4. Suppose a company\'s monthly production value Q, in thousands of dollars, is
ID: 2888321 • Letter: 4
Question
4. Suppose a company's monthly production value Q, in thousands of dollars, is given by the Cobb-Douglas production function Q= 10K".4510.55 where K is thousands of dollars of capital investment per month and L is the total hours of labor per month. Capital investment is currently $10,000 per month and monthly work-hours of labor total 1590. Find the monthly production value (to the nearest thousand dollars). (a) (b) Find the marginal productivity with respect to (c) capital investment, and interpret your result Find the marginal productivity with respect to total hours of labor, and interpret your result.Explanation / Answer
given monthly production value Q =10K0.45L0.55 thousands of dollars
(a)
when capital invest ment is $ 10000, K=10
L=1590
Q =10*100.45*15900.55
Q =1624.682 thousand dollars
monthly production value = 1625 thousand dollars
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(b)
marginal productivity ,Q/K =10*0.45K0.45-1L0.55
Q/K =4.5K-0.55L0.55
Q/K =4.5*10-0.55*15900.55
Q/K =73.11
monthly production value increasing at 73.11 thousand dollars per thousand dollar increase in capital investment
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c)
marginal productivity,Q/L =10*0.55K0.45L0.55-1
Q/L =5.5K0.45L-0.45
Q/L =5.5*100.45*1590-0.45
Q/L =0.562
monthly production value increasing at 0.562 thousand dollars per an hour increase in total hours of labour
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