Evren wants to go into the donut business. For $500 per month he can rent a bakery complete with all the equipment he needs to make a dozen different kinds of donuts (K = l, r = 500). He must pay unionized donut bakers a monthly salary of $400 each
He projects his monthly production function to be Q = 5KL where Q is tons of donuts. a. With the current level of capital, what is the marginal product of labor? Is the marginal product diminishing? Explain. b. If Evren wishes to make 25 tons of donuts, how many bakers are required given the current level of capital? How much will it cost to produce this (total cost)? c. Derive Evren's short-run cost function with K=1. d. Derive the marginal cost curve from your answer to c. and show the relationship between the marginal cost and marginal product of labor.
a. TP = 5L, so MP = dTP/dL = 5. It is not diminishing but is constant.
b. 25 = 5L, so L=5. The cost will be C = wL + rK = 5(400 ) + 1(500 ) = 2500
c. q = 5L, so L = q/5. C(q) = 80q + 500
d. The MP = 5 and the MC = 80. The relationship is MC = w/MP, or 80 = 400/5. The MP is constant so the MC is as well.
You might also like to view...
An autonomous easing of monetary policy results in a ________ level of equilibrium output, shifting the aggregate demand curve to the ________
A) higher; right B) lower; right C) higher; left D) lower; left
If you buy an insurance policy with a high deductible and co-payments, you would end up paying
a. A higher premium b. A lower premium c. The premium of a low risk individual d. Both B&C