201Winter2010Class9to10

201Winter2010Class9to10 - Class 9: Competitive Equilibrium...

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Class 9: Competitive Equilibrium An Exchange Economy Consider an economy with two goods and a large number of 2 types of agents. Each agent of type A has endowment ! A 1 of good 1 and endowment ! A 2 of good 2, and each agent of type B has endowment ! B 1 of good 1 and endowment ! B 2 of good 2 An allocation is denoted by X = x A 1 ; x A 2 ; x B 1 ; x B 2 ± ; where x j i denotes the consumption of good i by agent j: Assume that each agent takes prices p 1 and p 2 that there is a large number of each type of agents. The budget constraint of an agent with endowment ( ! 1 ; ! 2 ) is now p 1 x 1 + p 2 x 2 = p 1 ! 1 + p 2 ! 2 : This can be rewritten as x 2 = p 1 p 2 ( ! 1 x 1 ) + ! 2 . The budget constraint thus goes through the endowment point ( ! 1 ; ! 2 ) : FIGURE 9.1 HERE Competitive Equilibrium 1. Each agent takes prices as given. 2. Each agent makes optimal choice. 3. The equilibrium allocation is feasible. 1
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[SKIP TO CLASS 10; THE REST OF CLASS 9 WILL BE COVERED AFTER MIDTERM 1] thus characterized by conditions x A 1 + x B 1 = ! A
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201Winter2010Class9to10 - Class 9: Competitive Equilibrium...

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