We characterize the relationship between the distributions of two variables linked by a structural model. We then show that, in models of heterogeneous firms in monopolistic competition, this relationship implies a new demand function that we call “CREMR” (Constant Revenue Elasticity of Marginal Revenue). This demand function is the only one that is consistent with productivity and sales distributions having the same form (whether Pareto, lognormal, or Fréchet) in the cross section, and it is necessary and sufficient for Gibrat's Law to hold over time. Among the applications we consider, we use our methodology to characterize misallocation across firms; we derive the distribution of markups implied by any assumptions on demand and productivity; and we show empirically that CREMR‐based markup distributions provide an excellent parsimonious fit to Indian firm‐level data, which in turn allows us to calculate the proportion of firms that are of suboptimal size in the market equilibrium.

This paper adopts a new approach to the problem of generalizing the properties of the two-by-two Heckscher-Ohlin model, asking whether we can obtain results which hold in very general models for dichotomous categories of commodities and factors. Using duality theory, some results of this kind are derived, which generalize certain properties of the Heckscher-Ohlin model to models which allow for any number of goods and factors, joint production, international factor mobility, and substitution between primary factors and intermediate inputs. The consequences of assuming sector-specific factors and equal numbers of goods and factors' are also examined.

Quotas are the predominant means of protection in developed countries, with quota rents commonly shared between exporter and importer. This paper derives shadow prices appropriate to evaluating trade reform under these circumstances and provides a number of useful sufficient conditions for welfare-improving "piecemeal" reform. In doing so, the authors apply the distorted (quantity-constrained) expenditure function and use implicit separability to derive more powerful results than have previously been available.