aps5x313_s06

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

This preview shows pages 1–4. Sign up to view the full content.

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

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

View Full Document
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
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

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.

## This note was uploaded on 10/29/2009 for the course ECON 3130 taught by Professor Masson during the Fall '06 term at Cornell.

### Page1 / 11

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online