The local swimming pool charges non-members $10 per visit. Members pay $5 per visit, and an annual fee $F. Draw a diagram where the horizontal axis measures the annual number of visits, and the vertical axis measures $ spent on all other goods. Assume convex indifference curves, and suppose that as a non-member you would make some visits (reach an interior solution, not a corner). Use income and substitution effects to answer the following:

Show geometrically the value of F (as a particular height) that would make it just worthwhile for you to become a member instead of continuing as a non-member.

Suppose that the pool charged you exactly that value of F and you became a member. Would your number of visits increase or decrease from the level as a non-member?