Question

A market has N=38 firms each with identical costs C(q)=8q²+60. Demand is Q_D=1000-4p.

What will be the short-run equilibrium price?

Answer 1

Cost of a firm is given by : C = 8q² + 60

Marginal Cost(MC) = dC/dq = 16q

In general MC curve is considered as a supply curve of a firm(Note that here there are 38 identical firms which means that there is no product differentiation and large number of firms so result will be that these firms will be a price taking firm and hence charges price where p = MC)

So, p = MC => p = 16q => q = p/16

Market supply is sum of individual supply and thus :

Q = 38q = 38(p/16) where Q = Market supply

Thus At equilibrium we have Market supply = Market demand => Q = QD

=> 38(p/16) = 1000 - 4p

=> P = 156.86

Hence, the short-run equilibrium price = 156.86