Price Theory Assignment 1 – Consumer Theory
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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,
MUx = y and MUy = x + 100.
Use Px to represent the price of petrol, Py to represent the price of food, and I to represent
Question 1: Find Sally’s petrol demand function, and Sally’s food demand function. (8
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. (2 Marks)
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? (3
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
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? (8 Marks)
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. (4 Marks)