Suppose that Elsa's preferences over baskets containing gasoline (good x), and food (good y), are described by the utility function U (x; y) = xy + 100y. The marginal utilities for this function are, MUx = y and MUy = x + 100: Use Px to represent the price of gasoline, Py to represent the price of food, and I to represent Elsa's income.
a) Suppose that the price of gasoline is $2 per litre, the price of food is $5 per kilogram, and Elsa's income is $400. She consumes 50 units of gasoline and 60 units of food with level of utility at 9000. Now that the government is considering two alternative policies to improve Elsa's welfare. (Graph required)
Policy 1: Place a $0.4 per litre subsidy on gasoline, reducing the price of gasoline to $1.6 per litre.
Policy 2: Give Elsa a voucher that can be used to purchase food (but not gasoline).
What value of voucher will cause policy 2 to have the same effect on Elsa's utility as policy 1?
b) Which of the two policies, described in part (a), is least costly to the government? (Assume that the value of the voucher in Policy 2 is your answer to part a) .Briefly explain why this is the case.
Draw any graph if needed.