micro-fall-2007-19

micro-fall-2007-19 - Equilibrium and Production Equilibrium...

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Equilibrium and Production Equilibrium and Producton Household Preferences: u ( x ; ¯ l l ) Endowment: ( ¯ x = 0 ; ¯ l > 0 ) Firm Production function: y ± f ( v ) π = py wv Ani Guerdjikova ECON 313 Fall 2007 182 / 198

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Equilibrium and Production Assumptions of the model labor and on the market for the consumption good. each other, i.e. the household neglects the e/ect of its supply for labor and demand for consumption on the &rm±s pro&t; consumption on the household±s utility. Ani Guerdjikova ECON 313 Fall 2007 183 ² 198
Equilibrium and Production max x ; l u ( x ; ¯ l l ) , s.t. px ± wl + π 0 ± l ± ¯ l , x ² 0. Solution: x ³ = x ( p ; w ; π ) ± demand for consumption good l ³ = l ( p ; w ; π ) ± supply of labor Ani Guerdjikova ECON 313 Fall 2007 184 / 198

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Equilibrium and Production max y ; v π = py wv , s.t. y ± f ( v ) y ² 0, v ² 0. Solution : y ³ = y ( p ; w ) ² supply of consumption good v ³ = v ( p ; w ) ² demand for labor π ³ = π ( p ; w ) ² Ani Guerdjikova ECON 313 Fall 2007 185 / 198
Equilibrium and Production Market equilibrium Equilibrium prices ( p ; w ) and an equilibrium allocation ( x ; y ; l ; v ) such that The household maximizes its utility at ( p ; w ; π ) : ( p ; w ) : x = x ( p ; w ; π

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micro-fall-2007-19 - Equilibrium and Production Equilibrium...

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