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# fin07 - F E500 8:00 Name [email protected] All questions must...

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F  E  500, 8:00  December 12, 2007 Name: E-mail: @uiuc.edu All questions must be answered on this test form! For each question you must show your work and (or) provide a clear argument. If you need scratch paper, use the last two pages or the back of the form. Question 1 A production function is given by f ( z ) = 2 min { z 1 , z 2 } + z 3 . Then the cost function is given by 10 points c ( w, q ) = 1

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Question 2 Suppose a production function f ( z 1 , z 2 ) has the following properties. 1. The marginal product of input i only depends on the level of input i , not on that of the other input. 2. Changing both inputs by a factor of α 0 changes output by α 2 . The general form of a production function that satisfies both conditions is 10 points f ( z 1 , z 2 ) = Use a, b, . . . to denote general parameters. The parameters must satisfy the following conditions: No detailed proof needed. 2
Question 3 A bakery tells you the following two facts about its profit function: 1. “Currently, we use 100 units of white sugar in our production process. How-

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