A monopolist's demand function is P = 1624 - 4Q, and its total ...

[Pineappleeh]

A monopolist's demand function is P = 1624 - 4Q, and its total cost function is
 
  TC = 22,000 + 24Q -4Q2 + 1/3 Q3, where Q is output produced and sold.
 
  a. At what level of output and sales (Q) and price (P) will total profits be maximized?
  b. At what level of output and sales (Q) and price (P) will total revenue be maximized?
  c. At what price (P) should the monopolist shut down?

Question 2

One way a government can eliminate a market failure
 
  A) is to regulate the price so that it equals marginal cost.
  B) is to implement a price floor equal to marginal cost.
  C) is to regulate the price so that it is below average cost.
  D) None of the above solutions will eliminate a market failure.

[johnharpe]

Answer to Question 1

a. Total Profits are maximized where MR = MC, and MR = dTR/dQ, with TR = P(Q), and
MC = dTC/dQ. TR = 1624Q -4Q2, so MR = 1624 - 8Q. MC = 24 - 8Q + Q2.
MR = MC is 1624 - 8Q = 24 - 8Q + Q2, or 1600 = Q2, and Q = 40. With Q = 40, P = 1464.
b. Total Revenue is maximized when MR = 0, or 1624 - 8Q = 0, or Q = 203 with P = 203.
c. Shut down would occur whenever price(P) is less than average variable cost (AVC), or below P = AVC, or 1624 - 4Q = 24 - 4Q + 1/3 Q2, or 1600 =1/3 Q2, or Q2 = 4800, or Q = 69 (approximately). When Q = 69, P = 1348, so any price below 1348 would cause the firm to shut down since it is not covering its variable costs.

Answer to Question 2

A

[Pineappleeh]

Thank you

[johnharpe]

Happy to help you