Question

PROBLEM 2. Consider a firm (call it firm 1) selling a product in a monopolistically competitive market. The firm's total cost is given by the function T C(Q) = 40Q: A) Suppose that, initially, firm 1 is the only firm in the market, and that the demand for the product is QD = 100 − 0.5P. Calculate the profit-maximizing level of production and the profits made by firm 1. B) Given your answer to part A, what do you expect to happen to the number of firms in the industry? C) Suppose one more firm (call it firm 2) enters the industry, leading firm 1 to face a new demand curve, QD = 80 − P. Calculate firm 1's new profit-maximizing level of output and profits. D) What will happen to profits in the long run, as more and more firms enter the industry?

Answer 1

Monopolistically competitive firm maximizes profit at the point where MR = MC
TC = 40Q
So, MC = d(TC)/dQ = 40

A)QD = 100 − 0.5P
So, 0.5P = 100 - Q
So, P = (100/0.5) - (Q/0.5) = 200 - 2Q
So, total revenue, TR = P*Q = (200-2Q)*Q = 200Q - 2Q²
Marginal Revenue, MR = d(TR)/dQ = 200- 2(2Q) = 200 - 4Q

Now, MR = MC gives,
200 - 4Q = 40
So, 4Q = 200 - 40 = 160
So, Q = 160/4 = 40

So, Q = 40
P = 200 - 2Q = 200 - 2(40) = 200 - 80 = 120

TR = P*Q = 120*40 = 4800
TC = 40Q = 40*40 - 1600

So, Profit = TR - TC = 4800 - 1600 = 3200
Thus, profit = 3200

b) As there are positive economic profits, so more firms will enter in the industry.

c) QD = 80 − P.
So, P = 80 - Q
TR = P*Q = (80 - Q)*Q = 80Q - Q²
So, MR = d(TR)/dQ = 80 - 2Q

Now, MR = MC gives,
80 - 2Q = 40
So, 2Q = 80 - 40 = 40
So, Q = 40/2 = 20
Thus, Q = 20

P = 80 - Q = 80 - 20 = 60

TR = P*Q = 60*20 = 1200
TC = 40Q = 40*20 = 800

Profit - TR - TC = 1200 - 800 = 400
Thus, profit = 400

d) Economic profits will decrease and equal zero as more and more firm will enter in the long run.