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 production markets). For both models, we show three types of results: 1. When utility 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.