Profitable Mergers in a Cournot Model of Spatial Competition.

• Author: Norman, George

George Norman [*]

Lynne Pepall [+]

This paper investigates the profitability and locational effects of mergers when Cournot firms compete in spatially differentiated markets. A two-firm merger is generally profitable because the merged partners can coordinate their location decisions. The merged firm locates its plants outside the market quartiles with distance from the market center being an increasing function of the number of nonmerged firms remaining at the market center. Profitable two-firm mergers reduce competitive pressure, leading to higher prices and reduced consumer surplus. The merger increases total surplus by increased locational efficiency and the increased profits of the merged and nonmerged firms.

1. Introduction

   In the wake of an unprecedented wave of merger activity in the U.S. and abroad, there is considerable interest in understanding the market impact of horizontal mergers. A recent report by the Federal Trade Commission, "Anticipating the 21st Century" (FTC 1997), cites the prevention of anticompetitive mergers as one of its four key activities. This goal has focused policymakers' interest on the unilateral competitive effects of horizontal mergers, that is, on those mergers that in the absence of collusion make it profitable for the merging firms to reduce output and to cause market price to increase.

   The unilateral effects of mergers are exactly the kind of policy issue where we would expect the theory of industrial organization to make an important contribution. Unfortunately, our theory of horizontal mergers is not yet quite up to task. The standard Cournot model of quantity competition, so widely used in applied theory, is beset by the paradoxical result that the majority of horizontal mergers are simply not profitable. This profitability paradox of horizontal mergers in the Cournot model is particularly associated with the work of Szidarovzky and Yakowitz (1982) and Salant, Switzer, and Reynolds (1983) (also see Davidson and Deneckere 1984). They show, for example, that with linear demand and constant, identical marginal costs, no two-firm merger is profitable unless it is merger to monopoly. More generally, with the same linearity assumptions merger is unprofitable, and so should not occur, unless at least 80% of the firms in the market merge. This is a clear drawback to the use of the standard Cour not model in the formulation of merger policy.

   The logic behind the paradox is simply explained. A merger of two firms converts the n-firm premerger game into an n-1-firm postmerger game. The merger is equivalent to the formation of a coalition between the merged firms whose aim is to maximize their joint profit by coordinating their output choices. As a result, the merged firm reduces its combined output. Because firms' outputs are strategic substitutes, this is accompanied by an increase in the outputs of the nonmerged firms, with the result that the merged firm ends up looking just like any other firm in the industry. In other words, the merged firm's market share in the postmerger game is less than the sum of the two firms' premerger market shares, whereas the other firms, who did not merge, increase their market share. The combined impact on output increases price but the loss of market share by the merged firm is so sufficiently great that its profit falls.

   It is the combination of strategic substitution and the inability of the merged firm to make a credible commitment to exploit its potentially greater size in the postmerger game that lies at the heart of the Salant, Switzer, and Reynolds merger paradox. [1] Suppose, by contrast, that the strategic variables chosen by the rival firms are strategic complements--the most obvious choice being price--so that the firms are Bertrand competitors, then as long as the firms also produce different products, merger is generally profitable for the merged firms. This should not be particularly surprising. Merger induces the coalition members to increase their prices. As a result of strategic complementarity, this soft action is met by a soft response: an increase in the prices of the rival, nonmerged firms. Deneckere and Davidson (1985) show that merger of Bertrand competitors is profitable by assuming that the firms produce symmetrically differentiated products. Reitzes and Levy (1995) introduce a spatial element to the analysis and show that the merger of price-discriminating Bertrand firms is always profitable, and Pepall, Richards, and Norman (1999) show that the same result holds without price discrimination.

   In this paper, we maintain the assumption of strategic substitution--our firms are Cournot competitors--and instead focus on the role of commitment. Our goal in this paper is to provide support for the presumption that a two-firm merger, by combining the firms' assets, should in some sense lead to a "bigger" and perhaps "better" firm than either of the two firms was in the premerger market. In this regard, our paper shares common ground with Daughety (1990), who also recognizes the role of commitment. He does so by changing the timing of the postmerger output game. In his analysis, when two firms merge, they act as Cournot competitors against other merged firms but as Stackelberg leaders with respect to the remaining nonmerged firms. With linear demand and costs, any two-firm merger is profitable. We adopt a less extreme approach to commitment by introducing the assumption that our Cournot firms compete across a set of spatially differentiated markets. In this setting, firms choose not just the quantity of o utput to supply to the spatially differentiated markets but also where to locate their production plants to serve these markets. [2]

   Location is a key factor underlying why a merger can lead to a bigger and better firm. Firms that have different locations have different locational advantages in serving the set of spatially separated markets. As a result, in contrast to the standard nonspatial Cournot model, a merger between two firms need not result in one of them effectively being shut down. Rather, a merger between two firms allows them to coordinate their location decisions with the result that the merged firm becomes potentially bigger than its rivals, better adjusted to consumer locations. [3]

   Our analysis builds on the work of Anderson and Neven (1990) who show that when demand and costs are such that each Cournot firm wishes to serve the entire set of spatially separated markets, all firms choose to cluster or agglomerate at the center of the market area. This tendency to agglomeration is taken as the starting point of our analysis. We introduce commitment by assuming that merger of two firms confers a leadership advantage on the merging firms in that they can choose first whether and where they wish to relocate their production plants. In making this decision the merged firm is able to anticipate correctly the location choices of the remaining n - 1 nonmerged firms and the outcome of the simultaneous Cournot quantity game that will subsequently be played with these nonmerged rivals.

   We show that a two-firm merger results in the merged firm relocating its plants away from the market center, whereas the nonmerged firms remain at the center. Being a leader or Stackelberg first mover in location choice and coordinating the two plants' locations to serve certain segments of the market more efficiently lead to a merged firm with a larger overall market share than its nonmerged rivals. This explains why, in sharp contrast to the standard Cournot model, a two-firm merger can be profitable even in relatively unconcentrated markets.

   A two-firm merger not only improves locational efficiency, but it also increases market concentration and reduces competitive pressure across the set of markets. The net effect is that it generally leads to higher prices across the set of consumer markets. However, and again in sharp contrast to nonspatial analysis, the increased profit of both the merged firm and the nonmerged firms, together with improved locational efficiency, is such that the merger increases total surplus. In other words, the introduction of commitment through location leadership means that merger can indeed lead to a bigger firm, which so far as total welfare is concerned serves the market "better." [4]

   The remainder of the paper is organized as follows. In section 2, we present the Cournot model of spatial competition with all firms located at the center of the market and derive the equilibrium conditions that characterize a two-firm merger. In section 3, we derive the optimal distance from the center that the merged firm locates its plants and identify the conditions under which such a merger is profitable. In section 4, we evaluate the welfare effects of a two-firm merger in the spatial model. Concluding remarks are presented in the final section.

2. The Model

   We begin by describing a general model of Cournot competition in which firms supply output across a set of spatially differentiated markets. Specifically, suppose there are n identical firms, each with a single production plant located on a Hotelling line whose length is normalized to unity. The location of firm i on the line is denoted by [x.sub.i], i = 1, ..., n. Each firm produces a homogeneous product at constant marginal cost, which without loss of generality is set equal to zero. We ignore any set-up costs that the firms might incur. Demand at each consumer location x on the line is identical and is described by the linear inverse demand function p(x) = v - Q(x) where p(x) is the product...