Lorenz curve

Topic: Poverty and Inequality: Measurement and Policy · NCERT: Beyond NCERT

Meaning

A Lorenz curve is a graph that shows how income, spending or wealth is shared across a population. People are lined up from poorest to richest. The graph plots the cumulative (running total) share of population on the x-axis against the cumulative share of income, consumption or wealth they hold on the y-axis.

• The 45° line stands for perfect equality.
• The more the curve bows (sags) below the 45° line, the greater the inequality.

It matters because it shows the whole distribution in one picture, not just an average. The most widely used inequality number, the Gini coefficient, is calculated from it: G = A / (A + B) = 2A = 1 − 2B. Here A is the area between the 45° line and the Lorenz curve, and B is the area under the Lorenz curve.

Explanation

How the curve is drawn

• It was developed by Max Lorenz in 1905.
• Step 1: Rank everyone from the poorest to the richest.
• Step 2: Move along the x-axis: the poorest 20%, the poorest 40%, and so on up to 100%.
• Step 3: At each point, mark on the y-axis what share of total income that group holds.
• Fixed end points: the curve always starts at (0%, 0%) and ends at (100%, 100%).
• Shape: the curve can never rise above the 45° line, because the poorest 20% can never hold more than 20% of income. It bends upward, getting steeper as it moves towards the rich.

Reading the curve: equality to extreme inequality

• Perfect equality: the curve lies on the 45° line.

• The poorest 20% hold 20% of income, the poorest 40% hold 40%, and so on.

• Some inequality: the curve sags below the line.

• The bigger the gap (area A), the more unequal the society.

• Perfect inequality: one person has everything.

• The curve runs flat along the x-axis. At the very last point it shoots straight up to 100%.

• What moves the curve:

• Towards the 45° line (less inequality): when the poor gain faster than the rich, for example through welfare transfers or faster growth at the bottom.
• Away from the line (more inequality): when the rich gain faster, for example through inheritance or compounding returns on assets.

Worked example: same average, very different curves (Class 10, Development)

Both countries have five citizens. Both have an average monthly income of ₹10,000.

Cumulative population	20%	40%	60%	80%	100%
Country A: cumulative income share	19%	38.6%	58.6%	79%	100%
Country B: cumulative income share	1%	2%	3%	4%	100%

• Country A: incomes are ₹9,500, ₹9,800, ₹10,000, ₹10,200 and ₹10,500.
• Its curve stays almost on the 45° line, so income is shared almost equally.

• Gini ≈ 0.02

• Country B: four citizens earn ₹500 each and one earns ₹48,000.

• Its curve hugs the x-axis, then shoots up at the end. The bottom 80% hold only 4% of income.

• Gini = 0.76

• Lesson: an average cannot tell these two countries apart. The Lorenz curve can.

Crossing curves: the main weakness

• If one curve lies wholly above another: that society is clearly more equal, at every level of the distribution.
• If two curves cross, the ranking is ambiguous (unclear).
• Example: Society X gives its poorest people a bigger share, while Society Y gives its middle class a bigger share.
• No single number can then say which society is "more equal" without a value judgement (a choice about which group matters more).
• Because of this, two very different Lorenz curves can give the same Gini.

In India

• India's official inequality data are consumption-based. Consumption means household spending. The data come from MoSPI's Household Consumption Expenditure Survey (HCES). A consumption Lorenz curve usually sits closer to the 45° line than an income curve would, for two reasons:
• Consumption smoothing: people spread their spending over good and bad years.

• The rich save more: so the gap in spending is smaller than the gap in income.

• HCES 2023-24 consumption Gini (the numbers taken from the Lorenz curve):

• Rural 0.237 (down from 0.266 in 2022-23) and urban 0.284 (down from 0.314) [1].
• So both curves moved closer to the equality line in one year.

• The rural curve lies closer to the 45° line than the urban curve.

• Bottom of the curve lifted:

• The fastest growth in average MPCE (Monthly Per Capita Consumption Expenditure, i.e. average spending per person per month) was in the bottom 5–10% of the population [2].

• This means the lowest part of the curve rose.

• World Bank consumption Gini:

• 25.5 (2022-23), down from 28.8 (2011-12) [4].

• On this measure India is the 4th most equal country, after the Slovak Republic, Slovenia and Belarus [3].

• An income curve gives a different picture:

• The World Bank brief cites the World Inequality Database, which shows India's income Gini rising from 52 (2005) to 61 (2023) [4].
• So India's income Lorenz curve is bowing further away from the line.

• The brief also says consumption data may understate inequality [4].

• Wealth curve:

• Wealth data come from the NSS All-India Debt and Investment Survey (AIDIS). Its latest round was the 77th round (January–December 2019), conducted by the NSO under MoSPI [5].
• Wealth is far more concentrated than income, so a wealth Lorenz curve bows much more.

Don't confuse with

• Gini coefficient: the Lorenz curve is a graph, while the Gini is a single number (0 to 1) calculated from it (G = A/(A+B)). The curve shows where the inequality is. The Gini only shows how much there is.
• Kuznets curve: it shows how inequality changes over time as an economy grows (an inverted U). The Lorenz curve is a snapshot of the distribution at one point in time.
• Poverty ratio / poverty line: poverty counts only the people below a threshold. The Lorenz curve covers the whole distribution. Poverty can fall while the curve bows further out, for example when the rich gain much faster than the poor.
• 45° line vs the Lorenz curve: the 45° line is the benchmark of perfect equality, not the actual distribution. The gap between the two (area A) measures inequality.

Prelims Hooks

• Axes: x-axis = cumulative % of population, ranked poorest first. y-axis = cumulative % of income or wealth. The 45° line = perfect equality.
• The more the curve bows below the 45° line, the greater the inequality. Under perfect inequality, the curve runs along the x-axis and then rises straight up at the end.
• Gini = A/(A+B) = 2A = 1 − 2B. It ranges from 0 (perfect equality) to 1 (perfect inequality).
• Trap: if two Lorenz curves cross, you cannot rank the two societies without a value judgement. The same Gini can come from different curves.
• Trap: India's World Bank Gini of 25.5 (2022-23) comes from a consumption curve, not an income curve [4]. HCES 2023-24: rural 0.237, urban 0.284 [1].
• Names and years: Lorenz curve, Max Lorenz (1905). Gini coefficient, Corrado Gini (1912).

Mains Points

• Which curve should guide policy?
• India's consumption curve shows falling inequality: Gini 28.8 → 25.5 from 2011-12 to 2022-23 [4].
• Income estimates show rising inequality: 52 → 61 from 2005 to 2023 [4].

• India needs a regular official income and wealth survey so it can draw income and wealth Lorenz curves. Policy built only on consumption data may miss how concentrated incomes are at the top.

• Crossing curves force a value choice:

• A single Gini can hide who gained.
• So pair it with checks on specific parts of the curve:
  • Bottom-40 growth tracking (SDG 10.1): is the income of the poorest 40% growing faster than the national average? [6]
  • Palma ratio: the income share of the top 10% ÷ the income share of the bottom 40%.

• Together these show whether growth is lifting the bottom of the curve or pulling the top away.

• Welfare transfers vs asset gaps:

• The Economic Survey 2024-25 credits welfare schemes with raising consumption of low-income households [7]. This lifts the bottom of the consumption curve quickly.
• But the wealth curve is shaped by inheritance and compounding. Moving it needs longer-term tools: access to land and assets, education, and progressive taxation.

Related concepts

• Income inequality
• Wealth inequality
• Gini coefficient
• Palma ratio
• Theil index
• Atkinson index

Read more

• Inequality: concepts and measures