Question

Show all your calculations. Answers without explanations or calculations will receive a mark of zero.

The long-run cost curve for a typical perfectly competitive firm in the tea market is given by the following: MC=AC=40

The market demand curve for tea is given by the following: P = 400 – 2Q

a) Find the long-run competitive equilibrium assuming the industry is constant-cost. That is, identify the equilibrium price, total quantity produced and output of each firm if there are 10 firms in the market.

b) Calculate the producer and consumer surplus, and deadweight loss. Show your answer in a graph. Label all the relevant curves, points and areas carefully.

Now suppose that the firms in tea industry collude and form a cartel that behaves as a monopolist. Also, no further entry in the tea industry is possible.

c) What will be the new equilibrium price and quantity in the tea market? How much will each member of the cartel produce if they share the production equally?

d) What will be consumer surplus, producer surplus, and deadweight loss with the cartel? Illustrate your answer with a graph. Label all the relevant curves, points and areas carefully.

 

Answer 1

MC=AC=40

P = 400 – 2Q

Pm= Price when Q=0= 400

a)

In long run, firms in competitive market earn Profit= 0. So

Condition: P= AC

400-2Q=40

2Q= 360

Q*= 180 Total quantity produced

q= 180/10= 18 Total quantity produced by each firm

Equilibrium price=P*= 40

b)

Producer surplus=0

Total consumer surplus(area in yellow)= 1/2 (Pm-P*)(Q*)= 1/2 (400-40)(180)= 32400

There will be no deadweight loss.

c)

If all firms collude to form monopoly:

Optimal condition:

MR=MC

For MR:

Total revenue= TR= P*Q= 400Q-2Q2

MR= differentiation of TR with respect to Q= 400-4Q

Put MC=MR

40=400-4Q

4Q= 360

Q**= 90

P**= 400-2Q= 400-2x90= 220

Each member will produce= 90/10= 9 units

d)

Producer surplus(in green)= 1/2 (P**-AC)(Q**)= 1/2 (220-40)(90)= 8100

Consumer surplus(in yellow)= (Pm-P**)(Q**)= (400-220)(90)= 16200

Deadweight loss(in orange)= 1/2 (P**-AC)(Q*-Q**)= 1/2 (220-40)(180-90)= 8100