# Suppose that Sally’s preferences over baskets containing petrol (good x), and food (goody), are described by the utility function U(x, y) = xy + 100y….

Suppose that Sally’s preferences over baskets containing petrol (good x), and food (goody), are described by the utility function U(x, y) = xy + 100y. The marginal utilities forthis function are,MUx = y and MUy = x + 100.Use Px to represent the price of petrol, Py to represent the price of food, and I to representSally’s income.Question 1: Find Sally’s petrol demand function, and Sally’s food demand function. (8Marks)Question 2: From Sally’s perspective, is food a normal good, an inferior good, or neithernormal nor inferior? Briefly explain with reference to your answer to question 1. (2 Marks)Question 3: Suppose that the price of petrol is \$2 per litre, the price of food is \$5 perkilogram, and Sally’s income is \$400. What quantities of food and petrol does Sallyconsume? What level of utility does Sally receive from this consumption basket? (3Marks)Question 4: Suppose that, as in question 3, the price of petrol is \$2 per litre, the priceof food is \$5 per kilogram, and Sally’s income is \$400. Now suppose that the governmentis considering two alternative policies to improve Sally’s welfare.Policy 1: Place a \$0.4 per litre subsidy on petrol, reducing the price of petrol to \$1.6per litre.Policy 2: Give Sally a voucher that can be used to purchase food (but not petrol).What value of voucher will cause policy 2 to have the same effect on Sally’s utility aspolicy 1? (8 Marks)Question 5: Which of the two policies, described in question 4, is least costly to thegovernment? (Assume that the value of the voucher in Policy 2 is your answer toquestion 4.) Briefly explain why this is the case. (4 Marks)