Anyone who uses a car regularly will often be frustrated by the perceived injustice of high fuel duty levied by government. Now two academics at the University of Derby have formulated a mathematical method for finding an optimum level of motor vehicle fuel duty that maximises government tax revenue. Motorists beware!
The duty that a government levies on motor vehicle fuel is nearly always controversial. Reducing the duty to stimulate economic growth means lower tax revenue – partly offset by people driving longer distances because of lower fuel prices. However, if a government tries to reduce its fiscal deficit by increasing fuel duty, its tax revenue increases – but again this may be partly offset by motorists driving shorter distance because of higher fuel prices.
Government aggregate fuel tax revenue depends on other factors not just fuel duty, such as the distance people travel by car, fuel consumption and the price of petrol in the absence of duty – ie the petrol price based on the price of oil alone. However, in this method the academics have considered government fuel duty revenue solely as a function of the fuel duty levied. For further simplification, the method does not consider vehicle excise duty and VAT.
Using their method the academics are able to produce a graph to show the optimal tax rate.
fuel duty that maximises the revenue on that duty is around £1.63 per litre: somewhat higher than it currently is at around 80p per litre. It needs to be emphasised that aggregate government revenue for fuel duty depends upon other factors affecting the amount people drive. However, this model presents a plausible approximation for solving, what is for some governments, a profound problem.
A key conclusion of the research, according to the authors, is that on the one hand motorists may take comfort from there being a finite limit to the level at which it is worthwhile for a government to raise fuel duty. On the other hand this comfort should be tempered by the realisation that governments could substantially raise fuel duty above its current level before it became fiscally disadvantageous for them to do so.
A full article – with a detailed explanation of the mathematics – is published in the October 2012 issue of Mathematics Today (http://www.ima.org.uk/_db/_documents/mt_optimising_government_fuel_duty_revenue1012.pdf).
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Notes for Editors
- The Institute of Mathematics and its Applications (IMA) is the learned and professional society for mathematics. It promotes mathematics research, education and careers, and the use of mathematics in business, industry and commerce. Amongst its activities the IMA produces academic journals, organises conferences, and engages with government. Founded in 1964, the Institute has 5,000 members. Forty percent of members are employed in education (schools through to universities), and the other 60% work in commercial, industrial and governmental organisations. In 1990 the Institute was incorporated by Royal Charter and was subsequently granted the right to award Chartered Mathematician and Chartered Mathematics Teacher designation.
- The IMA is a member of the Council for the Mathematical Sciences, which also incorporates the London Mathematical Society, Royal Statistical Society, the Edinburgh Mathematical Society and the Operational Research Society.
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