Abstract
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:
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When utility functions are Leontief and production functions are linear, it is NP-hard to decide if a market has an equilibrium.
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When utility functions and production functions are linear, equilibria are efficiently computable (which was already known for Ricardo).
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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.
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Wilkens, C.A. (2009). The Complexity of Models of International Trade. In: Leonardi, S. (eds) Internet and Network Economics. WINE 2009. Lecture Notes in Computer Science, vol 5929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10841-9_30
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DOI: https://doi.org/10.1007/978-3-642-10841-9_30
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