Pricing, Investments and Mergers with Intertemporal Capacity Constraints

Abstract

We set up a duopoly model with dynamic capacity constraints under demand uncertainty. We endogenize the investment decisions of the firms, examine their intertemporal pricing behavior, their incentives to merge, as well as the welfare implications of a merger. Whereas under known and constant demand the high capacity firm lets its low capacity rival sell out, under demand uncertainty we obtain a rich set of sales patterns. Each unit of available capacity has an option value (or opportunity cost), which depends on both firms' capacities, the current demand and the remaining horizon. This option value may be higher when the firms act non-cooperatively compared to the case when they merge to form a monopoly. Trade surplus may be higher when a merger takes place, as capacity is more efficiently managed over time. The prospect of a merger also leads to higher investment levels, as each firm wishes to appropriate a higher share of the total surplus. For some levels of the capacity instalment cost, a merger that turns the duopoly into a monopoly is welfare improving.

Keywords: capacity constraints, dynamic oligopoly, inventories, mergers, price competition

JEL Classification: D43, L13, L22