Evren wants to go into the donut business. For $100 per month he can rent a bake

Question

Evren wants to go into the donut business. For $100 per month he can rent a bakery complete with all the equipment he needs to make a dozen different kinds of donuts (K = 1, r = 100). He must pay unionized donut bakers a monthly salary (w) of $200 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)?

Explanation / Answer

Evren wants to go into the donut business. For $100 per month he can rent a bakery complete with all the equipment he needs to make a dozen different kinds of donuts (K = 1, r = 100). He must pay unionized donut bakers a monthly salary (w) of $200 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. a. TP = 5L, so MP = dTP/dL = 5. It is not diminishing but is constant. b. 25 = 5L, so L=5 =================================================================================== b. If Evren wishes to make 25 tons of donuts, how many bakers are required given the current level of capital? b. 25 = 5L, so L=5 The cost will be C = wL + rK = 5(200) + 1(100) =1100 ==================================================================================== How much will it cost to produce this (total cost)? 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.

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