The 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.

a. Use an indifference curve diagram to find the value of F that would make it just worthwhile for you to join the pool. (Not surprisingly, your answer will depend on the preferences that you draw, and everyone will draw the preferences differently.) Put visits on the horizontal axis and all other goods on the vertical axis. Assume the price of all other goods is $1 per unit and income = $500. (Note: a single curve cannot be tangent at the same point to two different lines with different slopes.)

b. Suppose that the pool charges you this exact amount in (a). Would you swim more or less than you did beforejoining? Even though everyone's graph will look different, everyone should get the same answerfor this question. Use income and/or substitution effects to explain why that is the case.