The Convexity Assumption in the Theory of Competitive Markets

The object of this paper is to examine how far the allocation of resources brought about by s perfectly competitive market remains optimal when indifference maps and production functions cease to be convex. It has recently been asserted that the allocative efficiency of a competitive system breaks down under these circumstances. If this true, it would constitute s serious limitation, for, as I shall argue. In the real world the relevant functions are often not convex. However, we shall see that the traditional assumptions of convexity are by no means essential to the optimality of competitive markets and that the assertions to the contrary are based on an elementary fallacy. I shall examine in some detail the behavior of competitive markets under conditions of certainty.

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