Suppose the The demand curve for a monopolist is QD = 47,000 -50 P, and the marginal revenue function is MR = 940 - 0.04Q. The monopolist's Marginal Cost = 40 + 0.02Q and its
Total Cost =250,000 + 40Q + 0.01Q2.
a. Find the monopolist's profit-maximizing output and price.
b. calculate the monopolist's profit/losses, if any.
c. What is the Lerner Index for this industry at the monopolist's profit-maximizing output and price.
I need to make sure that I am working this problem correctly in particular solving for P....
a. Profit maximizes where MR = MC
940 - 0.04Q = 40+0.02Q
Solving for Q:
900 = 0.06Q
Q = 15,000
Substituting Q in the demand curve, we can obtain P:
15,000 = 47,000 - 50P
P = 1,240
b. Re-arrange the demand curve equation to make P the subject
P = 940 - (Q/50)
TR = P * Q
TR = 940Q - ((Q^2)/50)
Substituting the Q found in part a.:
TR = (940*15,000) - (15000^2)/50)
= 14,100,000 - 4,500,000
= 9,600,000
TC = 250,000 + 40Q + 0.01Q^2
= 250,000 + (40*15000) + (0.01*15000^2)
= 250,000 + 600,000 + 2,250,000
= 3,100,000
Therefore profit = 9,600,000 - 3,100,000 = 6,500