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Government taxes motor fuel differently depending on the type of fuel. For many years, there was no tax on diesel fuel, but there was a substantial tax on petrol. At the
same time, the annual road tax on diesel powered vehicles was substantially higher than the road tax on petrol powered vehicles.
a) Suppose (the numbers are loosely based on reality) that the tax on petrol is raised from 40 cents per litre to 60 cents per litre. The before-tax total cost of retailing petrol
is $1.20 per litre. Assume that 100% of the tax is always passed through to consumers. After the increase in taxes, the quantity of petrol sold falls from 3,000,000
litres a day to 2,800,000 litres a day.
Calculate the price elasticity of demand for petrol using the mid-point formula, based on the change in price due to the tax. Use three decimal places in your calculations. What are the implications for policymakers who want to raise revenue, when considering raising taxes on petrol?
b) Predict the quantity of petrol sold if the before-tax total cost of retailing petrol rises from $1.20 to $1.50 per litre. The tax remains at 60 cents per litre. Assume that 100%
of the tax is always passed through to consumers. Use the elasticity estimate from (a) to provide the prediction in percentage change terms, and predict the final quantity of petrol sold after the price rises.
c) Also, provide the predicted quantity of petrol sold in (b) based on deriving the demand curve from the information provided. First derive a linear equation for the demand curve, then, provide the predicted quantity.
d) Identify i) the price elasticity of demand relationship between petrol and diesel-powered vehicles, and; ii) the price elasticity of demand relationship between vehicle ownership and fuel consumption. Provide the technical term (e.g. substitutes, complements, inferior) and the sign (e.g. positive, negative, neither). Justify your responses.
e) Explain how a policymaker who is considering how to raise tax revenues from fuel and vehicles should make use of the insights from your elasticity analysis in (d).
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