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...
As Sam moves rightward along his indifference curve, his marginal rate of substitution
A) is diminishing. B) is increasing. C) remains constant. D) shows the change in his income.
The main reason that many businesses fail when the price level is falling is that ________
A) deflation causes a decline in short-run aggregate supply B) as prices fall, businesses are unable to predict the quantity of output they will be able to sell C) the real value of the firms assets declines in proportion to the decrease in the price level D) falling prices mean that regular loan payments become increasingly difficult
Input efficiency:
A. means that holding constant the total amount of each input used in the economy, there is no way to increase any firm's output without decreasing the output of another firm. B. is not a requirement of Pareto efficiency in a production economy. C. exists when it is possible to produce more of one good and at least as much of every other good using the same inputs. D. is the same as efficient efficiency.
Compare and contrast the shapes of the short-run and long-run Phillips curves