Constrained Optimality and the Welfare Effects of Misallocation

Frictions that misallocate production factors across heterogeneous firms are costly. Not only it reduces the economy's average productivity, but it also carries a welfare loss, due to its general equilibrium effect on entry, exit and the number of firms. The goal of this paper is to provide an investigation of the different sources of welfare costs, and a quantification of their relative contributions. To this aim, we study the problem of a social planner that faces a distribution of productivity-specific distortions identical to that of the competitive equilibrium's, and explore the constrained efficiency properties of the allocation in the decentralized economy, both in terms of its distribution of factors across firms, and in the allocation of resources into production, entry and fixed production costs. The model features a single homogeneous good produced by heterogeneously productive competitive producers operating a decreasing returns to scale technology. Firms enter and exit the economy endogenously, and display life-cycle dynamics driven by a stochastic process for idiosyncratic productivity. Misallocation arises as a result of a stationary distribution of productivity-specific revenue taxes and subsidies. We show analytically that although the static problem of allocating resources across a given set of firms is efficiently performed by the competitive economy, the decisions to create and destroy firms are not. The direction of the inefficiency depends on the properties of the distribution of distortions. For the cases where distortions divert resources away from the most productive towards the least efficient firms, the social planner's long run optimal number of firms is smaller than the competitive equilibrium's. Had there been no misallocation frictions, the competitive equilibrium would have indeed satisfied Pareto Optimality. When calibrating the model, we find the welfare gain of transiting from the social planner's distorted long run allocation to the frictionless one to be 30% smaller than that of starting from the decentralized distorted long run equilibrium. That is, 30% of the aggregate welfare gains of misallocation reversal are accounted for by the inefficient response of entry and exit in the distorted competitive equilibrium.