Question

Consider a perfectly competitive market comprised of identical firms each facing the following cost function: C(q) = 4 +q? where q is the firm-specific level of production of the representative firm. The market demand function is Q(p) = 400 - 4p where Q(p) is the aggregate demand in the market (expressed as function of price) and p is the price a) Derive the firm-specific supply function of the representative firm as a function of price b) Assume there are N firms in operation in the market. Using your answer from part (a), find the aggregate supply function of the market expressed as a function of N and p. c) How many firms will remain in operation in the long run (show your work)? d) Find the long run, profit-maximizing equilibrium price of the good (show your work). e) Find the long run, profit-maximizing equilibrium output of each individual firm. f) Find the aggregate supply Q in the market B) How much profit will firms earn in the long-run?

Answer 1

A) The supply function of a perfect competition firm is Increasing part of marginal cost .

Because marginal cost is strictly increasing,so marginal cost will be supply function of firm.

TC=4+q^2

MC=2q

P=2q{ indirect supply function}

q=0.5P { supply function of firm}

B) market supply function is sum of all firms supply .

Given no. Of firms =N

Market supply;Q=0.5P*N

C)In long run all firms earn Normal Profit so,

Firm will operate at where average cost is Equal to price and marginal cost.

AC=(4/q)+q

MC=2q

AC=MC

2q=(4/q)+q

q^2=4

q=2

So each firm will produce 2 units in long run.

And Long run market price =average cost=marginal cost=2*2=4

Demand in long run;Qd=400-4*4=384

So 384=0.5p*N=2N

N=384/3=192

So In long run 192 firma will be in the market.

D) The long run price will be equal to average cost and marginal cost=4