Selection and Sorting of Heterogeneous Firms through Competitive Pressures

We study how heterogenous firms differ in their responses to increased competitive pressures caused by a lower entry cost, an increase in market size, and globalization, and how these changes affect selection and sorting of heterogeneous firms. To this end, we model a monopolistic competitive sector with heterogenous firms and free-entry using H.S.A. (Homothetic Single Aggregator) class of demand systems, which contains CES and translog as special cases. H.S.A. is tractable due to its homotheticity and to its single aggregator that serves as a sufficient statistic for competitive pressures. It is also flexible enough to allow for the choke price, the 2nd and 3rd laws of demand. We prove the existence and uniqueness of equilibrium and conduct comparative static analysis on the distributions of the markup and pass-through rates across firms, as well as the firm size distribution, measured in the revenue, profit, and employment with sharp analytical results, often just by using simple diagrams. A decline in the entry and overhead costs, and an increase in market size create more competitive pressures, which lead to a decline in the markup rate (under the 2nd law) and an increase in the pass-through rate (under the 3rd law) in all firms. At the same time, they cause reallocation to more productive firms with higher markup and lower pass-through rates. Due to such a composition effect, the average markup rate and the aggregate profit share may go up and the average pass-through rate may go down due to (not in spite of) more competitive pressures. We also characterize how heterogenous firms sort themselves across markets with different sizes and how the markup and pass-through rates of heterogenous firms in the domestic and export markets respond to globalization caused by a reduction in the iceberg cost.