Markups, pass-through, and firm heterogeneity with sequentially mixed search

We study the determination of market power at the firm and industry levels when heterogeneous firms compete for sales to ex ante homogeneous buyers in a market with both directed and random search and free entry of firms that differ in productivity. Search and the distribution of productivity across active firms generate distributions of equilibrium prices and markups that we relate to variation in the elasticity of demand at the firm level. With directed search at the outset, a shock that raises the matching rate for buyers improves conditions for them and tends to lower markups. Random matching follows sequentially, and the same shock can lower the productivity threshold for operation, pushing up prices and markups for all firms. The net effect on market power can be ambiguous depending on the forces driving matching rates. The distributions of prices and markups respond in equilibrium to changes in common and firm-specific costs, consumption utility, and fixed costs of both entry and operation. We characterize the differential pass-through of these changes to prices and markups at both the firm and market levels.