Pricing in a Frictional Product Market

Recent research argues that a key factor limiting firm growth is the gradual accumulation of product market demand. Motivated by this evidence, this paper studies firm price setting and growth in a frictional product market where firms accumulate customers over time. In this competitive search model of firm growth, firms face a trade-off in setting prices each period, between making profits on existing customers with high prices, and attracting new customers with low prices. Firms with more existing customers choose higher prices, attract fewer new customers, and grow more slowly, than those with less. I show that if a new firm has full commitment to future prices, it can attain efficient growth through its lifetime. This plan is not time consistent, however: if a firm with existing customers reoptimizes, it will choose a higher price today than planned. I study firm pricing and growth when the firm does not have commitment to future prices, focusing on Markov perfect equilibria. The baseline model considers an industry with a single monopolistically competitive firm, but I also consider the impact of a competitive fringe on the monopolist’s pricing, a version with a continuum of firms within the industry that delivers an equilibrium theory of price dispersion, as well as the implications for firm responses to shocks to demand and costs.