Question

8) Each of the 10 firms in a competitive market has a cost function of C=25+q2,soitsmarginal costisMC=2q.Themarket demand function is Q d = 120 - p . Determine the equilibrium price quantity per firm, and market quantity.

Answer 1

Answer:

Each firm will produce that level of output for which marginal cost=price

C = 25 + q^2

Marginal cost MC = 2q

Thus, each firm supply curve: P = 2q or q = P/2

There 10 such firms, so market supply curve is Q = 10*P/2 = 5P

demand function is Q = 120 - P

For equilibrium market supply = market demand

Thus 120 – P = 5P. Solving for P we get the equilibrium price P = 20

Quantity per firm= P/2 = 20/2 = 10

Market quantity = 5P = 5*20 = 100

Thus equilibrium price quantity per firm P = 20, and market quantity is 100