1) Suppose a monopolist faces a demand curve for its output of P = 300Q.

This means that the marginal revenue curve of the monopolist is MR = 300 2Q. Assume that there are no fixed costs, and the marginal cost of production is constant and equal to $40.

a) Write down an expression for the monopolists profit, as a function of the quantity of output it produces.

b) If the monopolist must charge the same price for all units of output that it sells (that is, if the monopolist is a single price monopolist), what level of output will maximise the monopolists profit? What price will the monopolist charge? What is its level of profit?

c) If this were a competitive market instead of a monopoly, what level of output would be produced and what price would be charged? What is the level of profit for firms if it were perfectly competitive?

d) Draw a diagram of demand, marginal revenue, and marginal cost that illustrates your answer to part b). From this work out consumer surplus and producer surplus.

e) Draw the same diagram but for your answer to c), the case of the competitive market. From this work out consumer surplus and producer surplus. How much deadweight loss is there from the monopoly? Why?

2) A monopolist is deciding how to allocate output between two markets.

The two markets are separated geographically (Australia and New Zealand).

The monopolists total cost is T C = 3(QA + QNZ ), where QA is output produced and sold in Australia and QNZ is output produced and sold in New Zealand.

From the T C function we can tell that the MC = 3. The monopolists inverse demand curves for Australia and New Zealand are:

PA = 15 QA

PNZ = 25 2QNZ T

or equivalently, demand curves:

QA = 15 PA

QNZ = 12.5 0.5PNZ

The marginal revenue curves for the two markets are:

MRA = 15 2QA

MRNZ = 25 4QNZ .

a) Calculate the perfectly competitive amount of output, price, and profit in each market.

b) Calculate the monopolist's price, output and profit if they can price discriminate between Australia and New Zealand.