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Testing for collusion during periods of input supply disruptions: the case of allocations.

I. Introduction

Because collusion generally is a clandestine activity, detection and proof of price-fixing conspiracies has always been problematic. In the absence of explicit admissions of guilt or other forms of direct evidence (e.g., eyewitness accounts, tape recordings, etc.), prosecutors traditionally have relied upon circumstantial evidence to infer the presence of collusive activity.(1) In general, evidence pertaining to economic factors that may either facilitate the formation and maintenance of a collusive agreement or signal the existence of such an agreement has been used to argue the presence of a conspiracy in such cases.(2) Such circumstantial evidence often is supported with an econometric (or statistical) analysis of observed prices that purports to show some significant increase over the alleged conspiracy period that is left "unexplained" by other market forces.

While the above approach may work reasonably well when vertically-related input markets are functioning smoothly, it suffers serious deficiencies in situations where abnormal (though, empirically, not uncommon) supply disruptions have occurred. Such disruptions, which may arise from a variety of causes, lead input suppliers to restrict sales quantities to their downstream customers. Moreover, these input supply restrictions sometimes involve simultaneous price increases for the affected inputs.(3) A common example of this behavior is the "allocation" in which historical purchase levels are used to apportion limited supplies. Importantly, where downstream firms have been placed on allocation by one or more of their major input supply industries, the traditional circumstantial approach outlined above breaks down and is likely to yield perverse results. Specifically, application of this approach under these circumstances will systematically tend to cause a Type I error--conviction of an innocent party. Moreover, this problem is exacerbated by the fact that input allocations also tend to cause industry behavior and performance to mimic those that would be expected to result from collusive activity. Thus, reliance upon the traditional approach is doubly dangerous--it creates conditions that normally may be associated with collusion (thereby raising suspicions of such activity) and simultaneously generates the sort of data that traditionally have been used to convict firms (and individuals) of collusion when, in fact, no collusive activity has transpired.

In this article, we explain the pitfalls associated with use of the traditional approach under input supply allocations and offer a simple direct test for conspiracy under such allocations. Our principal conclusions are:

1. Periods of input supply allocation represent relatively unlikely times for a collusive arrangement to arise;

2. Input supply allocations give rise to industry behavior and performance that tend to resemble those generally expected to be observed with collusion; and

3. Under allocations, an inference of collusion is warranted only if suspected firms sell less output than that which could be produced with the allocated quantity of the input.

Moreover, because the proposed test (conclusion 3, above) is applied to individual firms, it can be used to distinguish conspirators from nonconspirators in cases where only a subset of the firms are participants.(4)

The article is organized as follows. In section II, we explain the fundamental microeconomics of the traditional approach to distinguishing competitive from collusive performance and show how input allocations interfere with our ability to draw the standard sort of inferences from observed market behavior. Next, in section III, we develop a simple, yet superior, test that can be applied during allocation periods and that is not subject to the pitfalls of the traditional approach. Section IV, concludes the article.

II. Pitfalls of the traditional approach under allocations

We begin by presenting the standard microeconomic analysis of cartel versus competitive behavior, which provides the intellectual foundation for the traditional circumstantial approach to detecting and proving collusion. That analysis is presented in figure 1, below.


Here, we assume that the industry initially is competitive. Under competition, the market supply curve, [S.sub.C], indicates the quantities of output (per time period) that will be placed on the market at various prices. The conventional appearance of [S.sub.C] reflects the effectively unconstrained availability of all essential inputs at market-clearing prices. It is well known that, under competition, the market supply curve is identical to the industry's (as opposed to an individual firm's) marginal cost curve. Therefore, if this industry were monopolized (or, through collusion, behaved as if it were monopolized), [S.sub.C] would become the relevant marginal cost curve. Thus, we have labeled this curve [S.sub.C] = [MC.sub.M]--the supply curve under competition is the marginal cost curve under monopoly (or collusion). With market demand given by D, then, industry equilibrium under competition is given by the price/output combination [P.sub.C], [Q.sub.C]. At this equilibrium, price equals marginal cost.

Suppose, now, that the firms in this industry are able to collude successfully. With the objective of maximizing joint (total industry) profits, these firms will select a total market output that equates industry marginal cost, [MC.sub.M], to industry marginal revenue, where this latter curve is given by MR.(5) Thus, the cartel equilibrium is identical to the monopoly equilibrium, which is shown as [P.sub.M], [Q.sub.M] in the figure. At this equilibrium, output falls below the competitive level and price exceeds marginal cost. This restriction in output, of course, is the source of the allocative inefficiency normally attributed to monopoly and/or collusive behavior.(6)

As noted above, economists traditionally have attempted to distinguish empirically between these two alternative forms of market behavior--competitive versus collusive--by examining various indicia of industry structure, conduct, and performance. Relying upon a fairly large body of literature--both theoretical and empirical--that has identified a set of industry characteristics that may be associated with collusive behavior, inferences are drawn regarding the likelihood that such behavior is (or has been) occurring.(7) Five such indicia that typically have been used are (1) a reduction in output; (2) an increase in price that is "unexplained" by normal market forces such as demand growth, input price increases, etc.; (3) a heightened degree of pricing uniformity (e.g., increased adherence to list prices); (4) a period of relative stability of individual firms' market shares; and (5) a period of heightened communication between industry members. Traditionally, where these (and, perhaps, other) events have occurred contemporaneously, an inference of collusion tends to be supported.

A period of input supply allocation, however, alters the above equilibria--and our ability to draw the above sort of inferences--in important ways. Under allocations, input suppliers restrict the quantity of the intermediate product that downstream firms are allowed to purchase below the quantity that was being purchased previously. Moreover, while the input price may be increased above the preallocation level, the magnitude of that price increase is not sufficient to clear the market at the restrained (allocated) quantity. That is, an allocation, as opposed to a simple price increase, is a potentially binding quota that limits the amount of the input that may be purchased at any feasible price.

The effect of an input supply allocation on the downstream market equilibrium is shown in figure 2. As before, the competitive equilibrium yields [P.sub.C], [Q.sub.C] in the absence of an allocation. Once placed on allocation, however, downstream firms are constrained to a maximum practical output of [Q.sub.A], where [Q.sub.A] [is less than] [Q.sub.C] must hold for allocation to represent a binding constraint.


The price charged for the input may or may not be raised during the allocation period. If the allocation is not accompanied by an increase in the price of the input, the portion of [S.sub.C] below [Q.sub.A] remains unchanged. If the input price is increased, the downstream industry supply curve will shift up vertically to reflect the increased marginal costs caused by the higher input price. Obviously, however, for the quantity restriction (allocation) to be binding, the input price increase must be less than that required to clear the input market at the allocated quantity (i.e., allocations are, by definition, a form of nonprice rationing). In the event the input price is increased, the lower segment of the supply curve will shift upward, as illustrated by the dashed line. That vertical shift is caused (and, therefore, "explained") by the higher input price. By definition, however, the dashed segment of [S.sub.A] must intersect the vertical segment below [P.sub.A]. Otherwise, the quantity restriction associated with the allocation would not be binding. As a result, some portion of the observed price increase will be left "unexplained" by the increased input price under allocation.

Regardless of whether the input price is increased, competitive behavior under an input supply allocation produces a price, quantity equilibrium given by [P.sub.A], [Q.sub.A] in figure 2. Relative to the nonallocation competitive equilibrium, output quantity falls and price rises--purely as a result of the input allocation. Moreover, as noted above, the observed price increase will exceed that which is "explained" by any increases in the price of the input. Importantly, these results are identical to the price, output changes traditionally attributed to collusion.

In addition, other market impacts of an input allocation also tend to resemble collusive-type outcomes. For example, an allocation scheme that rations input supplies to downstream firms on the basis of previous period purchases automatically leads to output levels that preserve preallocation market shares. Market share stability, then, typically will exist over the allocation period. Such stability can be indicative of certain mechanisms used to implement price-fixing conspiracies.(8) Consequently, observed market share stability created by input allocations can heighten suspicions of collusive activity. In addition, when output price rises to [P.sub.A] under an allocation, firms will tend to "stick to" this higher price. The normal profit incentive to reduce price somewhat on particular orders (i.e., to charge a specific customer a discounted, below-list, price) is short-circuited by the output restriction imposed by the allocation. Specifically, if the firm cannot increase its sales above its "share" of [Q.sub.A] by discounting, it is unprofitable to charge a price below [P.sub.A]. Therefore, in addition to prices going up, we should expect to see increased pricing uniformity during an allocation period. Individual firms' prices and price changes will tend to be uncannily close during such periods, further increasing suspicions of collusive behavior.

Finally, it is also possible that an allocation period, which is a period of "shortage," could be used by input suppliers to reward favored customers (e.g., downstream affiliates of a vertically integrated input supplier) with larger allocation or, alternatively, to punish others with especially severe restrictions. It therefore seems likely that downstream competitors facing rationed supplies may seek to determine if they are, in fact, being subjected to extraordinary treatment. This circumstance, which is not indicative of conspiracy, could motivate an increase in interfirm communications regarding supply experiences and the like. Such heightened communications once again resemble activities one might observe during a period of conspiracy.

Thus, input supply allocations produce market outcomes that closely resemble those that traditionally have been used to signal the presence of a collusive agreement, even when the industry remains fully competitive. As a result, considerable circumspection is called for in inferring anticompetitive behavior during periods of input supply disruptions. The traditional circumstantial approach is likely to yield a false positive finding--indicating collusion where none is present. An alternative test is, therefore, required in these situations.

III. An exact test for collusion under allocations

Although the behaviors of colluding firms and competitive, allocation-constrained firms may appear extraordinarily similar, economic analysis allows us to describe an exact test for the presence of a conspiracy under allocation constraints. This test, which requires only readily observable information to implement, is based on the assumption that firms will not enter into a criminal conspiracy when no increase in profit is gained from doing so. Because conviction on conspiracy charges carries substantial penalties, participation in a conspiracy is in the firm's interest only when the rewards are sufficiently great. In the absence of such rewards, participation is irrational and, therefore, will not occur.

Figure 3 illustrates the circumstances faced by a cartel during a period of binding allocation. As before, the cartel maximizes joint profit by selecting price and output levels where marginal revenue, MR, equals industry marginal cost, [MC.sub.M]. Under a binding allocation, [MC.sub.M] has the truncated appearance given in figure 3--marginal cost becomes vertical at output [Q.sub.A]. As a result, output levels beyond [Q.sub.A] are impossible.


Given an input allocation, then, precisely two sorts of profit-maximizing equilibria can occur. First, MR may intersect [MC.sub.M] in the nonvertical segment of the latter curve--i.e., at a quantity less than [Q.sub.A]. This result occurs with the marginal revenue curve [MR.sub.1], which, in turn, results in price [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and sales [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Alternatively, MR may intersect [MC.sub.M] in the vertical segment of the latter curve--i.e., at the quantity [Q.sub.A]. This outcome is illustrated with the marginal revenue curve marked [MR.sub.2], yielding price [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and quantity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. These are the only two possible results. Which of these outcomes occurs in a particular case depends solely on the size of the allocation-determined quantity [Q.sub.A], and the location of the market demand curve.

The two possible outcomes described above can be characterized as follows: First, if MR intersects [MC.sub.M] in the vertical segment, as [MR.sub.2] does in figure 3, then the competitive and cartel outcomes are identical (see figure 2: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. This implies that profits to sellers in the industry under collusion are precisely the same as those obtained under competitive behavior--a consequence of the output restriction imposed by the allocation. Clearly, there is, in this circumstance, no incentive whatsoever for sellers to form a price-fixing conspiracy. On the contrary, there is a disincentive to do so, as such an action would create only potential costs and no benefits.

Alternatively, if MR intersects [MC.sub.M] in the upward-sloping segment (i.e., at some output rate below [Q.sub.A]), then the cartel outcome is more profitable than the competitive outcome, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Our analysis, then, illustrates an important difference between these two equilibria. A cartel is more profitable than purely competitive behavior only when the cartel raises prices to the point that cartel sales are below the allocation-determined maximum output rate. Thus, a cartel is more profitable than competition only if the cartel reduces industry output below [Q.sub.A]. And, importantly, production of such output levels will lead the colluding firms to purchase less than the allocated quantity of the supply-restrained input. Therefore, we obtain the following conclusion.

CONCLUSION Under any allocation scheme that limits output to levels below the unconstrained competitive output, collusion will be profitable only if it results in sales below the allocation maximum, [Q.sub.A], and input purchases below the allocated levels.

This conclusion immediately provides a straightforward and theoretically rigorous test for the presence of a price-fixing conspiracy under allocative restrictions. Because one would never expect collusion to occur unless it was, in fact, seen to be profitable, an observation that industry output under allocations equals the allocation-determined maximum is prima facie evidence that no conspiracy exists. Where sellers laboring under allocation restrictions are shown to be utilizing their whole allocation in production, then the economic evidence strongly suggests that these firms are not engaged in a conspiracy. Evidence that a firm was, for example, seeking to increase its output beyond [Q.sub.A] by obtaining alternative input supply sources would, in fact, further substantiate a finding of no collusion.

Two potential complications to this analysis do not alter the conclusion. First, should the allocation be accompanied by a price increase for the rationed input, then our analysis is affected only to the extent that [S.sub.A] would reflect not just the quantity limitation, but also the higher price for the essential commodity. Nonetheless, the conclusion above would be unaltered. Should the price increase be sufficient to cause [S.sub.A] to intersect D at a quantity below [Q.sub.A], then the allocation restriction is ineffective and, therefore, irrelevant.

Second, any inability of the price-fixing conspiracy to raise prices to the full joint-profit-maximizing level, perhaps due to potential cheating by members or monitoring costs, also does nothing to alter our conclusion. Again, a conspiracy can make money only if it is able to reduce output below the allocation level, [Q.sub.A]. Otherwise, competition provides profits equal to any cartel.

IV. Conclusion

Empirical evidence suggests that prosecution and punishment of price fixers has a deterrent effect. Imposition of fines, payment of damages, and incarceration of guilty parties appears to reduce the likelihood of future collusive behavior. In so doing, it benefits consumers by fostering more competitive pricing throughout the industry.

At the same time, however, it must be recognized that unwarranted prosecution and, particularly, conviction of innocent parties can have a chilling effect on the vigor of competition. Conviction of innocent parties makes enforcement a purely random event--a lightening bolt that may strike anyone without warning. Such randomization, in turn, may cause enforcement to lose its deterrent effect. If one's behavior does not affect enforcement decisions (both prosecution and conviction), then enforcement decisions will no longer influence behavior. In addition, such random enforcement increases the overall costs of all firms operating in the affected (and, perhaps, other) industries, which, in turn, causes prices to be higher than they would be with selective and accurate enforcement. Therefore, just as a positive probability of punishment of guilty parties tends to improve industry performance, a positive probability of punishment of innocent parties tends to impair performance. As a result, even leaving aside the issue of fairness to the individuals involved, avoidance of Type I errors in enforcement decisions is crucial to the overall effectiveness Of antitrust policy.

We have shown here that certain industry conditions can arise that will tend to lead to the commission of such errors. Specifically, periods of input supply allocations can easily mislead enforcement officials and courts to conclude that price fixing has occurred when, in fact, it has not. Such a mistaken conclusion is very likely to occur when the traditional sorts of circumstantial economic evidence are relied upon to infer collusion during periods of input supply allocations. During such periods, the alternative (and much simpler) test proposed here provides a far more accurate indicator of collusive versus noncollusive behavior.

(1) Even when direct eyewitness testimony is available, it frequently is not altogether conclusive. For example, such testimony may be somewhat ambiguous or, possibly, tainted by questions of witnesses' motivation or reliability. In these cases, such "direct" evidence often is buttressed with the sort of circumstantial economic evidence described here.

(2) Typically, such evidence has focused upon (1) structural characteristics, such as concentration, entry barriers, product homogeneity, etc.; (2) behavioral characteristics, such as information gathering and dissemination activities, price announcement policies, meetings at trade shows, etc.; and (3) performance characteristics, such as unpredicted price increases, increased adherence to list prices, market share stability, etc. A fairly large literature exists connecting such industry characteristics to collusive activity. The seminal theoretical paper on this subject is George Stigler, A Theory of Oligopoly, 72 J. POL. ECON. 44 (Feb. 1964). Subsequent empirical analyses include Richard Posner, A Statistical Study of Antitrust Enforcement, 13 J. L. ECON. 374 (Oct. 1970); John Palmer, Some Economic Conditions Conducive to Collusion, 16 J. ECON. ISSUES 29 (Sept. 1972); George Hay & Daniel Kelley, An Empirical Survey of Price Fixing Conspiracies, 17 J. L. & ECON. 13 (Apr. 1974), Peter Asch & Joseph Seneca, Characteristics of Collusive Firms, 23 J. IND. ECON. 233 (Mar. 1975); Arthur Fraas & Douglas Greer, Market Structure and Price Collusion: An Empirical Analysis, 26 J. IND. ECON. 29 (Sept. 1977); Robert Porter, A Study of Cartel Stability: The Joint Executive Committee, 1880-1886, 14 BELL J. ECON. 301 (1983); and Jon Joyce, Effect of Firm Organizational Structure on Incentives to Engage in Price Fixing, 7 CONTEMP. POL'Y ISSUES 19 (Oct. 1989).

(3) The most famous recent example of an allocation arose as a consequence of the "voluntary" export restrictions on Japanese-made automobiles destined for U.S. domestic markets in the early 1980s. However, supply disruptions that lead to allocations among downstream sellers, in fact, are quite common. KARL AIGINGER, PRODUCTION AND DECISION THEORY UNDER UNCERTAINTY (1987) provides extensive empirical evidence on the involuntary nature of inventory fluctuations and shortfalls in capacity for many industrial sectors. When backlogged orders are taken into account, Aiginger finds that net inventories are often negative in many industries.

(4) On the subject of distinguishing conspirators from nonconspirators in the absence of input allocations, see Roger Blair & Richard Romano, Distinguishing Participants from Nonparticipants in a Price-Fixing Conspiracy: Liability and Damages, 28 AM. Bus. L. J. 33 (1990). See also Mehmet Karaaslan, Identifying Participants in a Price-Fixing Conspiracy: Output & Market Share Tests Reexamined, 12 REV. INDUS. ORGANIZATION 279 (1997); and Blair & Romano, Identifying Participants in a Price-Fixing Conspiracy: Output & Market Share Tests Reexamined--Reply, 12 REV. INDUS. ORGANIZATION 291 (1997).

(5) Although it is certainly true that a cartel may fail (for a variety of reasons discussed in the literature) to implement full joint-profit-maximizing prices, it is useful here to describe the cartel's best strategy prior to allowing for potential inefficiencies in its operation. As will be seen below, our results are independent of whether or not one assumes the cartel operates in the most profitable manner.

(6) For a more complete discussion of this standard result, see DAVID KASERMAN & JOHN MAYO, GOVERNMENT AND BUSINESS: THE ECONOMICS OF ANTITRUST AND REGULATION (1995), at chs. 3 & 5.

(7) See the references in note 2, supra.

(8) The importance of market share stability in supporting an allegation of collusion is emphasized in Richard Schmalensee, Inter-Industry Studies of Structure and Performance, in HANDBOOK OF INDUSTRIAL ORGANIZATION ch. 16 (R. Schmalensee & Robert Willig eds., 1989). Specifically, at 999, Schmalensee writes: "While stable market shares and firm ranks are consistent in principle with either collusion or competition, most would argue that unstable shares and ranks are inconsistent with effective collusion."


(*) Associate Professor of Economics, Auburn University.

(**) Torchmark Professor of Economics, Auburn University.
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Author:Beard, T. Randolph; Kaserman, David L.
Publication:Antitrust Bulletin
Geographic Code:1USA
Date:Mar 22, 2000
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