Ch12. Welfare Economics and Income Distribution — Market Fairness and the Limits of Government Intervention

What Is Welfare Economics?

Welfare Economics is the branch of economics that analyzes how resource allocation affects the well-being (welfare) of society as a whole.

Core question: “Which allocation is more desirable?”

Pareto Efficiency

Pareto Efficiency: A state in which no one’s welfare can be improved without reducing someone else’s welfare.

Pareto Improvement: A change that makes at least one person better off without making anyone worse off.

Pareto Optimal State:
- No further Pareto improvements are possible
- The general equilibrium of a perfectly competitive market is Pareto efficient

Limits of Pareto efficiency: Multiple Pareto efficient allocations can exist, and the criterion says nothing about distributional fairness.

To overcome the limits of Pareto efficiency, economists use social welfare functions to evaluate overall societal well-being.

Type	Formula	Key Feature
Utilitarian	W = U₁ + U₂ + … + Uₙ	Maximizes the total; allows inequality
Rawlsian	W = min(U₁, U₂, …, Uₙ)	Maximizes the welfare of the worst-off
Egalitarian	Equal weights for all members	Emphasizes equal distribution

Rawls’s Veil of Ignorance: If you did not know which position you would occupy in society, you would choose institutions that protect the worst-off — the argument for the Rawlsian criterion.

Measuring Income Distribution

The Lorenz Curve

A curve that visually depicts the degree of income inequality.

X-axis: cumulative share of population (ranked lowest to highest income)
Y-axis: cumulative share of income held by that population share
Line of perfect equality: 45-degree diagonal
Lorenz curve: Actual distribution (lies below the 45-degree line)

The Gini Coefficient

Gini coefficient = (Area between equality line and Lorenz curve)
                   / (Area of triangle below equality line)

Range: 0 (perfect equality) to 1 (perfect inequality)

Below 0.30: relatively equal
0.40 and above: significant inequality
OECD average: approximately 0.31–0.32

The US Gini coefficient (post-tax-and-transfer) is approximately 0.39, among the higher end of OECD nations. The Census Bureau and BEA publish income distribution data.

Decile Distribution Ratio

Bottom 40% income share / Top 20% income share → Higher value = more equal distribution

Quintile Ratio (Palma Ratio variant)

Mean income of top quintile / Mean income of bottom quintile → Lower value = more equal distribution

Causes of Worsening Income Distribution

Skill-biased technological change: Rising demand for high-skilled labor; displacement of low-skilled workers
Globalization: Offshoring of labor-intensive jobs
Asset price appreciation: Growing gap between asset holders and non-holders
Returns to education: Widening gap between college-educated and non-college workers

Redistribution Policy

Progressive Taxation

Higher income → higher marginal tax rate.

US Federal Income Tax Brackets (2024, Single Filer):
- Up to $11,600: 10%
- $11,601–$47,150: 12%
- $47,151–$100,525: 22%
- $100,526–$191,950: 24%
- $191,951–$243,725: 32%
- $243,726–$609,350: 35%
- Over $609,350: 37%

Medicaid / CHIP: Health coverage for low-income households
Social Security / Medicare: Social insurance against retirement and health risks
EITC (Earned Income Tax Credit): Wage subsidy for low-income workers
SNAP (Supplemental Nutrition Assistance Program): Food assistance

Limits of Redistribution Policy

Efficiency–Equity Trade-off: Strong redistribution may reduce incentives to work, save, and invest. The Laffer Curve illustrates the potential peak-revenue tax rate.

Externalities and Public Goods (Link to Public Finance)

Main Causes of Market Failure

Externalities: Effects on third parties (negative/positive)
Public goods: Non-excludable + non-rival → free-rider problem
Information asymmetry: Adverse selection, moral hazard
Monopoly: Price distortion, deadweight loss

Coase Theorem: If transaction costs are zero, parties affected by an externality can negotiate to a socially efficient outcome without government intervention.

Key Concept Cards

Pareto Efficiency ★★★★★ : An allocation in which no one can be made better off without making someone else worse off. Memory tip: Pareto efficient = no further Pareto improvements possible

Gini Coefficient ★★★★★ : An index of income inequality derived from the Lorenz curve, ranging from 0 to 1. Closer to 1 = more unequal. Memory tip: Gini = (area between Lorenz curve and equality line) / (triangle area)

Rawlsian Social Welfare Function ★★★★☆ : Defines social welfare as the utility of the worst-off member and prioritizes protecting the most disadvantaged. Memory tip: Rawls = Veil of Ignorance → maximize the minimum

Practice Quiz

Q. What does it mean when the Lorenz curve is close to the 45-degree line?

Income distribution is more equal. Since the 45-degree line represents perfect equality, a Lorenz curve closer to it corresponds to a Gini coefficient closer to 0, indicating lower inequality.

Q. What are the effects of progressive taxation on efficiency and equity?

On equity: it redistributes income and reduces inequality. On efficiency: it may reduce the incentive to work and invest for high earners, creating an efficiency-equity trade-off.

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