Existence of an exact walrasian equilibrium in nonconvex economies

The existence of an exact Walrasian equilibrium in nonconvex economies is still a largely unexplored issue. This paper shows that such an equilibrium exists in nonconvex economies by following the ‘nearby economy’ approach introduced by Postlewaite and Schmeidler (Approximate Walrasian Equilibrium and Nearby Economies, 1981) for convex economies. More precisely, the paper shows that any equilibrium price of the convexified version of a nonconvex economy is an equilibrium price also for a set of ‘perturbed’ economies with the same number of agents. It shows that in this set there are economies that differ from the original economy only as regards preferences or initial endowments.