Discussion paper

DP17092 Selection and Sorting of Heterogeneous Firms through Competitive Pressures

We apply the H.S.A. (Homotheticity with a Single Aggregator) class of demand systems to the Melitz (2003) model of monopolistic competition with firm heterogeneity. H.S.A., which contains CES and translog as special cases, 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 the free-entry equilibrium and conduct general equilibrium comparative static analysis with sharp analytical results, often just by using simple diagrams. Because the single aggregator enters all firm-specific variables proportionately with the firm-specific marginal cost, thereby acting as a magnifier of firm heterogeneity, we are able to characterize how a change in competitive pressures, whether due to a change in the entry cost, market size, or in the overhead cost, causes reallocation across firms and selection and sorting of firms across markets, thereby affecting the distribution of firm-specific variables. Furthermore, we are able to show that, due to such a composition effect, the average markup (pass-through) rate may move in the opposite direction of the firm-level markup (pass-through) rate, which means that the average markup rate and the aggregate profit share may go up due to (not in spite of) more competitive pressures.


Matsuyama, K and P Ushchev (2022), ‘DP17092 Selection and Sorting of Heterogeneous Firms through Competitive Pressures‘, CEPR Discussion Paper No. 17092. CEPR Press, Paris & London. https://cepr.org/publications/dp17092