7- consider a monopolistically competitve market with N firms.each firms\'s busi

Question

7- consider a monopolistically competitve market with N firms.each firms's business opportunities are described by the following equations:

Demand:Q = 100/N - P

Marginal Revenue = 100/N -2Q

Total Cost= 50+ Q 2

Marginal Cost= 2Q

a. how does N, the number of firms in the market,affect each firms's demand curve? why?

b.how many units does each firm produce?(the answers to this and the next two questions depends 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

Monopolistic competition describes markets with many firms that sell goods and services that are similar, but slightly different.

a. Monopolistic Competiton has downward sloping demand curve and affect is N is change of intercept on graph. Therefore as no of firms increase intercept will start decreasing which means consumer surplus will start coming down. Thus each firm will affect the consumer surplus the other firm is providing in market

b. Each firm should produce at profit maximization which is when MC = MR

100/N - 2Q = 2Q

4Q = 100/N

Depend on value of N, Q will come. Suppose there are 5 firms in market then each firm should produce 5 units of goods

c. Taking same example as b above, then Price charged by each firm

Q = 100/N - P

N=5; Q=5

P = $15

d. Profit = Total Revenue - Total cost

Profit = P*Q - 50 - Q2

Profit = 100P/N - P2 - 50 - Q2

Depend on value of N we can solve above equation. For assumption as in b above

Profit = $ 20

e. In the long run Total revenue became equal to Total Cost, therefore,

100P/N - P2 = 50 + Q2 -------------1

In per-unit terms, zero profit means that price is equal to average total cost (ATC)

or, P = (50+Q2)/N -------------------2

and MR = MC

100/N = 4Q ---------3

Solving for N and we get N =5

Thus in long run there will be 5 firms

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