Question

You manage a golf course and you know that the demand curve of each patron is identical with P = 30 – 2Q. Your marginal cost of providing services to your members is constant at 15. If you wanted to maximize your profits you will charge a fee of $15 and then charge a membership fee of ___________________ per member? Graph this problem and show the area on your graph that represents the membership fee that each member pays at the beginning of the year. Show how much profit you make if you charged $20 and made $5 on each round of golf.

Answer 1

You charge a price of $15. In this two part tariff, the membership fee is the consumer surplus at P = 15. This is given by Fee = CS = 0.5*(30 - 15)*7.5 = 56.2 Thus, if you wanted to maximize your profits you will charge a fee of $15 and then charge a membership fee of 56.25 per member

This is shown below by a triangular area drawn as green shaded region on the graph that represents the membership fee that each member pays at the beginning of the year.

The profit you make if you charged $20 and made $5 on each round of golf will be 5*5 = $25. This is shown as a rectangular region shaded blue