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The One Dimensional Kakutanis Fixed Point Theorem in Problems of Fair Division: A Classroom Capsule

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  • Lahiri Somdeb

Abstract

In this paper, we provide a simple proof of the one-dimensional version of the Kakutani’s fixed point theorem, which is required to prove the existence of a Walrasian equilibrium in a two commodity multi-agent economy where preferences are convex. In a final section of this paper we apply the Kakutani’s fixed point theorem to prove the existence of what we call an equitable equilibrium with rationing in a model where each individual is endowed with positive quantities of two goods. The solution is very similar to the solution due to Dreze (1975) except that ours is not a fixed price solution. It is a problem of resource allocation from an initial position and the solution we propose falls within the general category of non-Walrasian equilibria.

Suggested Citation

  • Lahiri Somdeb, 2000. "The One Dimensional Kakutanis Fixed Point Theorem in Problems of Fair Division: A Classroom Capsule," IIMA Working Papers WP2000-04-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    • Handle: RePEc:iim:iimawp:wp01674
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