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Unformatted text preview: Homework 4, Spring 08 (Total 20 points), Due on Mar. 4, Tue. Q1 (2pt. each): The production function of Bevo Chemical, Co. is f ( x 1 ,x 2 ) = x 1 4 1 x 1 3 2 . (i) What is the marginal product of each input, MP 1 ( x 1 ,x 2 ), MP 2 ( x 1 ,x 2 ), respectively? (ii) What is the technological rate of substitution TRS ( x 1 ,x 2 )? (iii) Given output price p and input price ( w 1 ,w 2 ), solve the profit max imization problem and obtain the factor demand functions x 1 ( p,w 1 ,w 2 ), x 2 ( p,w 1 ,w 2 ) and supply function y ( p,w 1 ,w 2 ). (iv) Given output level y and input price ( w 1 ,w 2 ), solve the costminimization problem and obtain the conditional factor demand functions x 1 ( y,w 1 ,w 2 ), x 2 ( y,w 1 ,w 2 ) and cost function C ( y,w 1 ,w 2 ). Answer : (i) MP 1 ( x 1 ,x 2 ) = 1 4 x 3 4 1 x 1 3 2 MP 2 ( x 1 ,x 2 ) = 1 3 x 1 4 1 x 2 3 2 (ii) TRS ( x 1 ,x 2 ) = MP 1 ( x 1 ,x 2 ) MP 2 ( x 1 ,x 2 ) = 3 x 2 4 x 1 (iii) The problem is max x 1 ,x 2 px 1 4 1 x 1 3 2 w 1 x 1 w 2 x 2 Since the maximization condition is...
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 Spring '10
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