Assume that Jean has an annual income of $50,000, and she spends her income on milk (X) and all other goods (AOG) (Y). The price of milk is $2, and the price of AOG is $1/unit. Her preferences can be represented by convex indifference curves.
 a. (4 pts) Illustrate her optimal choice (X*,Y*) on a graph, using indifference curve-budget line analysis. (Note: you do not have enough information to have numerical answers for X* and Y*).
 b. (11 pts) In an attempt to increase the consumption of milk, the government is considering two subsidy programs: (1) per unit subsidy on milk (effectively lowering the price of milk) or (2) cash subsidy (spend on all goods). The amount of subsidy is the same under both programs.
 i. (9 pts) Which option would leave Jean better off? Using your graph from part a, use an indifference curve and budget line analysis to explain and support your answer. Your answer should include a budget line, indifference curve, and optimal choice for each type of subsidy (per unit and lump sum) as well as for the initial bundle.
ii. (2 pts) Both subsidy programs increase the consumption of milk. Under which program is this
increase the greatest?