Doug wants to go into the donut business. For $500 per month he can rent a baker

Question

Doug 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=1). He must pay unionized donut bakers a monthly salary of $400 each. He projects his production function to be Q=5KL (where Q is tons of donuts).

a) What is Dougs monthly total cost function, variable cost function, and marginal cost? (Write the TC as a function of FC and VC and then, rewrite it in terms of Q to get started).

b) How many bakers will Doug hire to mae 25 tons of donuts?

c) What will happen to Doug's total cost if his production function turns out to be Q=2KL? (Do a and b again with new Q)

Explanation / Answer

a. What is Doug's monthly total cost function, variable cost function, and marginal cost?
K=1 L=Q/5
TC = 500 + 400(Q/5) = 500 + 80Q
VC = 80Q
The marginal cost is equal to the slope of the total cost curve which is MC = 80.

b. How many bakers will Doug hire to make 25 tons of donuts?
L = Q/5 = 25/5 = 5

c. What will happen to Doug's total cost if his production function turns out to be Q=2KL?
K = 1, L = Q/2, TC = 500 + (400/2)Q = 500 + 200Q

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