Measuring Market Power in Bilateral Oligopoly: The Wholesale Market for Beef.

AuthorSchroeter, John R.

John R. Schroeter [*]

Azzeddine M. Azzam [+]

Mingxia Zhang [++]

Econometric methods for assessing the degree of market power typically rely on a maintained hypothesis of price-taking behavior on one side of the market or the other. In the analysis of bilateral oligopoly, however, one would like to leave open the question of whether buyers or sellers (or both) behave competitively while allowing for the possible exercise of market power on either side. In this paper, we address the problem of measuring market power in bilateral oligopoly. This requires that we first distinguish among three candidate equilibrium concepts: bilateral price-taking, seller price-taking, and buyer price-taking. Choosing among them comes down to a test of nonnested, nonlinear, simultaneous equation models. Our application to the U.S. wholesale market for beef, characterized by high degrees of concentration among both sellers (beef packers) and buyers (primarily retail grocery chains), reveals seller price-taking among the three candidates to be the most consistent with the data. In particular, th e hypothesis of price-taking conduct on both sides of the market can be rejected. This is a conclusion that would not have been reached had we considered monopoly conduct by sellers as the only alternative to perfect competition.

  1. Introduction

    The last two decades have witnessed the development of a variety of approaches to the measurement of market power. [1] In general, these studies base their inferences of market power on econometric models of firm conduct, in which monopoly (or monopsony) and price-taking behavior have empirically distinguishable comparative static properties. One often-cited and particularly illuminating example of this work is a paper by Bresnahan (1982). In it, he developed a simple two-equation empirical model of price and quantity determination in a homogeneous product oligopoly. The model consists of a linear market demand equation and a generalized supply relation incorporating a "conduct parameter" that indexes the degree of market power and nests some conventional oligopoly solution concepts: With [lambda] (the conduct parameter) equal to zero, the model's equations reduce to perfectly competitive supply and demand. A value of one for [lambda] implies the monopoly, or perfect cartel solution. Intermediate values of [lambda] correspond to outcomes "between" the polar cases of perfect competition and pure monopoly. Within this context, Bresnahan's fundamental insight is that the comparative statics of price and quantity with respect to exogenous parallel shifts of demand or marginal cost are, by themselves, insufficient to reveal the degree of competition. In order for [gamma] to be econometrically identified, it is necessary that the model admit exogenous rotations of the demand curve as well.

    Bresnahan's use of a conduct parameter as a means of parametrizing a range of potential solution concepts is a modeling device that has been applied in a wide variety of approaches using several different means of achieving econometric identification of the degree of market power. [2] This "conduct parameter method" can be readily adapted, moreover, to the measurement of oligopsony power. [3] To the best of our knowledge, however, all previous applications of these methods assume that the participants on a particular side of the market take price as given while the agents on the other side may or may not exercise market power. For example, in studies of oligopoly, buyers are assumed to be passive price-takers while sellers might exploit their influence on price. In studies of oligopsony, sellers are viewed as price-takers while buyers may or may not take advantage of an upward sloping supply relation.

    In this paper, we address the problem of measuring market power without a maintained hypothesis of price-taking behavior on one side of the market or the other. This issue arises naturally in the context of "bilateral oligopoly," a market structure in which both sides, buyer and seller, are relatively concentrated. [4] In such settings, there are at least three stylized equilibrium concepts that suggest themselves: bilateral price-taking (leading to the competitive outcome; both buyers and sellers treat price as given), seller price taking (sellers behave passively while buyers may or may not exercise some degree of monopsony power), and buyer price-taking (buyers behave passively while sellers may or may not exercise some degree of monopoly power). Given the structural relations which specify the model's "primitives" (demand and marginal costs), a set of equations jointly determining price and quantity can be derived for each of the equilibrium concepts. For the seller price-taking and the buyer price-takin g equilibrium concepts, moreover, a conduct parameter can be used, just as in Bresnahan's model, to index the degree of market power, but it is at this point that the identification issue arises. For certain formulations of the model's structural relations, the equilibrium concepts are not empirically distinguishable from one another. We will see that the easiest way to ensure that the alternative equilibrium concepts for the bilateral oligopoly model do possess empirically distinguishable comparative static properties, and that the degrees of market power are identified within each, is to employ a device very closely parallel to the Bresnahan solution to the identification problem in the oligopoly case: Allow the sellers' marginal cost to rotate (not merely shift) with changes in exogenous variables. In formulations of the models that possess this feature, the task of choosing among the equilibrium concepts comes down to a test of nonnested, nonlinear, simultaneous equation models. [5] In this paper, we will show how to apply existing econometric procedures to carry out such tests. To summarize, this paper first makes a modest contribution to the methodology of market power measurement: It shifts the assumption of price-taking behavior on a particular side of the market from the category of maintained hypothesis to the category of testable hypothesis.

    The larger contribution of this paper stems from its findings pertaining to a specific bilateral oligopoly application. It is very rare for final consumers of a product to exhibit any appreciable degree of concentration, so the standard paradigm for discussions of bilateral oligopoly is that of a wholesale market in which a concentrated manufacturing industry produces a product and sells it to a concentrated retailing industry. In the U.S., the wholesale market for fresh beef, in particular, is a good fit for this paradigm. National concentration levels are high among both sellers (beef packers) and buyers (primarily retail grocery chains) and concerns about market power have supplied the motivation for a number of previous economic studies of both of these industries. So, ideally, an econometric analysis of price and quantity determination in the wholesale beef market should leave open the question of whether buyers or sellers (or both) behave competitively while allowing for the possible exercise of market power on either side. Such an analysis is carried out in section 6.

    Our starting point in the next section is a brief outline of the alternative equilibrium concepts that we will consider for bilateral oligopoly. Sections 3 and 4 address the identification issue in a simple illustrative way. Section 3 provides an example of a structural model in which the solution concept is not identified. Section 4 shows how a slight modeling alteration, a la Bresnahan, yields an example in which the solution concept and the degree of market power are identified. Estimation and testing issues are discussed in section 5. Following the application in section 6, a final section summarizes and concludes.

  2. Equilibrium Concepts for Bilateral Oligopoly

    Consider a wholesale market in which a concentrated manufacturing industry produces a product and sells it to a concentrated retailing industry. Retailers, in turn, sell the product to final consumers. We assume that the product is homogeneous at both the wholesale and retail levels. Retail firms may effect some transformation of the wholesale version of the product through packaging, transportation, storage, bundling with customer services, or possibly some physical alteration of the product itself. It is assumed that any transformation of the product from wholesale to retail versions is one of fixed proportions, so with appropriately chosen units, wholesale and retail quantities can be measured with the same variable. Final consumers of the product are assumed to be price takers but retailers may exercise some degree of monopoly power.

    Our interest focuses primarily on the determination of price and quantity in the wholesale market. Because both sides of the market (i.e., both manufacturing and retailing industries) are relatively concentrated, the outcome need not be competitive. In fact, at least three stylized equilibrium concepts suggest themselves as plausible candidates.

    The wholesale market may be competitive; that is, it may be characterized by bilateral price-taking (BPT). In this scenario, illustrated in Figure 1, the derived demand curve of the retail industry is obtained by the following construction. Start with the industry's perceived marginal revenue curve ([PMR.sub.r]). If retailers exercise no monopoly power over final consumers, [PMR.sub.r] is coincident with retail demand ([D.sub.r]). On the other hand, if the retail market is perfectly cartelized, [PMR.sub.r] will be the curve marginal to [D.sub.r]. With some intermediate degree of oligopoly power, [PMR.sub.r] will assume a position between these two extremes. From [PMR.sub.r], subtract retailers' marginal cost ([MC.sub.r]) to get perceived marginal revenue net of marginal cost ([PNMR.sub.r]), which in the bilateral price-taking case, is the retail...

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