Boundary Behaviour of Equilibria for Linear Exchange Economies

We study the Walras equilibrium price function of a linear exchange economy. We show that it is locally Lipschitz with respect to utility functions and initial endowments on the relative interior of the set of parameters where the price is unique. We also prove that it is never locally Lipschitz on the boundary. This extend previous result of J. M. Bonnisseau, M. Florig and A. Jofre [J. Optimization Theory Applications 109 (2001) 237--263, 264--288].