Microeconomics guide, Unit 6, step 25 of 28Previous step Next step

Step 25: Inequality and Redistribution

By the EconTutorials team. 11-minute read with 6 practice questions.

SyllabusAP Micro 6.5 · Cambridge 3.3, 8.2 · IB 2.12 (HL), 3.4

In 30 seconds

Income is a flow (what you earn each year); wealth is a stock (what you own). Wealth is usually shared out far more unequally than income.
The Lorenz curve shows how unequal a country is, and the Gini coefficient turns it into one number: $ G = \frac{A}{A+B} $, from 0 (perfect equality) to 1 (one person has everything).
Governments redistribute with progressive taxes, transfer payments and minimum wages, but each tool has costs for efficiency.
Exam point: a tax is progressive, proportional or regressive depending on what happens to the average tax rate as income rises.

Video lesson coming soonA short animated lesson for this step will appear here.

Income, wealth and what “inequality” means

Sara and Omar both earn $40,000 a year. Sara rents her flat; Omar inherited a house and some shares. Their incomes are equal, but their wealth is not. Looking only at income misses a large part of the gap.

Wealth produces income (a house can be rented out, shares pay dividends), so wealth gaps tend to grow into income gaps and can be passed down the generations.

Key termIncome inequality: unequal distribution of the flow of income (earned and unearned) between people or households over a period of time.

Key termWealth inequality: unequal distribution of the stock of assets (property, savings, shares) owned by people or households at a point in time.

Measuring inequality: the Lorenz curve and Gini coefficient

Line up every household from poorest to richest and ask: what share of total income do the poorest 20% receive? The poorest 40%? Plotting these cumulative shares gives the Lorenz curve.

DiagramDraw a square with “cumulative % of population” (poorest first) on the horizontal axis and “cumulative % of income” on the vertical axis. The 45-degree diagonal is the line of perfect equality (the poorest 20% get 20% of income, and so on). The Lorenz curve joins the same two corners but sags below the diagonal. Label the area between the diagonal and the Lorenz curve A, and the area under the Lorenz curve B. The further the curve bends away from the diagonal, the more unequal the country. If inequality falls (for example after a more progressive tax), the Lorenz curve moves closer to the diagonal and area A shrinks.

The Gini coefficient turns the picture into one number: the share of the triangle under the diagonal taken up by area A.

\[ G = \frac{A}{A+B} \]

Because the diagonal cuts the unit square in half, $ A + B = 0.5 $ when both axes run from 0 to 1. So you can also write $ G = 2A $. A Gini of 0 means perfect equality (the Lorenz curve is the diagonal, so A = 0). A Gini of 1 means perfect inequality (one household receives all the income). Some sources multiply by 100 and quote a “Gini index” such as 35 instead of 0.35.

Worked example

For example, in a country the area between the line of equality and the Lorenz curve is A = 0.16, and the area under the Lorenz curve is B = 0.34. Find the Gini coefficient. After new taxes and benefits, A falls to 0.12. What is the new Gini?

Step 1$ A + B = 0.16 + 0.34 = 0.50 $

Step 2$ G = \frac{0.16}{0.50} = 0.32 $

Step 3New B $ = 0.50 – 0.12 = 0.38 $, so new $ G = \frac{0.12}{0.50} = 0.24 $

The Gini falls from 0.32 to 0.24. The Lorenz curve has moved towards the line of equality, so income is now shared out more evenly.

Why are incomes unequal?

The best exam answers link each cause back to the labour market (wages set by demand for and supply of each type of labour) or to the ownership of assets.

Human capital. Human capital is the skills, education and experience a worker has. A surgeon has rare, productive skills, so demand for their labour is high and supply is low: wages are high. Less-skilled workers face more competition and earn less.
Discrimination. If employers pay some groups less, or refuse to hire them, for reasons of gender, ethnicity, religion or disability rather than productivity, those groups earn less for the same work.
Inheritance and wealth. Inherited property and shares pay rent and dividends on top of wages, and wealth buys better education, so advantage repeats over generations.
Market power. Monopoly owners earn supernormal profit. Powerful trade unions can push their members’ wages above the market rate. A monopsony employer (a single dominant buyer of labour) can pay workers less than their value to the firm.

Taxes: progressive, proportional and regressive

The key idea is the average tax rate: total tax paid divided by income. The marginal tax rate is the tax paid on the next dollar earned.

\[ \text{Average tax rate} = \frac{\text{Total tax paid}}{\text{Income}} \times 100 \]

Type	What happens as income rises	Effect on inequality
Progressive	Average tax rate rises	Reduces it
Proportional (flat)	Average tax rate stays the same	No change in shares
Regressive	Average tax rate falls	Increases it

Worked example

For example, a country taxes income at 0% on the first $10,000, 20% on income from $10,000 to $50,000, and 40% on income above $50,000. How much tax do Lina (income $20,000) and Karim (income $100,000) pay, and what are their average tax rates?

Step 1Lina: $ 0.20 \times (20{,}000 – 10{,}000) = 0.20 \times 10{,}000 = \$2{,}000 $

Step 2Lina’s average rate $ = \frac{2{,}000}{20{,}000} \times 100 = 10\% $

Step 3Karim: $ 0.20 \times 40{,}000 + 0.40 \times (100{,}000 – 50{,}000) = 8{,}000 + 20{,}000 = \$28{,}000 $

Step 4Karim’s average rate $ = \frac{28{,}000}{100{,}000} \times 100 = 28\% $

The average rate rises from 10% to 28% as income rises, so the tax is progressive. Karim’s marginal rate is 40%, but his average rate is only 28%, because the lower bands are taxed at lower rates.

Compare two other systems for the same two people:

Proportional: a flat 15% income tax. Lina pays $ 0.15 \times 20{,}000 = \$3{,}000 $; Karim pays $ 0.15 \times 100{,}000 = \$15{,}000 $. Both average rates are 15%.
Regressive: a 10% sales tax on spending. Lina spends $18,000 and pays $1,800, which is 9% of her income. Karim spends $60,000 and pays $6,000, which is 6% of his income. Karim pays more dollars, but a smaller share of his income, so the tax is regressive. Poorer households spend a bigger fraction of their income, which is why sales taxes and VAT are usually regressive.

Common mistakeSaying a tax is progressive “because the rich pay more money”. Under the sales tax above, Karim pays more dollars, yet the tax is regressive. Always judge by the average tax rate (tax as a percentage of income), not the amount paid.

Other ways to redistribute

Transfer payments are payments from the government to households with nothing produced in return: unemployment benefits, state pensions, child benefit, disability payments and housing support. Means-tested benefits go only to households below an income limit. They target help well but can create a poverty trap: if earning an extra $100 means losing $70 of benefit plus tax, working more barely pays.

A minimum wage is a price floor in the labour market. Workers who keep their jobs earn more. But in a competitive labour market, a minimum wage above equilibrium raises the quantity of labour supplied and cuts the quantity demanded, creating unemployment; the more elastic labour demand, the bigger the job loss. Under monopsony, a well-set minimum wage can raise both pay and employment.

A universal basic income (UBI) is a regular cash payment given to every adult, with no conditions and no means test. Supporters say it removes the poverty trap, is simple to run and has no stigma. Critics say it is very expensive, gives money to people who do not need it, and may reduce the incentive to work. Evidence so far comes mostly from small, short trials.

Key termEquity vs efficiency trade-off: policies that share income more fairly (equity) often reduce incentives to work, save or invest, which can shrink total output (efficiency).

The economist Arthur Okun called this the “leaky bucket”: money carried from rich to poor leaks away through administration costs and weaker incentives. But too much inequality can also harm efficiency: poorer families cannot afford education, so talent is wasted. Good evaluation says the size of the trade-off depends on how the policy is designed.

Absolute and relative poverty

Absolute poverty means a household’s income is too low to buy the basic necessities for survival: food, clean water, shelter and basic clothing. It is measured against a fixed line, such as the World Bank’s international poverty line of a few dollars per person per day. Relative poverty means a household’s income is far below the typical income in its own society, so it cannot take part in normal life. A common measure is income below 60% of the median household income.

For example, if median household income is $30,000, the relative poverty line is $ 0.60 \times 30{,}000 = \$18{,}000 $. If every income doubles, absolute poverty falls but relative poverty is unchanged, because the line doubles too.

Exam tipAP Micro (6.5): draw the Lorenz curve, show which way it moves when inequality changes, compare Gini values, and classify a tax by its average rate. Cambridge 9708: define income and wealth precisely, explain causes using wage determination, and evaluate every policy with the equity vs efficiency trade-off. IB: calculate a Gini from A and B and end policy evaluations with a clear judgement.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. Area A = 0.20 and area B = 0.30. Calculate the Gini coefficient. Show worked answer

$ G = \frac{A}{A+B} = \frac{0.20}{0.20 + 0.30} = \frac{0.20}{0.50} = 0.40 $.
A Gini of 0.40 shows moderate inequality.

EasyQ2. Explain the difference between income and wealth, giving one example of each. Show worked answer

Income is a flow of money received over a period, e.g. a monthly salary.
Wealth is a stock of assets owned at a point in time, e.g. a house or shares.

MediumQ3. A person earns $60,000. Tax is 0% on the first $12,000, 25% on income from $12,000 to $40,000, and 40% above $40,000. Find total tax, the average tax rate and the marginal tax rate. Show worked answer

Band 1: $12,000 at 0% = $0.
Band 2: $ 0.25 \times (40{,}000 – 12{,}000) = 0.25 \times 28{,}000 = \$7{,}000 $.
Band 3: $ 0.40 \times (60{,}000 – 40{,}000) = 0.40 \times 20{,}000 = \$8{,}000 $.
Total tax = $15,000.
Average rate = $ \frac{15{,}000}{60{,}000} \times 100 = 25\% $.
Marginal rate = 40% (the rate on the next dollar earned).

MediumQ4. A $500 TV licence fee is charged to every household. Household X earns $10,000 and Household Y earns $50,000. Is this tax progressive, proportional or regressive? Show your working. Show worked answer

X: $ \frac{500}{10{,}000} \times 100 = 5\% $.
Y: $ \frac{500}{50{,}000} \times 100 = 1\% $.
The average tax rate falls as income rises, so the fee is regressive, even though both pay the same amount.

MediumQ5. Five groups of 20% of households receive these shares of income, poorest first: 5%, 10%, 15%, 25%, 45%. Using trapezia of width 0.2, estimate area B and the Gini coefficient. Show worked answer

Cumulative shares: 0, 0.05, 0.15, 0.30, 0.55, 1.00.
Each trapezium = 0.2 × (left height + right height) ÷ 2.
Sum of average heights: $ 0.025 + 0.10 + 0.225 + 0.425 + 0.775 = 1.55 $.
$ B = 0.2 \times 1.55 = 0.31 $.
$ A = 0.50 – 0.31 = 0.19 $.
$ G = \frac{0.19}{0.50} = 0.38 $.

ExamQ6. Evaluate whether introducing a universal basic income is the best way for a government to reduce poverty. [12 marks] Show worked answer

Knowledge and understanding (up to 4): define UBI (unconditional, regular payment to every adult); distinguish absolute and relative poverty; contrast with means-tested benefits.
Analysis (up to 4): UBI guarantees a minimum income, reducing absolute poverty directly. It is not withdrawn as earnings rise, so it removes the poverty trap; it has low admin costs and full take-up. But it needs higher taxes, which may weaken incentives (equity vs efficiency), and much of the money goes to non-poor households.
Evaluation (up to 4): means-tested benefits are cheaper per dollar of poverty reduction; a minimum wage helps only those in work; education tackles a root cause but takes years. Judgement: UBI is most likely to be best where means-tested systems have severe poverty traps and the government can raise the revenue; long-run effects on labour supply are uncertain.

Check yourself

1. If a country’s Lorenz curve moves further away from the line of perfect equality, the Gini coefficient will:

Area A gets bigger, so A/(A+B) rises: inequality has increased.

2. A tax takes 8% of a poor household’s income and 3% of a rich household’s income. The tax is:

The average tax rate falls as income rises, so it is regressive.

3. If every household’s income doubles, what happens to relative poverty?

The relative poverty line (e.g. 60% of median) also doubles, so the same households stay below it.

Your score: 0 out of 3

The short version

Income is a flow, wealth is a stock; wealth is usually more unequal and can pass between generations.
The Lorenz curve sags below the line of equality; the Gini coefficient $ G = \frac{A}{A+B} $ runs from 0 to 1.
Inequality comes from differences in human capital, discrimination, inheritance and market power.
Progressive, proportional and regressive taxes are classified by the average tax rate as income rises.
Transfers, minimum wages and UBI all reduce poverty in some way, but face an equity vs efficiency trade-off; absolute poverty is about basic needs, relative poverty is about the gap with typical incomes.