Suppose that the price of COVID tests is strictly controlled. Claudia has an income of $425 per week with which she purchases tests, good x, and other goods, good y, where the price of other goods is $1 per unit. Suppose that Claudia's preferences are convex (her MRSX,Y is a decreasing function of x and an increasing function of y).

Old policy: Claudia can buy up to five tests per week and pay $5 each at the government store. However, any additional test beyond the 5th costs $50 on the black market.

a. Draw Claudia's budget constraint.

b. New policy: suppose the market for tests is decontrolled and the price is now $25 per test. Include the new budget line on the graph of part a. Why do the two budget lines intersect at x = 9?

c. Suppose that, under the old policy, Claudia chose to purchase 4 tests per week. Which policy will she prefer? Explain and illustrate your answer on a new graph with the two budget lines and Claudia's old choice.

d. Suppose that, under the old policy, Claudia chose to purchase 10 tests per week. Which policy will she prefer? Explain and illustrate your answer on a new graph with the two budget lines and Claudia's old choice.

e. Finally, suppose that, under the old policy, Claudia chose to purchase 7 tests per week. By referring to a new graph, clearly discuss why, without having information about her utility function) we cannot predict which of the two policies she prefers.