Question

A competitive industry consists of m identical firms, each with a cost function of C(Y)=Y²+1. Suppose also that the market demand is given by P=100-Y. Calculate the equilibrium number of firms in the market.

Answer 1

C(Y)= Y²+1

Average cost, AC=C(Y)/Y= (Y²+1)/Y

AC=Y+1/Y

Marginal cost, MC= c'(Y)=2Y

At break even point (BEP);

AC = MC

Y+1/Y = 2Y

Y* = 1

However, MC = P

MC=2Y=P

hence, P=2y but Y*=1

P*=2

Marginal cost for each firm is;

MC=2Y but MC=P

therefore, P=2Y

hence Y=P/2

therefore, Y(P)= ∑Y = (mP)/2

At Equilibrium

Aggregate demand (AD) = Aggregate supply (AS)

(mP)/2 = 100-P

m = 2(100-P)/P but P=2

m = 98 firms

The equilibrium number of firms in the market is 98 firms.

m is the equilibrium number of firms in a competitive market. It is the largest number of firms that can break even.