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Unformatted text preview: PAD? 6950 Spring 2011
Fertig UGA Homework 5 Solution 1. The technical rate of substitution between factors X2 and x1 is 4~. lfyou desire to
produce the same amount of output but cut your use ofxl by 3 units, how many
more units ofX2 will you need? TRS measures the rate at which the firm will have to substitute one input for another to keep output constant.
TRS=—4: Ifthe change in x; is ~3, then the change in xZ is 3*4=12.
Will need 12 units of X2 to offset ioss of 3 units of X1. (note ifX1 if yaxis, then change in Kg : ~3/4=0.74). 2. The shortrun production function of a competitive firm is given by Q=6L3/3, where
l. is the amount oflabor and Q is the output. As a result, the marginal production of
labor is MPLn4L‘1/3. The cost per unit oflabor is w=6 and the price per unit of
output is p=3. a. How many units oflabor wili the firm hire? Profit maximizing condition: p*IViPL=w
3*4L'1/3=6
12 L'1/3=6
2=L1/3
23=L1/3*3
L=8 b. How much output wili it produce? Plug L from part a into production function: Q26L2/3
Q=6 8)2/3 c. If the firm has no other costs, how much will its total profits be? Profit = pQWL z 3(24)—6(8) = 72 — 48 = 24 z rofi cl. Suppose that the wage fails to w=4 and the price of the output remains at
p23. Wiii the firm increase its output? Explain why or why not. Redo proﬁt maximization and solve for Q.
Profit maximizing condition: p*MPL=w
3*4L‘1/3=4
121:1/324
3=L1/3
33=L1/3*3
L=27
Plug L from part a into production function: Q=6L2/3 n =6 27)2/3
H When labor is cheaper, the firm can produce at a cheaper cost so they can make more
profit by producing more. ...
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This note was uploaded on 01/18/2012 for the course PADP 6950 taught by Professor Fergi during the Spring '11 term at UGA.
 Spring '11
 Fergi

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