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Income inequality: the Lorenz curve, Gini coefficient and policies

Income inequality as a market failure of equity: income and wealth, absolute and relative poverty, the Lorenz curve drawn step by step, the Gini coefficient, the causes of inequality and the policies that reduce it, with their trade-offs. Through the latest ONS figures.

The richest fifth: 5.6 times the income of the poorest.

On 2 October 2026 the ONS reported that in the year to March 2025 the average disposable income of the richest fifth of UK households was 5.6 times that of the poorest fifth. The Gini coefficient, the standard measure of income inequality, was 32.7%, down 0.2 percentage points on the year before.

Before taxes and benefits the gap is far wider. In the year to March 2024 the richest fifth’s original income averaged £116,600 and the poorest fifth’s £9,600: 12.2 times as much.

Where you live matters too. In 2024 gross disposable household income per head was £36,487 in London, £22,258 in Northern Ireland, £21,469 in Wales and £20,562 in the North East.

Is a gap this size a market failure, and what can a government do about it?

Sources: ONS, Average household income, UK: financial year ending 2025 (2 October 2026); ONS, Effects of taxes and benefits on UK household income: financial year ending 2024 (25 September 2025); ONS, Regional gross disposable household income, UK: 1997 to 2024 (19 August 2026).

Income is a flow; wealth is a stock.

Income is a flow of money received as a reward for the services of a factor of production: wages for labour, rent for land, interest for capital and profit for enterprise. Wealth is a stock of assets held at a point in time, such as property, shares, pensions and savings. Wealth is spread far less evenly than income, and it earns income of its own.

Absolute poverty is a fixed standard, the same in every country and over time, such as living on less than a set number of dollars a day. Relative poverty is defined against the society you live in: the UK measure is a household income below 60% of the median.

The WJEC specification treats income inequality as a market failure. Unlike the others it is a failure of equity, not efficiency: a market can be efficient and still leave some households unable to afford the basics.

How a Lorenz curve is built.

A Lorenz curve shows how evenly income is shared out. It rests on three conditions:

  1. Every household is ranked from poorest to richest.
  2. Income is equivalised disposable income: after direct taxes and cash benefits, and adjusted for household size, because a family of four needs more than a single person for the same standard of living.
  3. Both axes are cumulative: each point adds in everyone poorer as well.

The figures on the diagram are for an illustrative country, close to the UK.

Think first

The poorest fifth of a country’s households receive 7% of its income.

The next fifth receive 12%. Every household is ranked from poorest to richest.

What share of the country’s income do the poorest 40% of households receive?

The poorest 40% are the poorest fifth plus the next fifth, so you add their shares: 7% + 12% = 19%. Adding up as you go is what a Lorenz curve does, and it is why both of its axes are cumulative.

Step by step

  1. Draw it in exam order. Axes first. Up the side: **cumulative % of income**. Along the bottom: **cumulative % of population**, ranked from poorest to richest. Both run from 0 to 100, so the diagram is a square.

    Teacher tip: Write the word cumulative on both axes. “Income” and “population” on their own are wrong, and it is the first thing an examiner checks.

    Check: Along the bottom axis of a Lorenz curve, households are ranked:

    Ranking from the poorest means each point shows the share of income going to the poorest part of the population.

  2. Next, the **line of perfect equality**: a straight 45° line from 0 to the top corner. Along it every household has the same income, so the poorest 20% receive 20% of income, the poorest half receive half and so on. Real distributions never sit on this line; it is the benchmark.

    Check: On the line of perfect equality, what share of income do the poorest 30% of households receive?

    With income shared equally, any 30% of households receive 30% of income.

  3. Now the **Lorenz curve**, built from a table of income by fifths. Here the poorest fifth receive 7% of income, so the curve passes through 20 along and 7 up. Add the next fifth’s 12% and the poorest 40% receive 19%. Keep adding: 36%, then 59%, then 100%. The curve starts at 0 and sags below the line.

    Check: Why must every Lorenz curve finish at the top right corner?

    At 100% of the population you have added up every household, so you must have 100% of income.

  4. Read it like any graph. Go up from the population axis to the curve, then across to the income axis. The poorest 40% receive 19% of income. The poorest 80% receive 59%. Draw the dotted lines and label both numbers, so the examiner can see the reading.

    Check: The poorest 80% receive 59% of income. What share do the richest 20% receive?

    Everyone together has 100%, so the richest fifth have 100 − 59 = 41%: more than twice an equal share.

  5. Now the two areas. Area A is the gap between the line of perfect equality and the Lorenz curve. Area B is everything under the curve. Together, A + B make the whole triangle under the line.

    Teacher tip: Shade A and label both letters. The Gini coefficient is built from them, so a diagram without A and B cannot show it.

    Check: Incomes become more unequal, so the Lorenz curve bows further from the line. What happens to area A?

    A is the gap between the line and the curve, so the further the curve sags, the bigger A becomes.

  6. The **Gini coefficient** is A ÷ (A + B). Here A = 16 and B = 34, so the Gini is 16 ÷ 50 = 0.32. It runs from 0 to 1, or 0 to 100 as a percentage: the ONS figure of 32.7% is 0.327. At 0 the curve lies on the line: perfect equality. At 1 one household has all the income: perfect inequality.

    Teacher tip: Higher Gini, more unequal. Under pressure students flip this. You will not be asked to measure the areas yourself, but you must know which way the number moves.

    Check: Another country has A = 10 and B = 40. Compared with this one, its income is:

    10 ÷ (10 + 40) = 0.2, lower than 0.32, so income is more evenly shared.

  7. The Gini measures how **evenly** income is shared, not how high it is. A country where everyone is equally poor can have a lower Gini than a rich one. A falling Gini does not mean everyone is better off. And inequality is not poverty: absolute poverty can fall while inequality rises.

    Check: A country’s Gini coefficient falls from 0.42 to 0.35. Which statement is definitely true?

    A lower Gini means income is less unevenly shared. It says nothing about how high incomes are.

  8. What causes inequality? Start in the labour market. **Wage differentials**: workers with scarce skills and high productivity earn far more than those with skills that are easy to find. **Unemployment**: a household with no one in work relies on benefits, which are well below average earnings. Low-paid and part-time work widens the gap further.

    Check: Which is a cause of income inequality that comes from the labour market?

    Different skills, qualifications and productivity earn very different wages, so earnings are spread unevenly.

  9. **Wealth and inheritance**: wealth earns income as rent, interest and dividends, and it is passed down, so gaps carry on across generations. **Tax and benefit design**: indirect taxes take a bigger share of poorer households’ income. In the year to March 2022 the poorest fifth paid 28.1% of their disposable income in indirect taxes and the richest fifth 9.8%. **Regional differences**: well-paid jobs cluster in London and the South East.

    Check: VAT is charged at 20% whatever your income. Why is it still regressive?

    Richer households save more of their income, and saving carries no VAT, so VAT takes a smaller percentage of a high income.

  10. So why is this a market failure? Follow the chain. A market can be perfectly efficient and still produce this result, so the failure is one of **equity**. Calling it a failure rests on a **value judgement** about what a fair distribution is, and people disagree.

    Teacher tip: Say it plainly in an answer: “this is an equity argument, which rests on a value judgement.” Writing “this is unfair” on its own is an opinion, not analysis.

    Check: Why is income inequality a different kind of market failure from pollution?

    Pollution means the wrong quantity is produced: an efficiency failure. Inequality is about how output is shared: an equity failure.

  11. Now the policies. A **progressive tax** takes a higher percentage of income as income rises. **Benefits** add to incomes at the bottom. Together they give the poorest a bigger share, so the Lorenz curve moves towards the line and the Gini falls. In the UK in the year to March 2024, direct taxes and cash benefits cut the Gini from 47.6% for original income to 32.9%.

    Check: Which describes a progressive tax?

    Progressive means the percentage of income paid rises with income, as with UK income tax.

  12. Benefits can be means-tested, paid only to those who pass a test of income, such as Universal Credit, or universal, paid to everyone in a group, such as the state pension. A minimum wage raises pay at the bottom of the labour market. Spending on education and training raises skills and productivity, which tackles wage differentials at their cause.

    Check: What is a drawback of means-tested benefits?

    Means tests need forms and proof of income; the complexity and the stigma mean many entitled households never claim.

  13. Redistribution has a cost. A higher **marginal rate** of income tax lowers the return to an extra hour of work and raises the reward for avoiding tax. On a **Laffer curve**, revenue rises with the tax rate up to t*, then falls: beyond t*, people work less, declare less or move abroad, and the tax base shrinks faster than the rate rises.

    Teacher tip: Nobody knows exactly where t* is. Say so, rather than claiming that a higher top rate must lose revenue.

    Check: A government raises its tax rate when it is already to the right of t*. What happens to tax revenue?

    Beyond t* the tax base shrinks faster than the rate rises, so revenue falls.

  14. So there is a trade-off between **equity** and **efficiency**. Taxes and benefits make the distribution fairer but can weaken the incentives to work, save and invest. Whether the gain in equity is worth the cost is a value judgement. A strong answer names the policy, shows how it moves the Lorenz curve and then weighs its cost.

    Check: Which of these is a value judgement?

    “Should” signals an opinion about what is fair; it cannot be tested with evidence.

What your diagram must show

  • Axes labelled: cumulative % of income and cumulative % of population
  • A straight 45° line of perfect equality from 0 to the top corner, labelled
  • The Lorenz curve below the line, starting at 0 and finishing at the top corner
  • One point read across to both axes, for example the poorest 40% receive 19% of income
  • Area A between the line and the curve shaded, area B under the curve labelled
  • Gini = A ÷ (A + B) written beside the diagram

A common mistake

The Lorenz curve is above the line of perfect equality. That would mean the poorest 20% receive 40% of income, more than an equal share, which cannot happen when households are ranked poorest first. A Lorenz curve always lies on or below the line.

Exam question

Using a Lorenz curve diagram, explain how a progressive income tax and benefits can reduce income inequality.

Model answer

A Lorenz curve plots the cumulative percentage of income against the cumulative percentage of the population, ranked from poorest to richest. The further it sags below the 45° line of perfect equality, the more unequal the distribution, and the higher the Gini coefficient, which is area A ÷ (A + B).

[Diagram: line of perfect equality and two Lorenz curves, original income further from the line and income after taxes and benefits closer to it. Area A between the line and the curve, area B under it.]

A progressive income tax takes a higher percentage of income from those on higher incomes, for example 40% on income above £50,270. Benefits such as Universal Credit add to the incomes of the poorest households. Together they give the poorest a bigger share of total income, so the Lorenz curve moves towards the line of perfect equality, area A shrinks and the Gini coefficient falls. In the UK in the year to March 2024, direct taxes and cash benefits cut the Gini from 47.6% to 32.9%.

**Good evaluation to add in:** a higher marginal rate lowers the return to extra work and raises the reward for avoiding tax, so beyond the peak of the Laffer curve revenue would fall and there would be less to redistribute. Means-tested benefits withdrawn as earnings rise can trap people in low pay. So redistribution trades some efficiency for equity, and how much is worth giving up is a value judgement.

Household income and Gini figures: ONS (September 2025 and October 2026). Regional income per head: ONS (August 2026). Indirect tax shares: ONS, as corrected in August 2024. Income tax bands: GOV.UK, 2026 to 2027. The Lorenz curve figures in the diagram are for an illustrative country. Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed.