Task: Profit maximization and Competitive Supply
List the conditions than need to hold for a long run competitive equilibrium.
Problem 1: A number of stores offer film developing as a service to their costumers. Suppose that each store that offers this service has a cost function C(q)=50+0.5q+0.08q2 .
(a) If the current rate for developing a roll of film is $8.5, is the industry in long run equilibrium? Explain.
(b) If the firm is not in a long run equilibrium, find the price associated with long run equilibrium.
(c) Suppose now that a new technology is developed which will reduce the cost of film developing (total cost) by %25. Assuming that the industry is in long run equilibrium, how much would any one store be willing to pay to purchase this new technology?
Problem 2: You are given the following information about a particular industry:
Qd=6500-100P
Qs=1200P
c(q)=722+q^2/200
Where QD is the market demand, QS is the market supply and MC(q) is the firm total cost function.
Assuming that all firms are identical, and that the market is characterized by pure competition,
(a) Find the equilibrium price, the equilibrium quantity, the output supplied by each firm and the profit of the firm in the short run.
(b) Would you expect to see entry into or exit from the industry in the long-run? Explain. What effect will entry or exit have on market equilibrium?
(c) What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative or zero at this price? Explain.