Suppose that you own a tennis club in an isolated wealthy community and hence you act as a monopolist. The market consists of 100 (identical) tennis players each with inverse demand p = 6 q, where p is the price per hour and q is court hours. Because you have plenty of courts, the marginal cost of court time is zero.

Suppose first that you set a uniform price per hour.

Aggregate demand for court hours is Q=600-100p.

The number of court hours that maximizes the profit=300 and the profit-maximizing price=3.

The maximum profit=pQ=3(300)=900

The consumer surplus=.5*3*300=450

A friend tells you that you could earn higher profits by designing a more sophisticated pricing schedule.

Find the maximum total surplus that you can extract from each type of player.[Hint: Recall that to find this, you need to assume that the price is equal to the marginal cost (zero in this case).] (1p)

Can you think of a (more sophisticated) pricing schedule that would allow you to increase your profits? (1p)