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The Homogeneity Postulate and the Laws of Comparative Statics in the Walrasian and Metzleric Systems
Robert A. Mundell
Abstract
The mathematical isomorphism between the Walrasian multi-commodity price system and the Metzleric multi-region income system is not complete even in the well-behaved case of gross substitutes (for the stable price system) and superior goods (for the stable income system). A difference arises because of the price system's characteristic of zero-degree homogeneity which imposes additional constraints upon the inverse. The inverse of the price system has diagonal elements dominating single off-diagonal elements in both the same row and the same column, while the inverse of the income system has diagonal elements which are necessarily dominant only over single elements in the same column. This leads to a whole class of comparative statics propositions for the price system which have no counterpart in the income system and to economic implications about our ability to aggregate sectors or markets for qualitative analysis.
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