Price Theory Assignment - Consumer Theory

Suppose that Sally's preferences over baskets containing petrol (good x), and food (good y), are described by the utility function U(x, y) = xy + 100y. The marginal utilities for this function are, MU_x = y and MU_y = x + 100.

Use P_x to represent the price of petrol, P_y to represent the price of food, and I to represent Sally's income.

Question 1: Find Sally's petrol demand function, and Sally's food demand function.

Question 2: From Sally's perspective, is food a normal good, an inferior good, or neither normal nor inferior? Briefly explain with reference to your answer to question 1.

Question 3: Suppose that the price of petrol is $2 per litre, the price of food is $5 per kilogram, and Sally's income is $400. What quantities of food and petrol does Sally consume? What level of utility does Sally receive from this consumption basket?

Question 4: Suppose that, as in question 3, the price of petrol is $2 per litre, the price of food is $5 per kilogram, and Sally's income is $400. Now suppose that the government is 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 $1.6 per 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 as policy 1?

Question 5: Which of the two policies, described in question 4, is least costly to the government? (Assume that the value of the voucher in Policy 2 is your answer to question 4.) Briefly explain why this is the case.