Maths in economics, finance and society · Accessible · Dissertation

How progressive is UK income tax?: a maths EPQ idea

Why it works as an EPQ

Piecewise functions, marginal and average rates, and graphs that reveal surprising features.

Scope and difficulty

Accessible. Accessible. Use the current published rates and thresholds from gov.uk and say which tax year.

The maths

Builds on these A Level topics: Algebra and functions · Coordinate geometry · Differentiation.

You would learn:

• Piecewise functions
• Marginal and average rates
• Measures of progressivity

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Model tax and National Insurance as piecewise functions of income for one tax year.
2. Plot marginal and average rates.
3. Find and explain any bands where the marginal rate jumps.
4. Judge how progressive the system is by a measure you justify.

Pitfalls

• Mixing rates from different tax years.
• Not stating which part of the UK the rates apply to.

Where to start reading

• Income Tax and National Insurance rates on gov.uk
• Search for: marginal tax rate average tax rate

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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