AQA A-level Economics: Income and wealth: Lorenz curve and Gini coefficient (7136) – Revision Notes

These notes condense the first part of the sub-section The distribution of income and wealth: poverty and inequality in the AQA AS and A-level Economics specification (version 1.3, 29 June 2022), first taught from September 2015: 3.1.7.1 on the AQA website, 4.1.7.1 in the combined PDF. Poverty and redistribution policy are covered in other units. All data are invented, for illustration only.

For full explanations read the study guide, then test yourself with the practice questions. Track progress on the printable checklist, find the rest of the course on the AQA A-level Economics hub and take the free 10-minute diagnostics to find weak spots.

Key definitions

Term	Meaning
Income	Receipts over a period (a flow): pay, profit, rent, interest, dividends, benefits
Wealth	Net assets at one moment (a stock): property, savings, shares, pension rights, minus debts
Equality	Everyone has the same share
Equity	A distribution judged fair and just; involves a value judgement
Lorenz curve	Running total of income (or wealth) held by households lined up poorest first
Line of perfect equality	The 45-degree line on the Lorenz diagram
Gini coefficient	Gap between curve and diagonal, divided by the triangle under the diagonal; 0 to 1

The specification says you interpret the Gini coefficient and do not calculate it.

Factors influencing distribution

Income	Wealth
Skills, education, experience	Gifts and bequests received
Bargaining power, unions, monopsony	Capacity to save (greater at higher income)
Discrimination	Age and the life cycle
Unemployment, part-time work	Asset price rises, especially housing
Asset ownership	Compound returns
Technology and globalisation	Pension rights
Household size and earners	Tax on capital and inheritance
State taxes, benefits, minimum wage

Compounding reminder. 50,000 at 5% for 10 years: 50,000 x 1.05^10 = 81,445. Early assets grow and pass on.

UK knowledge (general pattern, no figures needed)

• Wealth is much more unequal than income.
• Property and pension rights are the largest components of household wealth.
• Taxes and benefits narrow income inequality.
• Older households hold more wealth than younger ones.
• Regional gaps exist, with London and the South East typically higher.

Reading a Lorenz curve: method

1. Check the axes: cumulative % of households (poorest first) on the horizontal axis, cumulative % of income on the vertical.
2. Compare the curve with the line of equality. The further below it, the more unequal.
3. Pick out points: “the poorest 40% receive X%”.
4. If two curves are given, the one closer to the line is more equal, unless they cross.
5. If they cross, say the ranking depends on which part of the distribution you care about.
6. Link to the Gini: bigger area between line and curve means a higher coefficient.

Worked reminder. Country C’s household income by fifth, poorest to richest:

Fifth	Share before (%)	Cumulative before	Share after (%)	Cumulative after
1st	6	6	7	7
2nd	10	16	11	18
3rd	15	31	16	34
4th	22	53	23	57
5th	47	100	43	100

Suppose the Gini falls from 0.38 to 0.34.

• Fall: 0.38 - 0.34 = 0.04, which is 0.04/0.38 = 10.5%.
• Poorest 40%: 16% before, 18% after.
• Richest fifth share relative to poorest: 47/6 = 7.8 before, 43/7 = 6.1 after.
• Interpretation: the Lorenz curve moved towards the line; distribution became more equal. Say nothing about the size of anyone’s absolute income.

Gini: interpretation checklist

• 0 is perfect equality; 1 is the extreme where one household holds everything.
• Higher means more unequal.
• Compare like with like: same unit (person or household), before or after tax, income or wealth.
• A wealth Gini is usually above an income Gini for the same country.
• A fall is not proof that the poor are better off in absolute terms.
• Equal Ginis can hide different shapes if the curves cross.
• Limits: one number, hidden detail at the top, weak data on the very rich and on informal income.

Equality versus equity

• Equality is measurable. Equity is not, because it depends on values.
• Contribution rule: reward effort. Need rule: give more to the needy. Equal shares rule: same for all.
• The degree of inequality can be measured, but whether it is fair involves a value judgement.
• Value judgements shape which policies people support.

Benefits and costs

	More equal	More unequal
Benefits	Higher consumption; less poverty; social cohesion; better use of talent	Incentives; saving and investment; enterprise; reward for risk
Costs	Weaker incentives at high marginal tax rates; possible capital and skills flight	Waste of potential; weaker demand; social tension; political influence

Transfer reminder. 500 moves from a household with a marginal propensity to consume of 0.4 to one with 0.8: -200 + 400 = +200 of consumption.

Evaluation points. Degree (excessive inequality), method of change, time period, elasticity of effort and saving, and the value judgement behind the conclusion.

Chains of reasoning to rehearse

Why a rise in the top marginal tax rate may or may not narrow inequality.

1. Higher rate cuts the after-tax income of the richest.
2. Revenue can fund benefits and public services for the poorest.
3. So the Lorenz curve moves towards the line.
4. But some high earners may work less, move abroad or avoid tax.
5. If revenue falls short, the gain is smaller.
6. Judgement: it depends on how responsive effort and location are, and on how much weight you give to equality.

Why inequality can slow growth.

1. Low-income households cannot fund education or training.
2. Human capital is under-used.
3. Productivity and output grow more slowly.
4. But high earners save more, which can fund investment, so the net effect is uncertain.

Inequality and market failure

Cause. Low incomes limit ability to pay, so merit goods are under-consumed, credit constraints block skills investment and human capital is wasted. External benefits are lost.

Consequence. Monopoly profit goes to owners; monopsony cuts wages; poor areas bear more pollution; missing insurance and credit markets hit the poor hardest; immobile labour is stuck in low pay.

Chain. Market failure, then unequal income, then low ability to pay, then under-investment, then more market failure.

Must-know distinctions

• Income (flow) versus wealth (stock).
• Equality (same shares) versus equity (fair shares).
• Measuring inequality (positive) versus judging it (normative).
• Lorenz curve (a picture) versus Gini (a summary number).
• Relative change in the Gini versus a change in absolute living standards.
• Some inequality versus excessive inequality.

Quick self-test

1. Define wealth.
2. A household has a house worth 180,000, a mortgage of 120,000, savings of 20,000, and pension rights of 30,000. Annual income is 25,000. Find net wealth and its ratio to income.
3. Which way does a Lorenz curve move when inequality falls?
4. A Gini coefficient falls from 0.38 to 0.34. Calculate the percentage fall.
5. Two countries both have a Gini of 0.31. Give one reason their distributions could still differ.
6. Give one reason wealth is more unequally distributed than income.
7. 800 is moved from households with a marginal propensity to consume of 0.5 to households with 0.9. Calculate the net rise in consumption.
8. Distinguish equality from equity.
9. Give one way market failure can increase inequality.
10. Identify one route from inequality to market failure.

Answers

1. Net assets held at one point in time: what is owned minus what is owed.
2. 180,000 - 120,000 + 20,000 + 30,000 = 110,000; 110,000/25,000 = 4.4 times income.
3. Towards the line of perfect equality.
4. 0.04/0.38 = 10.5%.
5. Their Lorenz curves may cross, so the shares of the poorest and the richest differ.
6. Inheritance and compounding let assets build up over generations; saving needs spare income. Housing gains favour existing owners.
7. -0.5 x 800 + 0.9 x 800 = -400 + 720 = +320.
8. Equality means the same shares for everyone; equity means a fair distribution, which is a value judgement.
9. Monopoly profits flow to owners of firms, or monopsony pushes down wages.
10. Low-income households cannot afford merit goods such as health care, so consumption falls below the social optimum.

Where marks are usually lost

• Describing wealth as a flow, or swapping it with income.
• Reading a higher Gini as more equality.
• Calculating the Gini when the question asks for interpretation.
• Using “fair” and “equal” as if they mean the same.
• Stating the Lorenz axes without saying households are ranked poorest first.
• Saying a lower Gini means the poor are richer in absolute terms.
• Treating any inequality as a market failure rather than excessive inequality.
• Evaluating with a list of benefits and costs but no judgement or no reason for it.
• Quoting UK figures without a source instead of the general pattern.

Official syllabus

AQA, AS and A-level Economics specification (7135 and 7136), version 1.3, 29 June 2022, first teaching from September 2015: section 3.1.7.1 on the AQA website (printed as 4.1.7.1 in the combined PDF).