Model Answer
0 min readIntroduction
Inequality is a pervasive feature of most economies, and its impact on social welfare is a central concern in development economics. The Lorenz curve, a graphical representation of income distribution, provides a powerful tool for assessing inequality. Generalized Lorenz dominance (GLD) is a criterion used to compare income distributions and determine if one is unambiguously ‘better’ than another in terms of equity. This concept is fundamentally linked to the idea that reducing inequality enhances overall societal well-being, particularly when considering the diminishing marginal utility of income.
Understanding Lorenz Dominance
The Lorenz curve plots the cumulative percentage of total income earned against the cumulative percentage of the population, ranked from poorest to richest. A perfectly equal distribution would be represented by a 45-degree line (line of equality). The further the Lorenz curve deviates from this line, the greater the inequality.
Generalized Lorenz Dominance (GLD)
Generalized Lorenz dominance occurs when the Lorenz curve of one income distribution lies entirely below (or at least weakly below) the Lorenz curve of another. This implies that, at any given percentage of the population, the cumulative share of income received by that group is lower in the more unequal distribution. Mathematically, if L1(x) ≤ L2(x) for all x ∈ [0,1], where L1 and L2 are the Lorenz curves for distributions 1 and 2 respectively, then distribution 1 Lorenz dominates distribution 2.
Link to Social Welfare
The connection between lower inequality (as indicated by GLD) and higher social welfare stems from the principle of diminishing marginal utility. This principle states that each additional unit of income provides less additional utility (satisfaction) to an individual as their income increases. Therefore, transferring income from a richer individual (who experiences lower marginal utility) to a poorer individual (who experiences higher marginal utility) increases overall societal welfare.
Illustrative Example (Conceptual)
Imagine two income distributions. In Distribution A, the bottom 50% of the population receives 20% of the total income. In Distribution B, the bottom 50% receives 10% of the total income. The Lorenz curve for Distribution B will lie below that of Distribution A. This indicates that Distribution A is more equal. Because of diminishing marginal utility, the increase in welfare experienced by the bottom 50% in Distribution A outweighs the decrease in welfare experienced by the top 50%, resulting in higher overall social welfare.
Welfare Theorems and GLD
While the First Welfare Theorem states that competitive markets lead to Pareto efficiency, it doesn’t guarantee equity. GLD provides a criterion for ranking distributions based on welfare, even when Pareto improvements are not possible. It’s important to note that GLD doesn’t necessarily imply a unique ‘optimal’ distribution, but it does establish a clear ranking: a Lorenz-dominant distribution is unambiguously preferred from a welfare perspective.
Limitations
GLD relies on the assumption of diminishing marginal utility. If individuals have constant or increasing marginal utility, the welfare implications of income transfers are less clear. Furthermore, GLD doesn’t account for other factors influencing social welfare, such as individual preferences, effort, and risk aversion.
Conclusion
In conclusion, generalized Lorenz dominance provides a robust criterion for demonstrating that lower inequality, as represented by a Lorenz curve closer to the line of equality, corresponds to a higher social welfare state. This relationship is grounded in the principle of diminishing marginal utility, suggesting that redistributing income from the wealthy to the poor enhances overall societal well-being. While limitations exist, GLD remains a valuable tool for evaluating the welfare implications of different income distributions and informing policy decisions aimed at promoting greater equity.
Answer Length
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