Firm Dynamics and Pricing Under Customer Capital Accumulation

What is the relationship between the rate at which firms accumulate their stock of demand over time and the prices that they set for their products? This paper analyzes the implications of customer capital accumulation for pricing behavior and firm dynamics. We build a tractable directed search model of the product market in which firms are ex-post heterogeneous in their customer base and commit to the prices they post. The model features dynamic contracts with endogenous customer reallocation, endogenous entry and exit of firms, and allows for a tractable characterization of the firm distribution. In equilibrium, there is price rigidity at the firm level, and price dispersion in the cross-section because firms of different sizes use different pricing strategies to strike a balance between attracting new customers and retaining incumbent ones. We show that our mechanism can generate realistic firm dynamics, a right-skewed firm size distribution, and various predictions on the cross-sectional distribution of prices, markups, and the rate and frequency of price changes