Suppose there is a monopolistically competitive market with

Suppose there is a monopolistically competitive market with n identical firms, such that each firm produces the same quantity,q. Further, the market is in the monopolistically competitive long-run equilibrium. You are given the following Inverse market demand: P= 10-Q Total market output: Qnxq Marginal revenue: MR=10-(n+1)xq Total cost: C(g) 5+q Marginal cost: MC-2xq In long-run equilibrium, each firm earns | profit. In long-run equilibrium, the number of firms, n, isand each firm producesunit(s) of output at an equilibrium price of S. (Read carefully. The number of firms must be an integer. Round output to three decimal places and round the price to the nearest penny.)

Solution

In the long run under monopolistic competition profit earned by each firm = 0

TR –TC =0

This implies P = AC. Each firm will supply

P = (5+q²)/q

Market supply is obtained by adding the supply for all the firms

P = n(5+q²)/q

Using q= Q/n

P = (5+Q²/n²)*(n²/Q )is the market supply function

P =(5n²/Q) +Q,

Equate supply = demand

10-Q = (5n²/Q) +Q, Solve for n

[(10Q – 2Q²)/5]^1/2 =n, where n is the number of firms

q = Q/[(10Q – 2Q²)/5]^1/2 ;q is the output produced by each firm