Question

15. A typical firm in a monopolistically competitive industry faces the following demand and total cost equations for its product Q= 20- 1/3 P TC= 100-5Q+ Q2 a. What is the firm’s short-run profit-maximizing price and output level? b. What is the firm’s economic profit? c. Suppose that the existence of economic profit attracts new firms into the industry such that the new demand curve facing the typical firm in this industry is Q=35/3 - P/3. Assuming no change in the firm’s total cost function, find the new profit-maximizing price and output level. d. Is the firm earning an economic profit? e. What, if anything, can you say about the relationship between the firm’s demand and average cost curves? Is this result consistent with your answer to part c?

Answer 1

(a)

Demand equation is as follows -

Q = 20 - P/3

P/3 = 20 - Q

P = 60 - 3Q

Calculate the Total Revenue -

TR = P * Q = (60 - 3Q) * Q = 60Q - 3Q²

Calculate the marginal revenue -

MR = dTR/dQ = d(60Q - 3Q²)/dQ = 60 - 6Q

Total cost function is as follows -

TC = 100 - 5Q + Q²

Calculate the marginal cost -

MC = dTC/dQ = d(100 - 5Q + Q²)/dQ = -5 + 2Q

A monopolistically competitive firm maximizes profit when it produce that level of output corresponding to which MR equals MC.

MR = MC

60 - 6Q = -5 + 2Q

8Q = 65

Q = 8.125

P = 60 - 3Q = 60 - (3*8.125) = 60 - 24.375 = 35.625

Thus,

The firm's short-run profit-maximizing price is $35.625 per unit and output level is 8.125 units.

(b)

Calculate the economic profit -

Economic profit = TR - TC

Economic profit = (P*Q) - (100 - 5Q + Q²) = (35.625 * 8.125) - (100 -(5 * 8.125) + (8.125)²)

Economic profit = 289.45 - 125.4 = 164.05

The economic profit is $164.05

(c)

New demand is as follows -

Q = 35/3 - P/3

P/3 = 35/3 - Q

P = 35 - 3Q

TR = P*Q = (35 - 3Q) * Q = 35Q - 3Q²

MR = dTR/dQ = d(35Q-3Q²)/dQ = 35 - 6Q

Equating,

MR = MC

35 - 6Q = -5 + 2Q

8Q = 40

Q = 5

P = 35 - 3Q = 35 - (3*5) = 35 - 15 = 20

The new profit-maximizing price is $20 per unit and the output level is 5 units.

(d)

Calculate the economic profit -

Economic profit = TR - TC

Economic profit = (P*Q) - (100 - 5Q + Q²) = (20 * 5) - (100 -(5 * 5) + (5)²) = 100 - 100 = 0

After change in demand due to entry of new firms, the firm is not earning an economic profit.