On the pseudo-equilibrium manifold in semi-algebraic economies with real financial assets
The aim of this paper is to prove that if the consumption set of an economy with incomplete financial markets is semi-algebraic, then the corresponding pseudo-equilibrium manifold is also semi-algebraic. For this, we proceed by constructing an incomplete financial economy with real assets and semi-algebraic utility functions. Then, we show that the spot-equilibrium set and the pseudo-equilibrium set are smooth semi-algebraic manifolds. We extent this results by showing that the pseudo-equilibrium natural projection is a semi-algebraic diffeomorphism in each regular point of the semi-algebraic pseudo-equilibrium manifold. It is directly related with the local determinacy of pseudo-equilibrium.
|Date of creation:||09 Mar 2014|
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- Blume, Lawrence E & Zame, William R, 1994.
"The Algebraic Geometry of Perfect and Sequential Equilibrium,"
Econometric Society, vol. 62(4), pages 783-794, July.
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- Felix Kuber & Karl Schmedders, 2007. "Competitive Equilibria in Semi-Algebraic Economies," PIER Working Paper Archive 07-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
- DEBREU, Gérard, "undated". "Economies with a finite set of equilibria," CORE Discussion Papers RP 67, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Zhou, Yuqing, 1997. "Genericity Analysis on the Pseudo-Equilibrium Manifold," Journal of Economic Theory, Elsevier, vol. 73(1), pages 79-92, March. Full references (including those not matched with items on IDEAS)
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