Question

Consider a country with the following aggregate demand curve for cars.Q = 2000 – 20.P There is a industry with following marginal and average cost curves. MC = 10 + 0.01 QAC = 10 + 0.005Q Assume that the industry is a monopoly and there is no free trade. a. What is the monopolist’s marginal revenue curve? (Hint: Express demand curve as P = A – B.Q form, and estimate MR) b. What is the monopolist’s profit maximizing output? c. What is the profit maximizing price? d. What is the profit? e. Show this in a diagram.

Answer 1

(a) Q = 2,000 - 20P

20P = 2,000 - Q

P = 100 - 0.05Q

Total revenue (TR) = P x Q = 100Q - 0.05Q²

Marginal revenue (MR) = dTR/dQ = 100 - 0.1Q

(b) Profit is maximized when MR equals MC:

100 - 0.1Q = 10 + 0.01Q

0.11Q = 90

Q = 818 (Taking interger value for quantity)

(c) When Q = 818,

P = 100 - (0.05 x 818) = 100 - 40.9 = 59.1

(d) Profit = Q x (P - AC)

When Q = 818, AC = 10 + (0.005 x 818) = 10 + 4.09 = 14.09

Profit = 818 x (59.1 - 14.09) = 818 x 45.01 = 36,818.18

(e) In following graph, Demand (D), MR, MC and AC curves are shown. Profit is maximized at point E where MR intersects MC with price P0 (= 59.1) and quantity Q0 (= 818). Profit equals area P0ABC.