Price Theory
Assignment 1 { Consumer Theory
Carbon dioxide (CO2) is emitted when drivers use petrol to power their cars. CO2 emis-
sions are a negative externality of petrol use, as they contribute to global warming. One
way to correct this market failure is to levy a corrective tax (also known as a Pigovian
tax) on petrol.
Suppose that Sally has an income of $300 per week. Sally’s utility is given by the
function U(x; y) = pxy, where x is the quantity of petrol (measured in litres), and y is
the quantity of the composite good. The marginal utilities for this function are,
MUx =
py
2px
and MUy =
px
2py
:
Initially, the price of petrol is Px = $1:5 per litre. The price of the composite good is
Py = $1 per unit.
Question 1: Find Sally’s optimum consumption basket. What level of utility does Sally
receive from this basket? (4 Marks)
Question 2: Illustrate your solution to question 1 on a graph. Your graph should have
petrol on the horizontal axis, and the composite good on the vertical axis. Be sure to
show the budget line, the optimum consumption basket and the indierence curve that
passes through the optimum. (2 Marks)
Question 3: Now suppose that the government places a tax on petrol, raising the price
to Px = $2 per litre. How does the tax alter Sally’s behaviour and utility? (4 Marks)
Question 4: Add your solution to question 3, to your graph from question 2. Once
again, show the budget line, the optimum consumption basket and the indierence curve
that passes through the optimum. (2 Marks)
Question 5: How much compensation would Sally need to receive after the tax is im-
posed, to restore her original level of utility? How much petrol would Sally consume if
she received this compensation? (4 Marks)
Question 6: How does providing compensation to Sally, as in question 5, aect the
ecacy of the corrective tax? Brie y explain. (4 Marks)

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