Academic journal article Economic Inquiry

Delivered Pricing and Merger with Demand Constraints

Academic journal article Economic Inquiry

Delivered Pricing and Merger with Demand Constraints

Article excerpt

I. INTRODUCTION

Studies of merger activity in models of spatial price discrimination conventionally assume that pricing by firms is not constrained by demand. Instead, the only constraints on the discriminatory prices charged are the cost structures of the adjacent rivals. The issue of demand constraints has received attention by Wang and Yang (1999) in related literature but not in examining the consequences of a spatial merger.

We demonstrate that when discriminatory prices are constrained by willingness to pay (demand), the conclusions of existing models must be substantially modified. First, although introducing a demand constraint does not alter firm locations in the absence of merger, it does alter firm locations in the presence of merger. Second, the demand constraint results in equilibrium locations that depend on transport cost, which is not the case in previous models. Transport cost plays an important role in spatial models, and its absence to date from models of spatial merger is unrealistic. Moreover, the dependence of location on transport costs invites the possibility that a tax on transport costs can change locations in an efficient fashion. Third, introducing a demand constraint reverses previous results relating to the merger paradox. In particular, in the absence of a demand constraint, models of spatial price discrimination provide instances in which the parties to a merger gain profit and the excluded firms lose profits. There are no such instances in the presence of demand constraints.

In what follows, the second section places our work within the literature and highlights the issue of demand constraints. The third section presents the model, contrasting it with earlier models. The fourth section identifies the equilibrium locations that arise when there is the prospect of merger and contrasts these locations with those that arise in the absence of demand constraints. The section also demonstrates that when demand is constrained the model of spatial price discrimination yields no cases that resolve the merger paradox, a result contrasting with that offered by the model in which demand constraints are absent. The fifth section demonstrates that a tax on transport can increase welfare. Indeed, the optimal tax often completely eliminates spatial price competition by creating local monopolies. The sixth section considers the full range of cases in which some (but not all) firms may face constrained demand and also proves that in the fully constrained case considered earlier, the entire market will be served. A seventh section considers a partially constrained case, and the eighth section concludes.

II. SPATIAL PRICE DISCRIMINATION AND CONSTRAINED DEMAND

Spatial models have proven especially useful in capturing aspects of competition in horizontally differentiated markets as emphasized by Tirole (1988). In particular, they provide a general method for examining markets in which an ordered product characteristic differentiates output. (1) Among the more popular models is that of discriminatory pricing in which the price a firm is able to charge depends upon how "close" it is to its rivals. Thisse and Vives (1988) show that such pricing is the preferred alternative when firms are able to adopt it. Lederer and Hurter (1986) demonstrate that under such pricing rivals locate symmetrically along a linear market, thus minimizing total transport costs.

Early studies of merger in a model of spatial discrimination assumed that location choices do not anticipate the merger. Reitzes and Levy (1995) show that such a merger increases the prices and profits of the participants but leaves those of all other firms unchanged. Gupta et al. (1997) show that an anticipated horizontal merger alters the locations of spatially discriminating duopolists and increases transport cost, thereby reducing efficiency. Rothschild et al. (2000) confirm this finding in the case of two firms merging in a three firm market and also examine the effects of merger on the excluded rival. …

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