A note on continuously decomposed evolving exchange economies
It is routine to demonstrate in the exchange economy framework that small changes of individual preferences and endowments always result in small changes of the derived excess demand functions as one should expect. Though being as desirable for reasons of the consistency of the whole approach, however, a precise proof of the converse direction so far is still open to question. The present paper shows that it is actually true. We use a decomposition method for aggregate excess demand functions developed by Mas-Colell which is derived from the well-known decomposition method developed by Sonnenschein and perfected by Debreu and Mantel. Our result fills in a notorious gap in the line of economic justification usually given for this decomposition, or disaggregation, method in that comparative static analysis would be restricted if the decomposition of excess demand functions would not be continuous. Copyright Physica-Verlag 2006
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Volume (Year): 14 (2006)
Issue (Month): 3 (September)
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- Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
- Mas-Colell,Andreu, 1985.
"The Theory of General Economic Equilibrium,"
Cambridge University Press, number 9780521265140, December.
- Allen, Beth, 1981. "Utility perturbations and the equilibrium price set," Journal of Mathematical Economics, Elsevier, vol. 8(3), pages 277-307, October.
- Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
- Bottazzi, Jean-Marc & Hens, Thorsten, 1996. "Excess Demand Functions and Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 68(1), pages 49-63, January.
- A. P. Kirman & K. J. Koch, 1986. "Market Excess Demand in Exchange Economies with Identical Preferences and Collinear Endowments," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 457-463.
- Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
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