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Unformatted text preview: John Riley corrected 23 September 2006 Econ 200 Diagnostic Test Summer 2005 Time allowed: ninety (90) minutes. Attempt three (3) questions only. 1. Profit maximization A firm sells two products. The cost of producing 1 2 ( , ) q q q = is 2 1 2 ( ) ( ) C q q q = + . The demand price functions are 1 1 1 2 2 2 ( ) 2 , ( ) 40 p q a q p q q =  = . (a) If 20 a = show that the profitmaximizing output is (0,10) q = (b) Show that for all smaller a the profitmaximizing choice is still (0,10) q = . (c) Show that for all 20 a > the profitmaximizing output of product 1 is strictly positive. 2. Consumer choice Alex has utility function 2 1 2 ( ) , , , A U x x x x α β α β + = ∈ > R . His income is I and the price vector is p . (a) Explain why his utility maximizing choice is the solution to the following problem. 1 2 { ln ln  0, 0} x Max x x x I p x α β + ≥ ⋅ ≥ (b) Hence or otherwise solve for his utility maximizing consumption vector....
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 Fall '10
 riley

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