micro-fall2007-15 - Cost Minimization Cost Minimization...

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Cost Minimization Cost Minimization (contd.) The solution of the cost minimization problem determines: ( i ) the conditional factor demand: ˆ v 1 = ˆ v 1 ( w 1 ; w 2 ; ¯ y ) ˆ v 2 = ˆ v 2 ( w 1 ; w 2 ; ¯ y ) ( ii ) the cost function: ˆ e = c ( w 1 ; w 2 ; ¯ y ) Ani Guerdjikova ECON 313 Fall 2007 154 / 171
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Cost Minimization 6 - T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T v 1 v 2 f ( v 1 ; v 2 ) = ¯ y w 1 w 2 e 0 w 1 ˆ e w 1 e 00 w 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ˆ v 1 ˆ v 2 Cost minimization problem Ani Guerdjikova ECON 313 Fall 2007 155 / 171
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Cost Minimization Example Cobb-Douglas production function f ( v 1 ; v 2 ) = Av a 1 v b 2 Conditional factor demand: ˆ v 1 ( w 1 ; w 2 ; ¯ y ) = " ¯ y A a b w 2 w 1 ± b # 1 a + b ˆ v 2 ( w 1 ; w 2 ; ¯ y ) = ² ¯ y A b a w 1 w 2 ± a ³ 1 a + b Cost function: c ( w 1 ; w 2 ; ¯ y ) = w a a + b 1 w b a + b 2 ¯ y A ± 1 a + b ² ´ a b µ b a + b + ´ a b µ a a + b ³ . Ani Guerdjikova ECON 313 Fall 2007 156 / 171
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Example Limitational production function f ( v 1 ; v 2 ) = min f av 1 ; bv 2 g Conditional factor demand: ˆ v 1 ( w 1 ; w 2 ; ¯ y ) = ¯ y a ˆ v 2 ( w 1 ; w 2 ; ¯ y ) = ¯ y b Cost function: c ( w 1 ; w 2 ; ¯ y ) = ¯ y h w 1 a + w 2 b i . Ani Guerdjikova
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micro-fall2007-15 - Cost Minimization Cost Minimization...

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