11 - MS&E 241: ECONOMIC ANALYSIS Thomas A. Weber 11....

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MS&E 241: ECONOMIC ANALYSIS Thomas A. Weber 11. (Optional) General Equilibrium, Part I Winter 2009 Stanford University Copyright © 2009 T.A. Weber All Rights Reserved -2- MS&E-241-Winter-2009-TAW AGENDA General Equilibrium: The Standard Model Pure Exchange Production Economies Key Concepts to Remember
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-3- MS&E-241-Winter-2009-TAW THE STANDARD MODEL Basic Assumptions : goods , consumers , - Each consumer has a rational (i.e., complete and transitive) preference ordering over representable by a continuous utility function . Consumers are price takers firms , - Each firm has a production set · Nonempty and closed · No free lunch ( ; can’t produce something from nothing) · Possibility of inaction ( ) · Free disposal ( ) · Irreversibility ( ) Initial endowments : each consumer starts with an endowment vector and a fractional share distribution , where for each firm with N f Y N } ,..., 1 { N i C } ,..., 1 { C c F } ,..., 1 { F f } 0 { + N f Y f Y 0 f N f Y Y + f f Y y Y y } 0 { \ f c N + + N c u : N c + ω c } ,..., { 1 c F c c θ = ] 1 , 0 [ c f 1 1 = = C c c f ( Private Ownership Economy ) f -4- MS&E-241-Winter-2009-TAW WALRASIAN EQUILIBRIUM Definition : A Walrasian equilibrium (WE) is a specification of a price vector , a demand vector for each consumer , and a supply vector for each firm , such that profit maximization , i.e., utility maximization , i.e., where consumer c’s budget set is given by with total income demand = supply , hold. N p + N c x + c f f Y y f y p y f Y y f max arg ) ( max arg ) , ( x u x c I p B x c c } : { ) , ( c N c c I x p x I p B B = = + = + = F f f c f c c y p p I 1 ) ( = = = + = F f f C c c C c c y x 1 1 1 (i.e., allocation is feasible )
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-5- MS&E-241-Winter-2009-TAW AGENDA General Equilibrium: The Standard Model Pure Exchange Production Economies Key Concepts to Remember -6- MS&E-241-Winter-2009-TAW PURE EXCHANGE IS A SPECIAL CASE OF THE STANDARD MODEL Consider an “exchange economy” without firms and without production Two goods , 1 and 2 M consumers of each of two types , 1 and 2 Each consumer of type begins with an allocation (his endowment) and solves a utility maximization problem given a price vector , which defines his “offer curve” , Any feasible allocation satisfies This two-consumer two-good exchange economy can be represented graphically using a “ Edgeworth box ” (sometimes also referred to as “Edgeworth-Bowley Diagram”). ) ( max arg ) ( ) , ( x u p x c p p B x c c ω } 2 , 1 { c 2 + c 2 1 2 1 + = + x x 2 + p
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-7- MS&E-241-Winter-2009-TAW EDGEWORTH BOX Consider one consumer of each type , Ms. 1 and Mr. 2 Any allocation of the totally available quantities of good i can be represented as a point in the Edgeworth box 2 1 i i i ω + = -8- MS&E-241-Winter-2009-TAW THERE MAY BE GAINS FROM TRADE
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-9- MS&E-241-Winter-2009-TAW PARETO-OPTIMAL ALLOCATIONS AND CONTRACT CURVE -10- MS&E-241-Winter-2009-TAW BUDGET LINE AND BUDGET SETS
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11 - MS&E 241: ECONOMIC ANALYSIS Thomas A. Weber 11....

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