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http://hdl.handle.net/11718/784
Title: | One dimensional Kakutani's fixed point theorem in problems of fair division: a classroom capsule |
Authors: | Lahiri, Somdeb |
Keywords: | Fixed point theorems (Topology) |
Issue Date: | 16-Jan-2010 |
Series/Report no.: | WP;2000-04-01/1593 |
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. |
URI: | http://hdl.handle.net/11718/784 |
Appears in Collections: | Working Papers |
Files in This Item:
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WP 2000_1593.pdf | 423.51 kB | Adobe PDF | View/Open |
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