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micro-fall-2007-19

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

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Equilibrium and Production Equilibrium and Producton An economy with a single household and a single °rm Household Preferences: u ( x ; ¯ l ° l ) Endowment: ( ¯ x = 0 ; ¯ l > 0 ) Firm Production function: y ± f ( v ) Pro°t function: π = py ° wv Ani Guerdjikova Fall 2007 182 / 198

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Equilibrium and Production Assumptions of the model The household owns the °rm and receives its total pro°t. Both the household and the °rm are price-takers on the market for labor and on the market for the consumption good. The household and the °rm make their decisions independently of 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; the °rm neglects the e/ect of its demand for labor and supply of consumption on the household±s utility. Ani Guerdjikova Fall 2007 183 / 198
Equilibrium and Production The household±s utility maximization problem 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 ) ² demand for consumption good l ³ = l ( p ; w ; π ) ² supply of labor Ani Guerdjikova Fall 2007 184 / 198

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Equilibrium and Production The °rm±s pro°t maximization problem 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 pro°t functions Ani Guerdjikova Fall 2007 185 / 198
Equilibrium and Production Market equilibrium Equilibrium prices ( p ³ ; w ³ ) and an equilibrium allocation ( x ³ ; y ³ ; l ³ ; v ³ ) such that The household maximizes The °rm maximizes its utility at ( p

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