Every Saturday night Jane goes to the Beach Club for dinner and drinks. Jane has $50 budgeted for each visit, which she spends on Food and Milk. The Beach Club has an entry fee of $10, the price of a unit of Food is $1, and each glass of Milk is $2. Jane is a utility maximizer.

(a) Sketch Jane's budget line. (Graph consumption of Milk on the horizontal axis and consumption of Food on the vertical axis.) Let (M*,F*) denote Jane's optimal consumption of Milk and Food. Suppose that M*=5. On the same graph, sketch the indifference curve passing through (M*,F*). Assume that Jane has strictly convex preferences and "smooth" indifference curves.

b) Sketch Jane's budget line if, instead of charging an entry fee of $10, the Beach Club raises the price of milk to $4. [In the same graph, also draw the budget line and indifference curve from (a) and (b).] Denote by (M',F') Jane's optimal consumption and suppose that (M',F') is different from (M*,F*).

c) Is Jane better off, worse off, or just as well off when she pays $4 per glass of milk and no entry fee than when she pays $2 per glass of milk and a $10 entry fee. Is M'>M*, M'