Regular economies with non-ordered preferences
We consider exchange economies with non-ordered preferences and externalities. Under continuity and boundary conditions, we prove an index formula, which implies the existence of equilibria for all initial endowments, and the upper semi-continuity of the Walras correspondence. We then posit a differentiability assumption on the preferences. It allows us to prove that the equilibrium manifold is a nonempty differentiable sub-manifold of an Euclidean space. We define regular economies as the regular values of the natural projection. We show that the set of regular economies is open, dense and of full Lebesgue measure. From the index formula, one deduces that a regular economy has a finite odd number of equilibria, and, for each of them, the implicit function theorem implies that there exists a local differentiable selection. So, even with only non-ordered preferences and externalities, exchange economies have nice properties for equilibrium analysis.
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- Shannon, Chris, 1994. "Regular nonsmooth equations," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 147-165, March.
- Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May.
- Debreu, Gerard, 1970.
"Economies with a Finite Set of Equilibria,"
Econometric Society, vol. 38(3), pages 387-92, May.
- Smale, S., 1974. "Global analysis and economics IV : Finiteness and stability of equilibria with general consumption sets and production," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 119-127, August.
- Mas-Colell,Andreu, 1985.
"The Theory of General Economic Equilibrium,"
Cambridge University Press, number 9780521265140, Junio.
- Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-87, May.
- Smale, S., 1974. "Global analysis and economics IIA : Extension of a theorem of Debreu," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 1-14, March.
- Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 237-246, December.
- Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
- Dierker, Egbert, 1993. "Regular economies," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 17, pages 795-830 Elsevier.
- Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
- Rader, J Trout, 1973. "Nice Demand Functions," Econometrica, Econometric Society, vol. 41(5), pages 913-35, September.
- Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
- Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
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