Lorenz Curve

Lorenz Curve is a graphical representation used in economics to illustrate the distribution of income or wealth within a population. It plots the cumulative percentage of total income earned against the cumulative percentage of the population, ordered from the poorest to the richest. The curve starts at the origin (0,0) and typically bows towards the diagonal line of equality (where income is perfectly distributed among the population). The greater the bow or deviation from the diagonal, the greater the inequality. The Lorenz Curve is often used alongside the Gini coefficient, a numerical measure of income distribution derived from the curve.

The graph plots percentiles of the population on the horizontal axis according to income or wealth. It plots cumulative income or wealth on the vertical axis, so that an x-value of 45 and a y-value of 14.2 would mean that the bottom 45% of the population controls 14.2% of the total income or wealth.

• The Lorenz curve shows the percentage of total income earned by cumulative percentage of the population.

• In a perfectly equal society, the “poorest” 25% of the population would earn 25% of the total income, the “poorest” 50% of the population would earn 50% of the total income and the Lorenz curve would follow the path of the 45° line of equality.

• As inequality increases, the Lorenz curve deviates from the line of equality; the “poorest” 25% of the population may earn 10% of the total income; the “poorest” 50% of the population may earn 20% of the total income and so on.

The Lorenz curve is often accompanied by a straight diagonal line with a slope of 1, which represents perfect equality in income or wealth distribution; the Lorenz curve lies beneath it, showing the actual distribution. The area between the straight line and the curved line, expressed as a ratio of the area under the straight line, is the Gini coefficient, a measurement of inequality.

While the Lorenz curve is most often used to represent economic inequality, it can also demonstrate unequal distribution in any system. The farther away the curve is from the baseline, represented by the straight diagonal line, the higher the level of inequality. In economics, the Lorenz curve denotes inequality in the distribution of either wealth or income; these are not synonymous since it is possible to have high earnings but zero or negative net worth, or low earnings but a large net worth.

Lorenz Curve Assumptions:

• Homogeneous Units:

Lorenz Curve assumes that the units (e.g., individuals, households) being analyzed are comparable. This means that each unit contributes to total income or wealth and can be aggregated meaningfully. It disregards differences like age, employment status, or family size that might affect income or wealth levels.

• Accurate and Complete Data:

Accuracy of the Lorenz Curve depends on comprehensive and precise data regarding income or wealth. It assumes that all sources of income or wealth are reported and included in the analysis. Underreporting or missing data can skew the curve, leading to inaccurate representations of inequality.

• Consistent Income or Wealth Measurement:

Curve assumes that income or wealth is measured consistently across all units. This includes the same time period (e.g., annual income) and type of income or wealth considered (e.g., after-tax income).

• Ordered Data:

For constructing the Lorenz Curve, data must be ordered from the lowest to the highest income or wealth. This ordering is critical as the curve plots cumulative shares of income against cumulative shares of the population.

• Static Analysis:

Lorenz Curve typically represents a snapshot of income or wealth distribution at a single point in time. It does not reflect changes over time unless multiple curves from different time periods are compared.

• Focus on Distribution, Not Causes:

The Lorenz Curve illustrates the distribution of income or wealth but does not provide insights into the causes of inequality. It is purely descriptive and does not imply causality.

• No Negative Values:

Curve assumes that all values of income or wealth are non-negative. Negative income or debt isn’t typically represented in the Lorenz Curve, which can be a limitation if such factors are significant within a population.