Answer to Question #208599 in Microeconomics for Mubashir Ameenudee

Question

A local swimming pool charges nonmembers $10 per visit. If you join the pool, you can swim for $5 per visit but you have to pay an annual fee of F. Use an optimal choice model to find the value of F such that you are indifferent between joining and not joining. Suppose that the pool charged you exactly that F. Would you go to the pool more or fewer times than if you did not join? For simplicity, assume that the price of all other goods is $1.(Draw the graph)

Answer 1

Using an optimal choice model to find the value of F such that you are indifferent between joining and not joining.

Let N be the number of visits per year

1) N-number of visits per year 10N=5N+F

Given that 10N=5N+F

Hence F=5N

F = 5N

Therefore, if F is fixed and I join the local Swimming pool member, I would go more times.

Whether you are at A or B, you have the same utility. With joining the club, the relative price of

pool visits decreases and as a result you will visit more often with joining the club.