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201Lecture22006

201Lecture22006 - Economics 201B–Second Half Lecture 2...

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Unformatted text preview: Economics 201B–Second 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 ∈ Δ = { p ∈ R 2 ++ : p 1 + p 2 = 1 } ; Δ = { 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 ) − ω i Excess Demand of i • E ( p ) = E 1 ( p ) + E 2 ( p ) = D ( p ) − ¯ ω Market Excess Demand • Offer Curve: – OC i = { x : ∃ p ∈ Δ x ∈ D i ( p ) } This is a curve in the Edge- worth Box Diagram;...
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201Lecture22006 - Economics 201B–Second Half Lecture 2...

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