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General Equilibrium (without Production) or Exchange (Chapter 31) February 16, 2010
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General Equilibrium Events in one market have effects on other markets (spillovers) Demand for x depends upon prices of complements, substitutes; income Supply of x depends upon factor prices Previously, we’ve taken these as given– doing partial equilibrium analysis But its important to understand interdependence of markets– general equilibrium analysis Partial equilibrium analysis says that competitive markets yield efficient outcomes—is this still true in general equilibrium?
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General Equilibrium Our approach: Simple environment—the entire economy 2 kinds of goods 2 people Focus on exchange Abstract away from production of new goods Give people endowments Specify preferences Allow them to trade Make predictions about behavior of utility-maximizers Evaluate welfare
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Endowment Economy Consumers A and B ; goods 1 and 2 Endowments: ω A = ( ω A 1 , ω A 2 ) and ω B = ( ω B 1 , ω B 2 ) Example: ω A = (6 , 4) and ω B = (2 , 2) This means total endowment of good 1 is ω A 1 + ω B 1 = 6 + 2 = 8 and of good 2 is ω A 2 + ω B 2 = 4 + 2 = 6
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Allocations Endowment represents where people start, but through trade, their allocations may change General allocation or consumption: x A = ( x A 1 , x A 2 ) and x B = ( x B 1 , x B 2 ) ( x A , x B ) is feasible if it uses at most the aggregate endowment: x A 1 + x B 1 ω A 1 + ω B 1 and x A 2 + x B 2 ω A 2 + ω B 2 Helpful graphical tool: Edgeworth Box Allows us to simply depict all feasible allocations
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Edgeworth Box Z A ( , ) 6 4 Z B ( , ) 2 2 O A O B 6 8 4 6 2 2 The endowment allocation The Endowment Allocation
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Edgeworth Box Feasible Reallocations O A O B Z Z 1 1 A B . x A 2 Z Z 2 2 A B . x A 1 x B 1 x B 2
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How do we think about equilibrium? In partial equilibrium analysis: Treat each good separately Find p and q that equate supply and demand But this is general equilibrium analysis: where do supply and demand come from? A and B can trade with each other For everything to be balanced, the amount that A gives up has to equal amount that B receives (for each good, and vice versa) In other words Supply = Demand for each good This will determine prices for each good How do we find supply and demand curves? Go back to utility maximization problem Need to specify preferences to do this
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Utility maximization Preference are given Given prices for each good, endowment bundle serves as income Can write down budget constraint p 1 x 1 + p 2 x 2 p 1 ω 1 + p 2 ω 2 Solve utility maximization problem
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