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A Calculus Approach to the Theory of the Core of an Exchange Economy

Leif Johansen

American Economic Review 1978

The theory of the shrinking of the core of an exchange economy to the competitive equilibrium (or set of equilibria) when the number of participants increases is one of the most important and interesting contributions to general equilibrium theory in recent decades, and ought to become part of standard courses in economic theory. It is important to have an exposition of this idea which appears as a simple and natural extension of the tools of analysis familiar to most students of economics. The purpose of the present paper is to make an attempt at such an exposition along traditional calculus lines. The paper does not contain results which are new to specialists in the field. In the literature there are, of course, some expositions which point in the direction taken here, but I have not seen the approach spelled out in the way it is done in the sequel. (Some relevant references are given at the end of the paper.)

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