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Profit maximization and Competitive Supply

Profit maximization and Competitive Supply

List the conditions than need to hold for a long run competitive equilibrium.
Problem 2
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 3
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.

Solution Preview

Problem 1
List the conditions than need to hold for a long run competitive equilibrium.

The Conditions of Long-Run Competitive Equilibrium :
1. There is no incentive for firms to enter or exit the industry.
2. There is no incentive for firms to produce more or less output.
Firms Are Producing the Quantity of Output at Which Price Is Equal to Marginal Cost-Firms naturally move toward the profit-maximizing level of output. At that level of output, MR = MC, and as shown earlier, since P = MR, P = MC.
3. There is no incentive for firms to change plant size. Each firm is just breaking even in the short and long run.

Long-run competitive equilibrium exists when price equals marginal cost and average cost in the short and long run.
P = MC = SRATC = LRATC

Problem 2
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+0.08q^2 .
(a) If the current rate for developing a roll of film is $8.5, is the industry in long run equilibrium? Explain.

From the cost function, we know the firm's MC = d C(q) / dq = 0.5 + 0.16q
While its SRAC = C / q = 50/q + 0.5 + 0.08q
From problem 1 we know that in the long run equilibrium, MC = SRAC:
0.5 + 0.16q = 50/q + 0.5 + 0.08q
0.08q = 50 /q
q^2 = ...

Solution Summary

Discuss Profit maximization and Competitive Supply

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