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^2 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? (The answers 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?
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^2 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? (The answers 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?
Solution
a) The number of firms, N, inversely affects each firm's demand curve. As N increases, the demand for each firm's product decreases. This is because the demand equation Q=100/N-P shows that quantity demanded (Q) is a function of the number of firms (N) and the price (P). As N increases, the quantity demanded for each firm's product decreases, shifting the demand curve to the left.
b) To find out how many units each firm produces, we need to set Marginal Revenue (MR) equal to Marginal Cost (MC) and solve for Q.
MR = MC 100/N - 2Q = 2Q 100/N = 4Q Q = 25/N
So, each firm produces 25/N units.
c) To find the price each firm charges, we substitute Q from part b) into the demand equation and solve for P.
Q = 100/N - P 25/N = 100/N - P P = 100/N - 25/N P = 75/N
So, each firm charges a price of 75/N.
d) To find the profit each firm makes, we subtract Total Cost (TC) from Total Revenue (TR). TR is P*Q and TC is given by the equation TC=50+Q^2.
TR = PQ = (75/N)(25/N) = 1875/N^2 TC = 50 + Q^2 = 50 + (25/N)^2 = 50 + 625/N^2 Profit = TR - TC = 1875/N^2 - (50 + 625/N^2) = 1250/N^2 - 50
So, each firm makes a profit of 1250/N^2 - 50.
e) In the long run, firms will enter or exit the market until there are no profits to be made. This happens when Profit = 0.
1250/N^2 - 50 = 0 1250/N^2 = 50 N^2 = 1250/50 N^2 = 25 N = 5
So, in the long run, there will be 5 firms in the market.
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