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On short notice, Dr. Ford creates automatons according to the following production function: Q(L,K)=10L1/2. The wage...

On short notice, Dr. Ford creates automatons according to the following production function: Q(L,K)=10L1/2. The wage of a programmer such as Elsie is $100 per hour and the price of each automaton is $2000. His capital costs $10000 per hour total.

A. Find the profit function.

B. How many hours will Dr. Ford employ Elsie, if he is maximizing profits.

C. Now consider the long run in which Dr. Ford can choose how much capital to employ according to the production function: Q(L,K)=K1/4L1/2. The price of capital is $10 per unit per hour. Find the optimal mix of capital and labor to use in the long run. Use the wage from part a.

D. Find the optimal amount of employment and capital in the long run using the optimal mix of capital and labor from part c. Hint: Write out the new profit function with the new production function and the cost of capital now being 10 x K.

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Answer #1


A. brefit function at 2 TR-TC = PQ-C s aa 2050 (1014) - 10000 100L Be it equilibrium Ith 2000 x 1012 - 18 20 s) 100 TK21 La l

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