Structural screens in stochastic markets.

• Author: Shaffer, Sherrill

1. Introduction

   Antitrust policy in the U.S. has evolved into a sophisticated process that takes into account a variety of relevant factors, including potential entry and other dynamic or conduct-oriented considerations, in accordance with modern economic theory. However, simple structural tests are still used as an initial screen to identify those merger cases requiring more detailed analysis. This emphasis on market concentration, rooted in the structure-conduct-performance paradigm of Mason and Bain, is spelled out in written guidelines of the U.S. Department of Justice (DOJ) and has been reiterated in recent public statements by DOJ officials.(1) Moreover, a resurgence of academic support for structure-based antitrust policy has been evident in some recent literature [1].

   This structural emphasis means at a minimum that relatively more DOJ resources are deployed in the scrutiny of large mergers in concentrated markets, compared with other mergers. Such scrutiny can also consume resources from the merging firms. Moreover, even apart from involvement in a merger, a firm may be subject to closer scrutiny and a higher probability of sanctions or challenges as an increasing function of its market share. For example, a firm with a large market share may face a higher probability of being charged with collusive pricing or predatory pricing (the "lightning rod" effect). The policy of awarding treble damages makes a firm's expected costs of such charges non-negligible under any positive probability of being found liable.

   Since there are social costs to this sort of scrutiny, the optimal policy would attempt to minimize unnecessary scrutiny and focus as much of the scrutiny as possible on those firms most likely to be in violation of the law. The purpose of the DOJ's initial structural screen is precisely such optimization. This paper explores the theoretical implications of uncertainty in demand and cost on the efficacy of the structural screen in attaining that purpose.

   A long-standing literature maintains that competitive behavior results in more volatile market shares than would be observed in a collusive market [4; 5; 8; 9; 11; 12]. In a market of similar firms, this hypothesis would imply that competition induces a mean-preserving spread in the distribution over time of each firm's market shares, in the sense of Rothschild and Stiglitz. This, in turn, would imply a greater probability that a firm's market share will exceed a given high threshold in any given period, and hence a greater probability that a competitive firm might fail the DOJ's structural screen and draw closer scrutiny with its attendant costs than would a collusive firm. Thus, stochastic effects might tend to undermine the validity of a structure-based antitrust policy or the efficacy of structural screens as currently applied.

   We examine this argument in a simple framework of duopoly with linear demand and cost. This simple framework is chosen because it allows explicit solutions and, consequently, sharp results. At the same time, the model is formulated in terms of general patterns of symmetric conduct and general statistical distributions of the random components, with some additional results derived for the special case in which the stochastic factors vary independently across firms. The parameterization of conduct permits the model to characterize outcomes for firms exhibiting any degree of collusion from the perfectly competitive or contestable extreme to joint monopoly, whether sustained by explicit collusion or by an implicit dynamic enforcement mechanism as in Friedman [7]. In either extreme, of course, it is well known that pricing and output levels are independent of structure; in such cases, a structural antitrust policy would have no impact on social welfare apart from possible deadweight losses or the stochastic effects analyzed here. For certain intermediate patterns of conduct, such as Cournot, it is well known that structure is monotonically related to equilibrium pricing and output levels; in these cases, stochastic effects could still distort the impact of a structural screen or antitrust policy.

   Stochastic marginal costs, demand slopes, and demand intercepts are analyzed separately. We assume in each case that firms are able to observe the realizations of the stochastic variables before making their production decisions. For quantity-choosing risk-neutral firms, this is the only sequence by which a stochastic mechanism could affect market shares, and is therefore the only sequence relevant to our analysis of structural screens. Regardless of which variable is stochastic, the sign of the effect of a structural screen is shown to depend on parameter values. For homogeneous goods and independently distributed marginal costs, we show that stochastic shifts in marginal cost render the likelihood of failing the structural screen a decreasing function of the degree of market power, consistent with the argument outlined above; this result undermines the validity of structure-based antitrust.

   When products are differentiated, the probability of failing the structural screen is in general a function of the degree of differentiation. In the special case of independently distributed stochastic marginal costs, the probability of failing the structural screen is an increasing function of the degree of substitutability of the products of the two firms, when products are gross substitutes (equivalently, when firms compete in the same product market) and the threshold market share is sufficiently high. The outcome of structure-based antitrust in this case is again detrimental, since for a given pattern of conduct the degree of competition between two firms will be higher if their products are close substitutes. Thus, a structure-based antitrust policy will selectively attack those firms that are more direct rivals, constituting a second way in which stochastic costs subvert the validity of the policy.

   When the demand slope is stochastic, the probability of failing the structural screen is an increasing function of the degree of substitutability of products, for a sufficiently high threshold. This result, which does not require statistical independence of firm shocks, likewise undermines the validity of a structure-based antitrust policy. In other cases, the probability of failing the structural screen is an increasing function of the degree of competition between firms. Similar results are derived when the demand intercept varies across firms. All such cases further undermine the validity of a structure-based antitrust policy when products are differentiated. When products are homogeneous, random shifts in demand would affect both firms equally and have no effect on the incidence of a structural policy.

   The next section presents the homogeneous case with stochastic marginal cost, while section III introduces product differentiation. Section IV examines stochastic demand in the differentiated case, and section V concludes.

2. The Homogeneous Case with Stochastic Costs

   The calculations that follow require an explicit solution for each firm's equilibrium output...