Price TheoryAssignment 1 – Consumer TheoryCarbon dioxide (CO2 ) is emitted when drivers use petrol to power their cars. CO2 emissions are a negative externality of petrol use as they contribute to global warming. Oneway to correct this market failure is to levy a corrective tax (also known as a Pigoviantax) on petrol.Suppose that Sally has an income of $324 per week. Sally’s utility is given by thevfunction U (x y) = x 20 y where x is the quantity of petrol (measured in litres) andy is the quantity of the composite good. The marginal utilities for this function are 10MUx = 1 and MUy = v .yInitially the price of petrol is Px = $1.5 per litre. The price of the composite good isPy = $1 per unit.Question 1: Find Sally’s optimum consumption basket. What level of utility does Sallyreceive from this basket? (4 Marks)Question 2: Illustrate your solution to question 1 on a graph. Your graph should havepetrol on the horizontal axis and the composite good on the vertical axis. Be sure toshow the budget line the optimum consumption basket and the indi?erence curve thatpasses through the optimum. (2 Marks)Question 3: Now suppose that the government places a tax on petrol raising the priceto 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. Onceagain show the budget line the optimum consumption basket and the indi?erence curvethat passes through the optimum. (2 Marks)Question 5: How much compensation would Sally need to receive after the tax is imposed to restore her original level of utility? How much petrol would Sally consume ifshe received this compensation? (4 Marks)Question 6: What are the income and substitution e?ects of the tax? (2 Marks)Question 7: With reference to the income and substitution e?ects you calculated inquestion 6 brie?y explain how providing compensation to Sally as in question 5 e?ectsthe e?cacy of the corrective tax? (2 Marks)1
