Question

Consider a monopolistically competitive market with N firms. Each firm’s business opportunities are described by the following equations:

Demand: Q = 100/N − P

Marginal Revenue: MR = 100/N − 2Q

Total Cost: TC = 50 + Q²

Marginal Cost: MC = 2Q

1. How does N, the number of firms in the market, affect each firm’s demand curve? Why? [3 points]

2. How many units does each firm produce? (The answers to this and the next two questions depend on N.) [3 points]

3. What price does each firm charge? [3 points]

4. How much profit does each firm make? [3 points]

e. In the long run, how many firms will exist in this market? [3 points]

Answer 1

A.

Number of firms and the demand for each firm has inverse relationship. increase in the number of firms will cause decrease in the number of quantity demanded for each firm. It means that demand curve will decrease or shift to the left so that each firm will get less demand. It happens because market demand is fixed, but increase in number of firms, will cause each firm gets less quantity of demand to be catered by each firm.

B.

profit maximizing output is decided by,

MR = MC

100/N - 2Q = 2Q

100/N = 4Q

Q = 100/4N

So, each firm will produce quantity of 100/4N.

C.

Price to be charged is as follows.

P = 100/N - Q = 100/N - 100/4N

P = 75/N

D.

Profit = revenue - cost = P*Q - (50+Q^2)

Profit = 75/N * 100/4N - 50 - (100/4N)^2

Profit = 7500/4N^2 - 10000/16N^2 - 50