Continuity of equilibria for economies with vanishing external effects

Abstract

We consider in this paper the set of noncooperative equilibria of private ownership economies with external effects as defined in [1]. Using a mathematical description and apparatus similar to the one introduced in [2], we show that for most economies (in fact an open and dense subset) the set of equilibria contains only a finite number of points, which are continuous functions of the economy. This means, in particular, that for most economies the limit of the noncooperative equilibria when the external effects go to zero is the set of usual competitive equilibria of the limit economy.