Ed's construction company has the following short-run cost function: q3 - 10q2 + 36q
a. What level of output will minimize the average cost? What is the AC at this point?
b. Does the production process indicate diminishing returns? How can you tell?
a. When dAC/dq=0 or equivalently AC=MC, the AC is at a minimum. To derive:
AC = q2 - 10q + 36
MC = 3q2 - 20q + 36
Setting these equal
2q2 - 10q = 0
Solve to get q=5. Plug back into the AC to get AC = 25 - 50 + 36 = 11
b. The MC curve initially decreases but eventually rises. To see this, look at
dMC/dq = 6q - 20
When q > 10/3, the MC is rising. Since MC = w/MP, this implies the MP is decreasing.
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