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 + Q2Q2

Marginal Cost MC = 2Q

(a) How does N, the number of firms in the market, affect each firm's demand curve? Why?

(b) How many units does each firm produce?

(c) What price does each firm charge?

(d) How much profit does each firm make?

(e) In the long-run, how many firms will exist in this market?

a) As N increases, the quantity produced decreases, because N is inversely correlated with Q.

b) The firm produces such that MR = MC:

100N−2Q=2Q100N−2Q=2Q

100N=4Q100N=4Q

Q=1004NQ=1004N

c) To find price, plug quantity into the demand equation.

Q=100N−PQ=100N−P

1004N=100N−P1004N=100N−P

1004N=4004N−P1004N=4004N−P

P=75NP=75N

d) To find profit, subtract total revenue (which is price times quantity) from total cost.

Profit=PQ−TCProfit=PQ−TC

Profit=75N×1004N−(50+Q2)=75N×1004N−50−(1004N)2=2000016N2−50Profit=75N×1004N−(50+Q2)=75N×1004N−50−(1004N)2=2000016N2−50

e) Firms will exit the market until profit is at least zero:

2000016N2−50≥02000016N2−50≥0

Solving for N using algebra reveals that this equation solves to N≤5N≤5.

So in other words, in the long run, firms will exit the market until there are only five left.