No Equilibrium in Infinite Economies : Two Examples *
نویسنده
چکیده
The purpose of this paper is to present two examples of an economy possessing an optimum but no competitive equilibrium. Their essential features are having production and preferences over an infinite horizon; in fact, it seems similar examples may not occur in overlapping generations and/or pure exchange models. There is a growing literature of equilibrium existence theorems in this field. We choose to mention here the ones due to Bewley [ 31 and Toussaint [ 71 on production economies, and those of Peleg and Yaari [6] and Wilson [8] on exchange economies. In relation to these results, our first example shows (i) that the assumption in both [3] and [7] on “strongly adequate” endowments cannot be relaxed by itself and (ii) that [6] on [8] do not extend to production. Our second example also satisfies all but one of the assumptions in [3] and [7]. In this case it is continuity of preferences-amounting, roughly, to impatience-which is shown to be necessary for an equilibrium. We elaborate on these points in the section following the examples.
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