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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online