Global analysis and economics IIA: Extension of a theorem of Debreu
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Cited by (75)
Endowment-regarding preferences
2021, Journal of Mathematical EconomicsCompetitive equilibria in semi-algebraic economies
2010, Journal of Economic TheoryGeneral consumption constraints and regular economies
2008, Journal of Mathematical EconomicsCitation Excerpt :In the first works about regularity, the demand or excess demand functions are smooth everywhere. But, several extensions have been done to encompass various sorts of constraints, Smale (1974a, b), Mas-Colell (1985), Balasko et al. (1990), Cass (1990),Villanacci (1993), Polemarchakis and Siconolfi (1997), Cass et al. (2001), Villanacci and Zenginobuz (2005), Bonnisseau and Rivera Cayupi (2006), among others, which means that the demand functions exhibit non-differentiability since nothing prevents the equilibrium allocations to be on the boundary of the consumption sets. To prove generic differentiability and regularity results, we follow the strategy laid out in Cass et al. (2001), in which a general method for encompassing individual portfolio constraints while still permitting differential techniques is given.
The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?
2007, Journal of Economic Dynamics and ControlThe indeterminacy of equilibrium city formation under monopolistic competition and increasing returns
2006, Journal of Economic TheoryExistence of competitive equilibria with externalities: A differential viewpoint
2006, Journal of Mathematical EconomicsCitation Excerpt :The following theorem is the main result of the paper. Following the seminal work by Smale (1974), we use homotopy arguments (Theorem 7) to prove the above theorem. Theorem 7 is a consequence of the homotopy invariance of topological degree, a well-known result in degree theory.