aps5x313_s06

aps5x313_s06 - Econ 313-2 Spring 2006 TA : Seunghan Yoo...

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Econ 313-2 Spring 2006 TA : Seunghan Yoo Suggested Solution to Problem Set #5 1. a. First, you have to get L and K , which are cost minimizing labor and capital level given each output x . Given the PC production function, at the minimum, the following relationship must be satis f ed. L = K If you plug the above equation into the production function, you will get L = K = x Thus, L = x K = x Now, if you plug those into the long run cost, 1) lrtc ( x )= wL + rK =6 x It follows that 2) lrac ( x )=6 3) lrmc ( x 1
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b. Given K =20 , x =min { L, 20 } You can see that no matter what labor you have, you can not produce more than 20 outputs . So ,wehavethe capacity constraint as x 20 .F o reach x, L = x Now, if you plug it into the short run cost, 1) srtc ( x )= wL + r K =2 x +80 for x 20 ( K is the notation for the amount of the f xed capital. It is typical to draw the cost function curve as vertical line at x .) It follows that 2) srvc ( x )=2 x for x 20 3) srfc ( x )=8 0 for x 20 4) sratc ( x 2 x x for x 20 5) sravc ( x for x 20 6) srafc ( x 80 x for x 20 7) srmc ( x for x 20 2. a. To get L and K ,letus f rst get MRTS given the CD production function. = MP L k = 2 LK 2 2 L 2 K = K L From the condition = ERTS , K L = 1 2 (1) 2
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Rewrite it as L =2 K and plug it into the production function. Then, x =(2 K ) 2 K 2 =4 K 4 It follows that K = μ 1 2 1 / 2 x 1 / 4 Using (1), L 1 / 2 x 1 / 4 Now, if you plug those into the long run cost, 1) lrtc ( x )= wL + rK 5 / 2 x 1 / 4 It follows that
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This note was uploaded on 10/29/2009 for the course ECON 3130 taught by Professor Masson during the Fall '06 term at Cornell.

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aps5x313_s06 - Econ 313-2 Spring 2006 TA : Seunghan Yoo...

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