Inequality: concepts and measures

Detail

1. Poverty vs inequality

• Poverty is about a threshold. It asks one question: who lives below the poverty line?

• The poverty line is a minimum level of income or spending needed for basic needs.

• Inequality is about the whole distribution. It asks how income is spread among everyone, from the poorest to the richest.

• The two can move in opposite directions:
• Suppose everyone's income rises, but the rich gain much faster.
• Then fewer people are below the line, so poverty falls.

• But the gap between the top and the bottom grows, so inequality rises.

• Indian example (2011-12 to 2022-23):

• The share of Indians living on less than US$2.15 a day fell from 16.2% (2011-12) to 2.3% (2022-23) [5][4].
• Over the same period, the consumption Gini fell from 28.8 to 25.5 [5][4].
• So in this period, measured on consumption, poverty and inequality both fell. On income, however, inequality appears to have risen (see §4.2).

2. Forms of inequality

2.1 Income inequality

• Definition: income is shared unequally among people or households.
• How it is measured: the Gini coefficient, the Palma ratio, or income shares (for example, the share of the top 10%).
• Policy view:
• Indian planning aimed to reduce income inequality.
• Critics argue that market-led globalisation widened it.

2.2 Consumption inequality

• Definition: people's spending is shared unequally.
• It is usually lower than income inequality, for two reasons:
• Consumption smoothing: people spread their spending over good and bad years. They borrow or use savings when income falls.

• The rich save more: a large part of a rich person's income is saved, not spent. So the spending gap is smaller than the income gap.

• India's official inequality data are consumption-based. They come from MoSPI's Household Consumption Expenditure Survey (HCES).

• Latest data, HCES 2023-24 [2][3]:

Consumption Gini	2022-23	2023-24
Rural	0.266	0.237
Urban	0.314	0.284

• The Gini fell in almost all major states, in both rural and urban areas (2022-23 to 2023-24) [2].
• 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, in both rural and urban areas [3].
• Economic Survey 2024-25: government welfare schemes raised consumption in low-income households and helped reduce inequality [9].

2.3 Wealth inequality

• Definition: assets are held unequally. Assets include land, housing, gold, and financial holdings such as deposits and shares.
• Wealth is far more concentrated than income, for two reasons:
• Inheritance: wealth passes down families.

• Compounding: assets earn returns, those returns are reinvested, and wealth grows on itself.

• Indian data source: the NSS All-India Debt and Investment Survey (AIDIS).

• The latest AIDIS was the 77th round of the NSS (January–December 2019). It was conducted by the National Statistical Office (NSO), MoSPI [6].
• Average asset value per rural household (2019) [6]:
  • All rural households: ₹15,92,379
  • Cultivator households: ₹22,07,257
  • Non-cultivator households: ₹7,85,063
• So an average cultivator household held about 2.8 times the assets of a non-cultivator household (22,07,257 ÷ 7,85,063 ≈ 2.81).
• Average debt per rural household (2019): ₹59,748 [6].

2.4 Vertical vs horizontal inequality

• Vertical inequality: the gap between rich and poor individuals, with everyone ranked on one scale.
• Horizontal inequality: the gap between groups, such as castes, religions, regions, genders, or rural and urban areas.
• Example: rural–urban gap in India [3]:
  • Average MPCE in 2023-24 was ₹4,122 (rural) and ₹6,996 (urban). This excludes the value of items received free through welfare schemes.
  • The urban–rural consumption gap narrowed from 84% (2011-12) to 70% (2023-24).
• Horizontal gaps matter politically. Group-based gaps can feed social conflict even when the gap between individuals is modest.

3. Averages hide disparities (Class 10, Development, Table 1.2)

Country	I	II	III	IV	V	Average
A	9,500	10,500	9,800	10,000	10,200	₹10,000
B	500	500	500	500	48,000	₹10,000

• Both countries have the same average monthly income of ₹10,000.
• In Country B:
• The bottom 80% (four citizens) get only ₹2,000 of the total ₹50,000. That is just 4% of income.

• One citizen takes 96%.

• Lottery test: suppose a lottery decided your citizenship number. Most people would choose Country A, because it has a more equitable distribution (income is shared more fairly).

• Lesson: a rising average income does not mean that "all sections have become better". The average can rise even while most people's incomes fall.
• The rest of this note measures these two countries with each tool (see the worked examples below).

4. Measures of inequality

4.1 Lorenz curve (Max Lorenz, 1905)

• What it plots:
• x-axis: the cumulative share of the population, arranged poorest first.

• y-axis: the cumulative share of income or wealth held by that population.

• The 45° line is perfect equality. On this line, the poorest 20% hold 20% of income, the poorest 40% hold 40%, and so on.

• The more the curve bows below the 45° line, the greater the inequality.
• Crossing curves: if two Lorenz curves cross, the ranking of the two societies is ambiguous.
• For example, one society may treat its poorest people better, while the other treats its middle class better.

• No single number can then say which society is "more equal" without a value judgement.

• Worked example (Country B): cumulative income shares at 20%, 40%, 60%, 80% and 100% of the population are 1%, 2%, 3%, 4% and 100%.

• The curve hugs the x-axis and then shoots up at the end. This shows extreme inequality.

4.2 Gini coefficient (Corrado Gini, 1912)

• Formula: G = A / (A + B)
• A is the area between the 45° equality line and the Lorenz curve.
• B is the area under the Lorenz curve.

• The whole triangle under the 45° line has area ½, so A + B = ½. Therefore G = 2A = 1 − 2B.

• Range: from 0 (perfect equality: everyone has the same) to 1 (perfect inequality: one person has everything). It is often written on a scale of 0–100.

• Worked example: computing B with trapezoids (the population is split into 5 strips, each 0.2 wide):
• Country B: cumulative shares are 0, 0.01, 0.02, 0.03, 0.04, 1.0.
  • Strip areas = 0.2 × [(0+0.01)/2 + (0.01+0.02)/2 + (0.02+0.03)/2 + (0.03+0.04)/2 + (0.04+1.0)/2]
  • = 0.2 × 0.60 = 0.12
  • G = 1 − 2(0.12) = 0.76 (very unequal).
• Country A: sorted incomes are 9,500; 9,800; 10,000; 10,200; 10,500. Cumulative shares are 0.19, 0.386, 0.586, 0.79, 1.0.
  • This gives B ≈ 0.490, so G ≈ 0.02 (almost equal).

• Same average (₹10,000), but very different Ginis: 0.02 vs 0.76.

• Consumption Ginis are lower than income Ginis. Take care when comparing countries measured on different bases.

• India's World Bank Gini (consumption): 25.5 (2022-23), down from 28.8 (2011-12) [5].
• On this measure, India ranks as the 4th most equal country in the world, after the Slovak Republic, Slovenia and Belarus [4].
• The caveat: the World Bank brief itself says inequality may be understated because of data limitations [5].
• The same brief cites the World Inequality Database, which shows India's income Gini rising from 52 (2005) to 61 (2023) [5].

• Exam lesson: India's 25.5 is a consumption figure. Many countries report income Ginis. Comparing the two is like comparing apples and oranges.

• Limitations of the Gini:

• Two very different Lorenz curves can give the same Gini.
• The Gini is most sensitive to changes in the middle of the distribution, not at the extremes.

4.3 Palma ratio (José Gabriel Palma, 2011)

• Formula: Palma = (income share of the top 10%) ÷ (income share of the bottom 40%)
• The idea behind it:
• Palma observed that the middle deciles (5–9) hold about half of all income almost everywhere. A decile is one-tenth of the population.

• So differences in inequality between countries come mainly from the extremes: how much the top 10% take and how little the bottom 40% get.

• Worked example: the top 10% get 30% of income and the bottom 40% get 20%.

• Palma = 30 ÷ 20 = 1.5. The richest tenth earn 1.5 times what the poorest 40% earn together.

• Advantage: it is easy to understand and focuses directly on the policy question: "Are the rich pulling away from the poor?"

4.4 Bottom-40% tracking: shared prosperity and SDG 10.1

• Shared prosperity indicator (World Bank): the annualised growth rate of average consumption or income per person of the poorest 40% (the "bottom 40") [7].
• It tests whether growth is inclusive, i.e. whether growth reaches the poor [7].

• It is also SDG indicator 10.1.1 [7].

• SDG target 10.1: "progressively achieve and sustain income growth of the bottom 40 percent of the population at a rate higher than the national average" [7].

• Shared prosperity premium = growth of the bottom 40 minus growth of the average person [7].

• A positive premium means that SDG target 10.1 was met in that period [7].

• New World Bank measures (2023): the World Bank adopted the Global Prosperity Gap (GPG) and the number of countries with high inequality [7].

• GPG = the average factor by which incomes must be multiplied to reach a prosperity standard of $25 a day (PPP) [7][8].
• PPP (purchasing power parity) adjusts money values for price differences between countries.

4.5 Theil index

• Type: an entropy-based measure. It borrows the idea of "disorder" from information theory.
• Formula: T = (1/N) Σ (yᵢ/μ) ln(yᵢ/μ)
• N = number of people; yᵢ = income of person i; μ = mean income; ln = natural log.

• T = 0 means perfect equality. The maximum value is ln N.

• Worked example: two people with incomes 1 and 3, so μ = 2.

• T = ½ [0.5 × ln 0.5 + 1.5 × ln 1.5]

• = ½ [−0.347 + 0.608] = 0.13

• Key feature: it is decomposable.

• Total inequality = within-group inequality + between-group inequality
• Example: India's inequality can be split into (a) the gap inside rural areas and inside urban areas, plus (b) the gap between rural and urban averages.
• This is useful for rural–urban, state or caste analysis. The Gini cannot be split this cleanly.

4.6 Atkinson index (Anthony Atkinson, 1970)

• Type: a welfare-based measure. It builds a value judgement about fairness directly into the number.
• Inequality-aversion parameter ε (epsilon): it shows how much society cares about inequality.
• ε = 0 means society does not care about inequality at all.

• A higher ε gives more weight to the bottom of the distribution.

• Meaning: it shows the share of total income society would give up to achieve complete equality.

• Formula: Atkinson = 1 − (equally-distributed-equivalent income ÷ mean income)

• When ε = 1, the equally-distributed-equivalent income is the geometric mean.

• Worked example (ε = 1): two people earn ₹100 and ₹300. The mean is ₹200.

• Geometric mean = √(100 × 300) ≈ ₹173.
• Atkinson = 1 − 173/200 ≈ 0.13.

• So society would accept ₹173 each, shared equally, in place of an unequal average of ₹200. It would give up 13% of income for equality.

• Use: UNDP uses it in the Inequality-adjusted HDI (IHDI) (see development-and-hdi).

4.7 Other measures

• Top 1% / top 10% income share: the share of national income going to the richest group. It captures concentration at the very top.
• 20:20 ratio = income of the top 20% ÷ income of the bottom 20%.
• Country B: 48,000 ÷ 500 = 96.
• Country A: 10,500 ÷ 9,500 ≈ 1.1.

5. Quick comparison of the measures

Measure	Based on	Main strength	Main weakness
Lorenz curve	Graph	Shows the full picture	Ambiguous when curves cross
Gini	Area under Lorenz curve	Single number from 0 to 1, widely used	Sensitive to the middle; same Gini can come from different shapes
Palma	Top 10% ÷ bottom 40%	Focuses on the extremes; easy to read	Ignores the middle
Theil	Entropy	Decomposable (within + between groups)	Hard to interpret intuitively
Atkinson	Social welfare	Explicit value judgement (ε)	Result depends on the choice of ε
20:20 / top shares	Income shares	Simple	Uses only part of the distribution

Prelims Hooks

• Lorenz curve axes: cumulative % of population (poorest first) on the x-axis; cumulative % of income on the y-axis. The 45° line = perfect equality.
• Gini = A/(A+B) = 2A = 1 − 2B. It ranges from 0 (perfect equality) to 1 (perfect inequality).
• Trap: India's World Bank Gini of 25.5 (2022-23) is consumption-based, not income-based. India ranks 4th most equal, after the Slovak Republic, Slovenia and Belarus [4][5].
• HCES 2023-24 Gini: rural 0.237, urban 0.284. Both fell from 2022-23 (0.266 and 0.314) [2].
• Palma ratio = top 10% share ÷ bottom 40% share. It rests on the fact that deciles 5–9 hold about half of income almost everywhere.
• Decomposable measure (within-group + between-group) = Theil index, not the Gini.
• Atkinson index uses an inequality-aversion parameter ε. UNDP uses it in the IHDI.
• SDG 10.1 / indicator 10.1.1: income growth of the bottom 40% should be higher than the national average. This is the World Bank's shared prosperity indicator [7].
• Wealth data source: AIDIS. Its latest round was the NSS 77th round (January–December 2019), conducted by the NSO under MoSPI [6].
• World Bank Prosperity Gap (2023): the average factor by which incomes must rise to reach $25/day (PPP) [7][8].

Mains Points

• Which measure shows India's inequality correctly?
• Consumption surveys show India as highly equal (Gini 25.5 in 2022-23) [5].
• Income-based estimates show high and rising inequality (WID income Gini 52 → 61, 2005–2023, as cited by the World Bank) [5].

• India needs a regular official income and wealth survey to settle the debate. Policy built on consumption data alone may miss how concentrated incomes are at the top.

• Growth vs distribution:

• The Class 10 table shows that averages hide disparities.
• Rising per capita income does not mean everyone is better off.

• So growth targets should be paired with bottom-40 growth tracking (SDG 10.1) and a Palma-type check on the extremes.

• Horizontal inequality and federal policy:

• The urban–rural consumption gap fell from 84% (2011-12) to 70% (2023-24) [3].
• The cultivator vs non-cultivator asset gap was about 2.8× (2019) [6].

• Decomposable measures such as the Theil index help target transfers by region or group. This links to Finance Commission devolution criteria and to schemes for rural non-farm livelihoods.

• Welfare transfers and measured inequality:

• The Economic Survey 2024-25 credits welfare schemes with lifting consumption of low-income households [9].
• The trade-off: transfers reduce consumption inequality in the short run. But wealth inequality needs longer-term tools: land and asset access, education, and progressive taxation.