The Complexity of Models of International Trade

We show a range of complexity results for the Ricardo and Heckscher-Ohlin models of international trade (as Arrow-Debreu prodution markets). For both models, we show three types of results: 1. When functions are Leontief and production functions are linear, it is NP-hard to decide if a market has an equilibrium. 2. When utility functions and production functions are linear, equilibria are efficiently computable (which was already known for Ricardo). 3 When utility functions are Leontief, equilibria are still efficiently computable when the diversity of producers and inputs is limited. Our proofs are based on a general reduction between production and exchange equilibria. One interesting byproduct of our work is a generalization of Ricardo's Law of Comparative Advantage to more than two countries, a fact that does not seem to have been observed in the Economics literature.