Differentiability of equilibria for linear exchange economies

The purpose of this paper is to study the differentiability properties of e quilibrium prices and allocations in a linear exchange economy when the ini tial endowments and utility vectors vary. We characterize an open dense sub set of full measure of the initial endowment and utility vector space on wh ich the equilibrium price vector is a real analytic function, hence infinit ely 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 wh ole space. Finally, using the notion of the Clarke generalized gradient, we prove that linear exchange economies satisfy a property of gross substitut ion.