• Yes

We study the role of competitive pressures in selection and sorting of heterogeneous firms using a flexible class of homothetic demand systems we developed in our earlier work, the so-called HSA (Homothetic with a Single Aggregator). Although it is a nonparametric class, it retains much of the tractability of the well-known CES aggregator, which has restrictive properties, one of them being shutting down competitive pressure effects. Working with a non-specified productivity distribution and a non-specified shape of the demand functions, we are still able to obtain the existence result, the uniqueness result, and a rich set of cross-sectional implications and general-equilibrium implications. The cornerstone of the analysis is exploiting the linkages between the behavior of various elasticities and the log-supermodularity property. We also show that the 2nd Marshall's Law (i.e., the price elasticity of demand increases in price) is necessary and sufficient for perfect sorting in a multi-market extension of our model: more productive firms choose to operate at larger, hence more competitive, markets.