Step-by-step explanation:
The Lorenz curve is a graphical representation of income distribution within a population, and it is commonly used to illustrate income inequality. The curve is constructed by plotting the cumulative percentage of total income received by the bottom x% of the population against the cumulative percentage of the population, ranked by increasing income.
In terms of interpreting the Lorenz curve in relation to income inequality:
Perfect Equality: If every household or individual in the population has the same income, the Lorenz curve would coincide with the 45-degree line (line of perfect equality), representing perfect equality.
Income Inequality: The further the Lorenz curve is from the line of perfect equality, the greater the income inequality. A concave Lorenz curve, lying below the line of perfect equality, indicates income inequality. The larger the area between the Lorenz curve and the line of perfect equality, the higher the level of income inequality.
Gini Coefficient: The degree of income inequality can be summarized by the Gini coefficient, which is a numerical measure derived from the Lorenz curve. The Gini coefficient ranges from 0 (perfect equality) to 1 (perfect inequality), with higher values indicating greater inequality.
In summary, a Lorenz curve that deviates significantly from the line of perfect equality signals the presence of income inequality within a population. The shape and position of the Lorenz curve provide insights into the distribution of income among different segments of the population.