Answer to Question #85685 in Microeconomics for Taylor Sudduth

Question

If the competitive market is $60, total cost= 3q^2-18q+182 & Marginal cost=6q-18.
A. Solve for the profit-maximizing (or loss minimizing) quantity (q*)
B. What is the Market equilibrium price?
C. Should the competitive firm produce q*? Explain why using one of the four key questions and solutions.
D. Does the competitive firm make a profit? Explain why using one of the four key questions and solutions.
E. How much profit (or loss) does the competitive firm make?

Answer 1

P = $60, TC = 3q² - 18q + 182, MC = 6q - 18. 

A. The profit-maximizing (or loss minimizing) quantity (q*) is at P = MR = MC, so:

6q - 18 = 60,

6q = 78,

q = 13.

B. The Market equilibrium price is P = MR = $60.

C. The competitive firm should produce q*, if P > AVC.

AVC = VC/q = 3q - 18 = 21, 60 > 21, so the firm should produce.

D. The competitive firm will make a profit, if P > ATC. ATC = TC/q = 3*13 - 18 + 182/13 = 35, 60 > 35, so the firm will make a profit.

E. The profit of the competitive firm is:

TP = TR - TC = 60*13 - (3*13^2 - 18*13 + 182) = $325.