The purpose of this paper is to study the differentiability properties of equilibrium prices and allocations in a linear exchange economy when the initial endowments and utility vectors vary. We characterize an open dense subset of full measure of the initial endowment and utility vector space on which the equilibrium price vector is a real analytic function, hence infinitely differentiable function. We provide an explicit formula to compute the equilibrium price and allocation around a point where it is known. We also show that the equilibrium price is a locally Lipschitzian mapping on the whole space. Finally, using the notion of the Clarke generalized gradient, we prove that linear exchange economies satisfy a property of gross substitution.
Publié le : 2001-07-05
Classification:
equilibrium manifold,
sensitivity analysis,
general equilibrium,
linear utility functions,
[SHS.ECO]Humanities and Social Sciences/Economies and finances,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{halshs-00265685,
author = {Bonnisseau, Jean-Marc and Florig, Michael and Jofr\'e, Alejandro},
title = {Differentiability of Equilibria for Linear Exchange Economies},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/halshs-00265685}
}
Bonnisseau, Jean-Marc; Florig, Michael; Jofré, Alejandro. Differentiability of Equilibria for Linear Exchange Economies. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/halshs-00265685/