2. On the island of Sunnydale, the market for Christmas trees is a monopoly. The

Question

2. On the island of Sunnydale, the market for Christmas trees is a monopoly. The firm selling the trees, TreesRus, faces the following demand curve and cost information.

Demand: P = 100 – 2Q

Total Costs = 1000 + 4Q

(A) Provide four reasons why a monopoly may exist (i.e. four possible barriers to entry). (1 mark)

(B) What is the supply curve for this monopolist? (1 mark)

C) If the monopolist is a single-price monopolist, what price will he charge? How many trees will he sell? How much profit does the monopolist earn? (1 mark)

(D)Is this monopoly a natural monopoly? How do you know? (1 mark)

(E) Show the monopolists’ situation graphically. What is the total Consumer Surplus? What is Producer Surplus? What is the value of the deadweight loss? (2 marks)

(F) The monopolist takes a course in sales and is now able to perfectly price discriminate. Explain what this means. (2 marks)

(G)Under perfect price discrimination, how many trees does he sell? What is his total profit? What is the value of Consumer Surplus? What is the Deadweight Loss? What is the monopolists profit? (2 marks)

(H)Suppose the monopolists decides to price discriminate by providing a membership price and then allowing people to cut down as many trees as they would like for a lower price per tree. What would be the optimal charge for the membership? How much would each tree cost if you had a membership?

Explanation / Answer

A) Monopoly may exist when in a market there is only one seller and many buyers. Intellectual property protection, Government support, Ownership of one of the key inputs ini production etc.

B) Monopolist fiind optimum quantity by equalising Marignal Revenue with Marginal Cost and Price reflected on Demand curve hence no Supply curve exists for Monopoly.

C) For Monopolist MR=MC

TR =P*Q = 100Q-2Q^2

TC = 1000+4Q

MR = d/dQ(TR) = 100-4Q

MC= d/dQ(TC) = 4

100-4Q = 4

Q =24 would be the optimum quantity of trees he would sell.

Hence P = 100-2Q =100-48 =52

Profit = TR -TC = P*Q - 1000-4Q = 52*24 -1000-96 =1248-1096 =252

D)

These types of firms have unlimited increasing return to scale and to note if total fixed cost is higher and marginal cost is less this signifies the presence of natural monopoly. As it becomes very difficult for new entrants to cope with this cost structure.

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