Dynamic Price Competition with Capacity Constraints

Jose Betancourt, Ali Horta su, Aniko …ry and Kevin Williams
Additional contact information
Jose Betancourt: Yale University
Ali Horta su: University of Chicago
Aniko …ry: Carnegie Mellon University
Kevin Williams: Yale University

No 2394, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We study dynamic price competition between sellers offering differentiated products with limited capacity and a common sales deadline. In every period, firms simultaneously set prices, and a randomly arriving buyer decides whether to purchase a product or leave the market. Given remaining capacities, firms trade off selling today against shifting demand to competitors to obtain future market power. We provide conditions for the existence and uniqueness of pure-strategy Markov perfect equilibria. In the continuous-time limit, prices solve a system of ordinary differential equations. We derive properties of equilibrium dynamics and show that prices increase the most when the product with the lowest remaining capacity sells. Because firms do not fully internalize the social option value of future sales, equilibrium prices can be inefficiently low such that both firms and consumers would benefit if firms could commit to higher prices. We term this new welfare effect the Bertrand scarcity trap.

Pages: 71 pages
Date: 2024-06
New Economics Papers: this item is included in nep-com, nep-cta, nep-gth, nep-ind, nep-inv, nep-mic and nep-reg
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