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Unformatted text preview: John Riley 22 September 2006 Econ 200 Diagnostic Test Summer 2006 Time allowed: ninety (90) minutes. Answer three questions only. You must answer question 4 and any two of the first three questions. 1. Profit maximization A firm sells two products. The cost of producing 1 2 ( , ) q q q = is 2 1 2 ( ) ( 2 ) C q q q = + . The demand price functions are 1 1 1 2 2 2 ( ) , ( ) 180 p q a q p q q = - =- . (a) If 120 a = show that the profit-maximizing output is (20,10) q = (b) If 72 a , show that profit is maximized by producing only commodity 2. (c) For what values of the parameter a is it profitable to produce both commodities? 2. Production decision A division of a firm can, using input vector 1 2 ( , ) z z z = , produce 2 2 1 2 ( ) q z z z = . units of output. The manager is given a total budget C and told to produce as much output as possible. Units of input i can be produced at the fixed input price i r ....
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