Non-convex Preferences Research Articles

Market Games with Indivisible Commodities and Non-Convex Preferences

Market Games with Indivisible Commodities and Non-Convex Preferences

Quasi-Equilibria in Markets with Non-Convex Preferences

Quasi-Equilibria in Markets with Non-Convex Preferences

Quasi-Cores in a Monetary Economy with Nonconvex Preferences

Abstract : A model of a pure exchange economy is investigated without the usual assumption of convex preference sets for the participating traders. The concept of core, taken from the theory of games, is applied to show that if there are sufficiently many participants, the economy as a whole will possess a solution that is sociologically stable--i.e., that cannot profitably be upset by any coalition of traders.

On Convexity, Efficiency, and Markets

IN HIS stimulating article, Convexity Assumption in the Theory of Competitive Markets,1 Mr. M. J. Farrell proposes reduce the minimum assumptions necessary for the validity of the 'received theory' demonstrating the traditional assumptions of convexity are no means essential to the optimality of competitive markets. In the process, he chides Mr. J. de V. Graaff and me for having engaged in facile attacks on the theory of competitive allocation, in debunking which should be taken with a grain of salt. In particular, he claims that Graaff and I were led into elementary error by a rather farfetched analogy between competitive markets and one-man economies. The purpose of this note is (1) to substantiate a plea of not guilty to Farrell's charge; and (2) to raise a question about his suggestion for broadening the basis of the received theory. I shall restrict myself to discussing only those parts of the Farrell paper which deal with non-convexity in production functions, partly because it is production non-convexities which are alleged to have led me astray, and partly because, in an article in the October, 1960, issue of this Journal,2 Jerome Rothenberg has dealt rather fully with Farrell's treatment of nonconvex preferences.3