Question

A new gym which will be a monopolist in the area is opening and is trying to figure out its pricing mechanism. The owner has decided to set a one-time membership fee and then ask members to pay per visit. She knows that each consumer’s demand is given by P=60-2Q and her gym’s MC=10. What is the optimal membership fee she should charge? Group of answer choices $1250

$600

$800

$400

None of the other answers is correct.

Answer 1

In order to maximize profit in a two part pricing)(like charging a membership fee and per unit price), a firm charges per unit price(P) = Marginal Cost(MC) and whatever consumer surplus consumer is receiving, charges that as Fixed Fee or membership fee.  

Thus, P = MC => 60 - 2Q = 10 => Q = 25

Consumer surplus is the area above price line and below demand curve

Vertical intercept of demand curve is P = 60 - 2*0 = 60

Membership fee = (1/2)*(25)*(60 - P) = (1/2)*(25)*(60 - 10) = 625

Hence, Membership fee = $625

Hence, the correct answer is (e) None of the other answers is correct.