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.
Average cost, AC=C(Y)/Y= (Y2+1)/Y
Marginal cost, MC= c'(Y)=2Y
At break even point (BEP);
AC = MC
Y+1/Y = 2Y
Y* = 1
However, MC = P
hence, P=2y but Y*=1
Marginal cost for each firm is;
MC=2Y but MC=P
therefore, Y(P)= ∑Y = (mP)/2
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.