Market versus optimum allocation in open economies

A large body of theoretical and quantitative work concerns models of heterogeneous firms and monopolistic competition. But most of it relies on strong assumptions regarding demand structure, firm-productivity distribution, and country heterogeneity. This paper studies a general-equilibrium model with directly explicitly additive preferences, non-specified productivity distributions, and asymmetric countries, for which much less is known. We first prove the existence and uniqueness of the market equilibrium with a three-stage approach of analyzing competition intensities and wages. We then explore the market-allocation mechanism and provide a baseline comparison between the market and a utilitarian optimum from a global planner's perspective. We show that misallocation in open economies can be decomposed into two effects, driven by country asymmetry and the variable elasticity of substitution. We present two examples exhibiting constant and variable markups, respectively, to illustrate how to apply our general theorem.