Working Paper: CEPR ID: DP17092
Authors: Kiminori Matsuyama; Philip Ushchev
Abstract: 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.
Keywords: heterogeneous firms; the Melitz model; HSA; competitive pressures; the 2nd and 3rd laws; markup and passthrough rates; selection; sorting; the composition effect; log supermodularity
JEL Codes: D4; E2; L1; O4
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Decrease in entry cost (D49) | Increase in competitive pressures (L19) |
| Increase in competitive pressures (L19) | Decrease in markup rates of all firms (L11) |
| Decrease in entry cost (D49) | Decrease in markup rates of all firms (L11) |
| Increase in competitive pressures (L19) | Increase in average profit share (D33) |
| Increase in market size (F61) | Tougher selection among firms (L29) |
| Decrease in overhead costs (D21) | Tougher selection among firms (L29) |
| Increase in competitive pressures (L19) | Increase in average markup rates (D49) |