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Unformatted text preview: Economics 201BSecond Half Lecture 2 Two Graphical Proofs of the Existence of Walrasian Equilibrium in the Edgeworth Box Demand: D i ( p ) = { x B i ( p ) : y B i ( p ) x i y } Walrasian Equilibrium (in the Edgeworth Box) is a pair ( p, x ) where x is an exact allocation x i D i ( p ) ( i = 1 , 2) In the following Edgeworth Box Diagram, we give a graphical rep resentation of Walrasian Equilibrium. In fact, there are (at least) three Walrasian Equilibria in the drawing, and there is nothing apparently pathological in the preferences of the two agents. 1 Why the quotes on Proofs? Why the Proofs inside the quotes? graphical arguments prone to introduction of tacit assumptions these arguments can be turned into proofs; our real proof later follows the first of the two proofs Price Normalization: p = { p R 2 ++ : p 1 + p 2 = 1 } ; = { p R 2 + : p 1 + p 2 = 1 } Notation: D ( p ) = D 1 ( p ) + D 2 ( p ) Market Demand E i ( p ) = D i ( p ) i Excess Demand of i E ( p ) = E 1 ( p ) + E 2 ( p ) = D ( p ) Market Excess Demand Offer Curve: OC i = { x : p x D i ( p ) } This is a curve in the Edge worth Box Diagram;...
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This note was uploaded on 08/01/2008 for the course ECON 201B taught by Professor Anderson during the Spring '06 term at University of California, Berkeley.
 Spring '06
 ANDERSON
 Economics

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