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

This guide follows the AQA AS and A-level Economics specification (version 1.3, 29 June 2022), first taught from September 2015. It covers the first part of the sub-section The distribution of income and wealth: poverty and inequality, called The distribution of income and wealth (3.1.7.1 on the AQA website, printed as 4.1.7.1 in the combined PDF). Poverty and the policies that redistribute income are separate units and are not repeated here. Every country, household and number below is invented, for illustration only.

Use it with the revision notes and the practice questions. The course hub is AQA A-level Economics, the printable checklist tracks progress, and the free 10-minute diagnostics show weak spots. For the wider market-failure context, see the microeconomics overview.

Outcomes at a glance

Outcome in the specification	Where it is covered
The difference between income and wealth	Section 1
Factors influencing the distribution; some knowledge of UK household income and wealth	Sections 2 and 3
Equality versus equity	Section 4
The Lorenz curve and Gini coefficient (interpret, not calculate)	Section 5
Likely benefits and costs of more and less equal distributions	Section 6
Excessive inequality as a cause and consequence of market failure	Section 7
Value judgements and policy prescriptions	Section 8

1. Income and wealth

Income is what a household receives across a period of time: earnings from work, business profit, rent, interest, dividends and state benefits. It is a flow. Wealth is a stock: the value of what is owned at one moment, such as property, savings, shares, pension rights and other possessions, less debts.

Worked example. A household in Country A earns 30,000 a year. It owns a house worth 250,000 with a mortgage of 150,000, savings of 10,000 and pension rights of 40,000.

Net wealth = 250,000 - 150,000 + 10,000 + 40,000 = 150,000. That is 5 times annual income.

Two points follow. A household can be income-rich and wealth-poor (a high earner with debts) or the reverse (a retired owner of a paid-off house). And wealth generates income (rent, interest, dividends), so unequal wealth feeds unequal income.

2. Factors influencing the distribution

Income.

• Wage differences from skills, education, experience and the supply of and demand for each type of labour.
• Bargaining power, trade union coverage, and monopsony employers.
• Discrimination, by gender, ethnicity or age.
• Unemployment, inactivity and part-time work.
• Ownership of assets that pay returns.
• Technological change, which can raise the pay of skilled workers and cut demand for routine work.
• Household type and size, and the number of earners.
• Government taxes, benefits and the minimum wage (these shape income after redistribution).

Wealth.

• Inheritance and gifts received.
• Capacity to save, which is greater when income is higher.
• Age: people build assets over a working life and run them down in retirement.
• Asset price changes, such as a rise in house prices, which benefit existing owners.
• Compounding returns.

Worked example (compounding). Household X inherits 200,000 and invests it at 3% a year for 20 years. Household Y starts with nothing and saves 4,000 a year for 20 years at 3%.

X: 200,000 x 1.03^20 = 361,222. Y: 4,000 x (1.03^20 - 1)/0.03 = 107,481.

X ends with more than three times as much as Y, although Y saved 80,000 of its own income. The gap shows how wealth inequality can persist across generations.

3. Some knowledge of the UK

The specification expects some knowledge of UK household income and wealth. You do not need exact figures, but you should know the pattern. The Office for National Statistics publishes the data, so check the latest release before an exam.

• Wealth is distributed far more unequally than income.
• Property and pension rights are the largest parts of household wealth.
• Taxes and cash benefits narrow income inequality: the after-tax-and-benefit distribution is more equal than the earlier one.
• Older households tend to hold more wealth than younger ones.
• Incomes and wealth differ by region, with London and the South East typically higher.

4. Equality and equity

Equality means everyone gets the same share. Equity means a distribution that is fair and just. The two are different, and the specification says that deciding what is equitable involves a value judgement. The degree of inequality can be measured. Whether it is fair cannot be settled by measurement.

Worked example. Three households share a fund of 90 units.

• Equal shares: 30 each.
• Shares by effort or contribution: unequal, but some think this fairer because it rewards work.
• Shares by need, such as a household with children getting more: unequal again, but some think it fairest.

Only the first rule gives equality. People applying different value judgements will each call a different split equitable. An economist can show who gains and loses. The choice between rules is a normative one.

5. The Lorenz curve and the Gini coefficient

The Lorenz curve is drawn with households lined up from poorest to richest along the horizontal axis (as a cumulative percentage). The vertical axis shows the running total of income (or wealth) those households hold, also in percent. The line of perfect equality runs diagonally at 45 degrees from the origin, and on it the poorest 20% of households hold exactly 20% of the total. The Lorenz curve sags below this line. The further it sags, the greater the inequality.

Cumulative % of income
100 |                                        *
 80 |                                /    o
 60 |                        /         o
 40 |                /            o
 20 |        /           o
  0 |*
    +------------------------------------------
     0     cumulative % of households    100
     / line of equality     o Lorenz curve (sags below it)

The Gini coefficient is a ratio of areas: the gap between the Lorenz curve and the diagonal, divided by the whole triangle under the diagonal. Its value lies between 0, when every household has the same, and 1, when a single household holds the lot. A higher value means more inequality. The specification says you must interpret the coefficient and not calculate it, so the Gini values below are given.

Worked example (reading Lorenz data). Country A’s household income by fifth, from poorest to richest:

Fifth of households	Share before tax and benefits (%)	Cumulative (%)	Share after (%)	Cumulative (%)
Poorest	4	4	7	7
Second	9	13	12	19
Third	14	27	17	36
Fourth	22	49	23	59
Richest	51	100	41	100

Suppose the published Gini coefficients are 0.43 before and 0.32 after.

• The poorest 40% receive 13% before and 19% after.
• The richest fifth’s share is 51/4 = 12.75 times the poorest fifth’s before, and 41/7 = 5.9 times after.
• The Gini fell by 0.43 - 0.32 = 0.11, a fall of 0.11/0.43 = 25.6%.
• The Lorenz curve moved towards the line of equality. Taxes and benefits made the distribution more equal.

With 100 households and total income of 5,000, each household in the poorest fifth moves from 10 to 17.5, and each in the richest fifth from 127.5 to 102.5. The richest fifth lose 500 in total (10 points of 5,000), while the other four fifths gain 500 between them.

Limitations.

• One number hides the shape. Country B has shares of 4, 10, 22, 32 and 32 (cumulative 4, 14, 36, 68, 100) and a Gini of about 0.31, almost the same as Country A after tax. But B’s curve lies below A’s up to the 60% point and above it beyond, so the curves cross. Equal Ginis do not mean equal distributions.
• It says nothing about absolute living standards. A poor, equal country can have a low Gini.
• Results depend on the unit (individual or household), on income before or after tax, and on whether wealth is included.
• Data on the very rich and on informal income are often weak.

6. Benefits and costs of more or less equal distributions

	More equal	More unequal
Likely benefits	Higher spending, as poorer households spend more of extra income; less poverty; better health, education and social cohesion; use of talent that would otherwise be wasted	Rewards for effort, skill and risk-taking; higher saving and investment by high earners; incentive to work and to start firms
Likely costs	Weaker incentives if marginal tax rates are high; possible loss of savings, investment and skilled workers; administration costs	Poverty and wasted potential; weaker demand; social tension; political influence of the wealthy; lower mobility

Worked example. The government moves 1,000 from rich households with a marginal propensity to consume of 0.3 to poor households with 0.9.

Rich spending falls by 0.3 x 1,000 = 300. Poor spending rises by 0.9 x 1,000 = 900. Net consumption rises by 600.

Evaluation. The balance depends on the degree. Some inequality rewards effort. The specification speaks of excessive inequality, and each side’s costs rise as it goes further. It also depends on how equality is achieved (high tax rates or better education), how responsive effort and saving are, the time period, and which values you hold.

7. Inequality as a cause and consequence of market failure

As a cause. Inequality limits what low-income households can buy. Markets respond to ability to pay, not need. This can lead to under-consumption of merit goods such as health care and education, to credit constraints that block investment in skills, and to wasted human capital.

Worked example. Five households value a preventive check-up at 100, 90, 75, 62 and 38. It costs 60 to provide, and each check-up brings an external benefit of 20. The fourth household values it at 62 but can afford only 45.

Without the constraint, four households buy, which is also the socially efficient number because 38 + 20 = 58 is below the cost of 60. With the constraint, three buy. The fourth check-up has a social benefit of 62 + 20 = 82 against a cost of 60, so the welfare loss is 82 - 60 = 22.

As a consequence. Market failure can raise inequality: monopoly profits go to owners of firms, monopsony lowers wages, immobile labour gets stuck in low-paid areas, poor households bear more pollution, and missing insurance markets expose them to shocks.

Market failure --> unequal incomes and wealth
      ^                      |
      |                      v
Under-investment <-- low ability to pay

This loop is why inequality can be self-reinforcing.

8. Value judgements and policy views

A person who weights equality heavily will favour a flatter distribution and stronger redistribution. A person who weights incentives and individual reward will accept more inequality and prefer to target a minimum standard. Both can accept the same data. The specification says these value judgements influence policy prescriptions, so in evaluation state which value judgement your conclusion rests on.

Common errors

• Treating wealth and income as the same, or wealth as a flow.
• Reading a higher Gini as more equality.
• Describing the Lorenz curve as plotting income against income.
• Saying equity means equality.
• Claiming a fall in the Gini means the poor are better off in absolute terms.
• Calling any inequality a market failure instead of excessive inequality.

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).