Consider a monopolistically competitive market with N firms. Each firm\'s busine

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+Q(squared)
Marginal Cost: MC=2Q

a. How does N, the number of firms in the market, affect each firms demand curve? Why.
b. How many units does each firm produce? (The answer to this and the next two questions depend on N.)
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?

Explanation / Answer

As the no. of firms increase, the demand decreases if the prices remain unchanged due to increase in the no. of firms supplying in the market. Moreover, the entrants can only capture the market by reducing their prices, therfore each firm's demand curve shifts towardss the left.

for profit max, MR=MC

MR=100/N-2Q

MC=2Q

100/N - 2Q = 2Q

4Q = 100/N

Q = 25/N

P = 100/N - Q = 75/N

TC=50+Q(squared)

Profit = TR - TC

= P*Q - (50+Q^2)

= 1875/N^2 - ( 50 + 625/N^2)

= 1250/N^2 - 50

In the long run, Profit = 0

1250/N^2 = 50

N^2 =25

N =5

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