Question

Joe has just moved to a small town with only one golf​ course, the Northlands Golf Club. His inverse demand function is

p=140−22​q,

where q is the number of rounds of golf that he plays per year. The manager of the Northlands Club negotiates separately with each person who joins the club and can therefore charge individual prices. This manager has a good idea of what​ Joe's demand curve is and offers Joe a special​ deal, where Joe pays an annual membership fee and can play as many rounds as he wants at $40, which is the marginal cost his round imposes on the Club. What membership fee would maximize profit for the​ Club? The manager could have charged Joe a single price per round. How much extra profit does the Club earn by using​ two-part pricing?

The​ profit-maximizing membership fee​ (F) is

​$

​(Enter your response as a whole​ number.)

Answer 1

The fee is the consumer surplus at at a price of 40.

Hence the membership fee is 0.5*(140 - 40)*(140 - 40)/22 = $227

Profit from two part pricing = 227. When single price is charged, MR = MC gives 140 - 44Q = 40 or Q = 2.1818 and so price = 92. This gives a profit of (92 - 40)*2.1818 = 113.45.

Extra profit earned = 227 - 113 = 114.