Dynamic Competition With Random Demand and Costless Search: A Theory of Price Posting

Abstract

This paper studies a dynamic model of perfectly competitive price posting under demand uncertainty. Firms must produce output in advance. After observing aggregate sales in prior periods, firms post prices for their unsold output. In each period, the demand of a new batch of consumers is randomly activated. Existing customers who have not yet bought and then new customers arrive at the market in random order, observe the posted prices, and either purchase at the lowest available price or delay their purchase decision. We construct a sequential equilibrium in which the output produced and its allocation across consumers is efficient. Thus consumers endogenously sort themselves efficiently, with the highest valuations purchasing first. Transaction prices in each period rise continuously, as firms become more optimistic about demand, followed by a market correction. By the last period, prices are market clearing.