985. Price discrimination and social welfare. American Economic Review 75:870-5. Williamson, Oliver E. 1979. Assessing vertical market restrictions: Antitrust ramifications of the transaction cost approach. University of Pennsylvania Law Review 127:953-93.

Wright, Joshua D. 2006. Antitrust law and competition for distribution. Yale Journal on Regulation 23:169-207.

Wright (2006), however, argues that many of these vertical practices are indeed isomorphic in nature but are treated quite differently under the existing case law.

(1) See, for example, Baumol and Ordover (1985). See also Posner (1976, p. 228) and Easterbrook (1986).

(2) Scherer and Ross (1990, p. 515) write that "the Robinson-Patman Act is a complex and imperfect instrument. If it has not reduced the vigor of competition in American industry, credit must go more to the resilience of the forces of competition than to the act itself or its enforcement."

(3) One can argue--legitimately, we believe that this weakening of the competitive injury standard explains the popularity of Robinson-Patman claims in private antitrust actions. Scherer and Ross (1990, p. 516) report that "a sample survey estimated that 18.1 percent of all private federal antitrust suits initiated between 1973 and 1983 included Robinson-Patman Act claims ...."

(4) In Congressional testimony, Professor Herbert Hovenkamp recently argued for a repeal of the Act, stating that "as currently enforced [the Act] is a socially costly statute that produces no benefits to competition that could not be secured by means of litigation under the Sherman Act." See Wright (2006, ft. 60, p. 186). Havenkamp's view was echoed by the Antitrust Modernization Commission (see 2007 Report and Recommendations at www.amc.gov), which also recommended the repeal of the Robinson-Patman Act.

(5) In Perry's (1978) model, vertical integration provides a mechanism to prevent arbitrage. In the Katz (1987) model, the threat of vertical integration by the larger chain store is what motivates the upstream firm to price discriminate in its favor (that is, against the smaller, local distributor). Both Katz (1987) and DeGraba (1990) have upstream firms that price discriminate in favor of inefficient downstream firms.

(6) Coase (1972, p. 67) writes that "... if an economist finds something--a business practice of one sort or another--that he does not understand, he looks for a monopoly explanation." Williamson (1979) refers to this tendency as the "inhospitality tradition" in antitrust.

(7) The upstream firm may be a pure monopolist, or it may compete with other manufacturers at the downstream stage selling differentiated products.

(8) This assumption is made to simplify the analysis. It is not essential for our results.

(9) DeGraba (1990) uses a linear downstream market demand curve, and Kaftal and Pal (2008) use a linear specification across all markets.

(10) Formally, D([w.sup.*.sub.e] + c) >0, where [w.sup.*.sub.e] is defined by Equation 1.

T. Randolph Beard,* Roger D. Blair, [[dagger]] David L. Kaserman, [[double dagger] [section]] and Michael L. Stern [[parallel]]

* Department of Economics, Auburn University, Auburn, AL 36849, USA; E-mail beardtr@auburn.edu; corresponding author.

[[dagger]] Department of Economics, University of Florida, Gainesville, FL 32611, USA; E-mail Roger.Blair@cba.ufl.edu.

[[double dagger]] Department of Economics, Auburn University, Auburn, AL 36849, USA; E-mail kaserdl@auburn.edu.

[[parallel]] Department of Economics, Auburn University, Auburn, AL 36849, USA; E-mail sternml@auburn.edu.

[[section]] Professor David Kaserman died January 24, 2008. This was one of his final works. The authors would like to thank Richard Romano, Jeremy Bulow, and David Sappington for their helpful comments. Roger Blair appreciates the financial support of the Warrington College of Business Administration at the University of Florida.

(11) If D(w) = a - bw, then [w.sup.*] = al(2b) - (1 - [pi])(c/2).

(12) Specifically, [pi][D([w.sup.*])-D([w.sup.*.sub.e])] +(1--[pi])[D([w.sup.*]+c)-D([w.sup.*] + c)] = 0.

(13) This welfare result in favor of uniform wholesale pricing mirrors Katz (1987) and DeGraba (1990); although, our framework is, of course, not identical. The theorem can be considered an ordinal version of Layson's (1988) result concerning the welfare changes resulting from price discrimination in a linear demand framework.

(14) It is very important to note that the price discrimination now favors the efficient firm. This breaks with the tradition of Katz (1987) and DeGraba (1990), in which the price discrimination favors the inefficient firm, and the welfare implications are consequently in favor of uniform pricing.

(15) This extreme result arises as a consequence of our assumption that driving the inefficient firms from the market in this fashion is costless. Clearly, if there are costs associated with this action then a more complex result could occur. Hence, our results can be viewed as the limiting case on one side (that is, very low costs associated with consumers switching between inefficient and efficient firms); whereas, Katz (1987) can be viewed as the other extreme (that is, infinitely high switching costs).

(16) Recall that [w.sup.*] is the optimal monopoly price in the efficient market.

(17) We are assuming that a portion of the consumers prefer the atmosphere and service at the small "morn and pop" retailers compared to the large chain superstores. The consumers initially at the efficient retailers are assumed to care only about price. Other interpretations are possible.

(18) In order to induce switching with uniform wholesale pricing, the wholesale price would have to be reduced all the way to $17, which would result in a switching utility of $124 (per unit of mass). The profits, however, would be only $561, clearly less than $576.

(19) Specifically, 1/2[(25).sup.2] - 1/2(124)= $250.50.

(20) In these cases the price discrimination is a result of derived demand elasticity differences between the efficient and inefficient downstream firms.

(21) The basic results in Lemma 1 and Theorem 1 are known to break down for certain types of nonlinear demand functions. See Robinson (1933), Schmalensee (1981), and Varian (1985).

(22) A full analysis of these alternative strategies and their treatment under antitrust law is beyond the scope of this article.

(23) For a compact treatment, see Blair and Kaserman (2009, pp. 296-310).

(24) Under Section 2 of the Sherman Act, 15 U.S.C. [section] 2, monopolizing or attempting to monopolize a market is illegal.

(25) See Albrecht v. Herald Co., 390 U.S. 145 (1968). The judicial treatment of maximum resale price fixing is summarized in Blair and Kaserman (2009, pp. 366-9). For a more extensive treatment of the law and economics, see Blair and Lopatka (1998).

(26) See State Oil Co. v. Khan, 522 U.S. 3 (1997).

(27) The Robinson-Patman Act contains an explicit cost justification defense: "... nothing herein contained shall prevent [price] differentials which make only due allowance for differences in the cost of manufacture, sale, or delivery resulting from the differing methods or quantities in which such commodities are to such purchasers sold or delivered" (15 U.S.C. 13a). This defense has seldom worked in practice, however, because price differentials can rarely be fully cost justified ex post.

(28) If the injury occurs at the seller's level, this is referred to as "primary-line" injury. If the injury occurs at the buyers'

(29) The second requirement might appear to be self-evident, but the Supreme Court had to clear this up in Volvo Trucks North America, Inc. v. Reeder-Simco GMC, Inc., 126 S. Ct. 860 (2006).

(30) Elsewhere, the Court has found that the antitrust laws protect competition rather than competitors. Consequently, the law on price discrimination is an exception to this widely accepted principle. See Brown Shoe Co. v. United States, 370 U.S. 294 (1962), for the original statement, which has been reiterated many times.

(31) Federal Trade Commission v. Morton Salt Co., 334 U.S. 37 (1948).

(32) Ibid. at 41.

(33) Ibid. at 48.

(34) Of course, discriminatory pricing of salt by itself was unlikely to accelerate the exit of the smaller grocery stores. But to the extent that other upstream suppliers adopted similar pricing strategies, the cumulative effect may have been substantial.

(35) Falls City Industries, Inc. v. Vanco Beverage, Inc., 460 U.S. 428 (1983).

(36) Texaco, Inc. v. Hasbrouck, 496 U.S. 543 (1990).

(37) 126 S. Ct. 860, 873 (2006).