sol_fin07 - S F E500 8:00 Question 1 The production...

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S  : F  E  500, 8:00  December 12, 2007 Question 1 The production function is f ( z ) = 2 min { z 1 , z 2 } + z 3 . Clearly z 1 = z 2 . In order to produce q units of output, one can use z 1 = z 2 = q / 2 or z 3 = q , whichever has lower costs. Thus, z 1 = z 2 = q / 2 will be used if w 1 + w 2 < w 3 , resulting in costs ( w 1 + w 2 ) q and z 3 = q will be used if w 1 + w 2 > w 3 , resulting in costs w 3 q . Thus, c ( w, q ) = q min b w 1 + w 2 2 , w 3 B . 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 changes output by α 2 . Let f ( z 1 , z 2 ) z i = g i ( z i ). Then it follows that f ( z 1 , z 2 ) = G 1 ( z 1 ) + G 2 ( z 2 ), where G i = g i (the integration constant k can be included into G i ). We can also define
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sol_fin07 - S F E500 8:00 Question 1 The production...

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