theoryfinal08 - Final Exam, Econ 210A, December, 2008...

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Unformatted text preview: Final Exam, Econ 210A, December, 2008 Please use a blue book for your answers. 1) Firm A has production function f ( x 1 ,x 2 ) = x 1 / 2 1 + x 1 / 2 2 2 k where k > 0. a) For what values of k is f a quasi-concave function? For what values of k is f a concave function? Explain your answers. Firm B has production function g ( x 1 ,x 2 ) = ( x 2 1 + x 2 2 ) k/ 2 where k > 0. b) For what values of k is g a quasi-concave function? For what values of k is g a concave function? Explain your answers. 2) Firm A, described in Problem 1, is a price-taker in the factor market and must pay w 1 per unit of factor 1 and w 2 per unit of factor 2 that it uses. a) Find its conditional input demand functions x 1 ( w 1 ,w 2 , 1) and x 2 ( w 1 ,w 2 , 1) for producing one unit of output. b) Find its conditional input demand functions x 1 ( w 1 ,w 2 ,y ) and x 2 ( w 1 ,w 2 ,y ) for producing y units of output in the case where k = 1. c) Find its conditional input demand functions x 1 ( w 1 ,w 2 ,y ) and x 2 ( w 1 ,w 2 ,y ) for producing y units of output for arbitrary k . 3) Firm B, described in Problem 1, is a price-taker in the factor market and must pay w 1 per unit of factor 1 and w 2 per unit of factor 2 that it uses....
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theoryfinal08 - Final Exam, Econ 210A, December, 2008...

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