lec25 - Economics 101A (Lecture 25) Stefano DellaVigna...

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Economics 101A (Lecture 25) Stefano DellaVigna April 28, 2009
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Outline 1. Walrasian Equilibrium II 2. Example 3. Existence and Welfare Theorems 4. Asymmetric Information: Introduction
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1 Walrasian Equilibrium Walrasian Equilibrium. ³ ( x 1 1 ,x 1 2 ) , ( x 2 1 ,x 2 2 ) ,p 1 ,p 2 ´ is a Walrasian Equilibrium if: Each consumer maximizes utility subject to bud- get constraint: ( x i 1 ,x i 2 )=a r g m a x x i 1 ,x i 2 u i ³ ( x i 1 ,x i 2 ´ s.t. p 1 x i 1 + p 2 x i 2 p 1 ω i 1 + p 2 ω i 2 All markets clear: x 1 j + x 2 j ω 1 j + ω 2 j for all j.
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O f er curve for consumer 1 : ( x 1 1 ( p 1 ,p 2 , ( ω 1 2 )) ,x 1 2 ( p 1 ,p 2 , ( ω 1 2 ))) O f er curve is set of points that maximize utility as function of prices p 1 and p 2 . Then f nd o f er curve for consumer 2 : ( x 2 1 ( p 1 ,p 2 , ( ω 1 2 )) ,x 2 2 ( p 1 ,p 2 , ( ω 1 2 ))) Figure
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Step 2. Find intersection(s) of two o f er curves Walrasian Equilibrium is intersection of the two o f er curves! Both individuals maximize utility given prices Total quantity demanded equals total endowment
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Relate Walrasian Equilibrium to barter equilbrium. Walrasian Equilibrium is a subset of barter equilib- rium: Does WE satisfy Individual Rationality condition? Does WE satisfy the Pareto E ciency condition? Walrasian Equilibrium therefore picks one (or more)
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lec25 - Economics 101A (Lecture 25) Stefano DellaVigna...

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