201Lecture22006 - Economics 201BSecond Half Lecture 2 Two...

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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.

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201Lecture22006 - Economics 201BSecond Half Lecture 2 Two...

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