Answer to Question #85686 in Microeconomics for Taylor

Question

If the UPM's price equation is: 120-2Q; the UPM's marginal revenue is: 120-4Q; the UPM's total cost is: 3Q^2 +5Q+132; and the UPM's marginal cost is: 6Q +5.
A. Solve for the profit-maximizing (or loss minimizing) quantity (Q*).
B. Solve for the profit-maximizing (or loss minimizing) price (P*).
C. should the uniform pricing monopolist produce Q*? Explain why using one of the four key questions and solutions
D. Does the uniform pricing monopolist make profit? Explain why using one of the four key questions and solutions
E. How much profit (or loss) does the uniform pricing monopolist make?

Answer 1

P = 120 - 2Q; MR = 120 - 4Q; TC = 3Q² + 5Q + 132; MC = 6Q + 5.​ 

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

120 - 4Q = 6Q + 5,

10Q = 115,

Q* = 11.5 units.

B. The profit-maximizing (or loss minimizing) price​ is: P* = 120 - 2*11.5 = 97.

C. The uniform pricing monopolist should produce Q*, if P > AVC. 

AVC = VC/Q = (3Q² + 5Q)/Q = 3Q + 5 = 3*11.5 + 5 = 39.5 < 97. So, the monopolist should produce.

D. The uniform pricing monopolist's will face profit, if P > ATC.

ATC = TC/Q = 3*11.5 + 5 + 132/11.5 = 50.97 < 97.

So, the monopolist will face profit. 

E. The profit (or loss) of the uniform pricing monopolist is:

TP = TR - TC = 97*11.5 - (3*11.5^2 + 5*11.5 + 132) = 529.25.