Welfare Economics: Equity-Efficiency Trade-off (Lecture 1)

Public Economics studies the role of government intervention in the market, including regulation (e.g., environmental) and social insurance (unemployment benefits, disability, pensions).
Key question: is government intervention necessary to improve market outcomes, or can markets be left alone?

First Theorem of Welfare Economics: with a complete set of markets and perfect competition, the economy attains a Pareto Efficient allocation of resources.
Government intervention is twofold:
- Efficiency grounds: when markets are incomplete or not perfectly competitive (externalities, public goods, adverse selection, monopoly power).
- Equity grounds: even if efficiency is achieved, intervene to reduce poverty and inequality (affirmative action, progressive taxes, minimum wage).

Two desirable properties of a redistributive system:
- Efficiency: minimize distortions (incentive effects, etc.).
- Equity/Fairness: redistribute toward the less well-off.

Debates about redistributive policy often concern whether current systems discourage saving/work and distort behavior (e.g., labor-leisure choices due to income taxes).
Distortions largely arise from the substitution effect.

Individuals try to minimize tax liability or maximize transfers, inducing distorted choices.
All taxes/subsidies involve an income effect, but instruments differ in their substitution effects (indirect burden beyond the direct burden).

Different taxes/subsidies have different substitution effects; the substitution effect yields the excess burden (deadweight loss) beyond the direct tax burden.

Most efficient form of taxation is one that eliminates substitution effects: a lump-sum tax.
Example: a head tax—fixed levy per person, independent of choices (subject to migration considerations).
Taxes based on exogenous attributes (e.g., height, age) entail no excess burden.

Height is exogenous and correlates with economic success; using height as a tax base yields no substitution effect and induces progressivity due to observed correlations.

Lump-sum taxes are hard to implement because earning capacity is not directly observable/verifiable; a universal lump-sum tax raises equity concerns.
Exceptions: corrective taxes (Pigouvian taxes) like green taxes, congestion tolls, and sin taxes that internalize negative externalities.

Pigouvian taxes are designed to improve efficiency by internalizing negative externalities.

The tax system also redistributes to achieve a more equitable allocation of resources (income, wealth).
Two notions of equity: Horizontal Equity (HE) and Vertical Equity (VE).

HE requires that individuals who are the same in all relevant respects be treated equally.
Anti-discrimination (AD) legislation is a common HE application.

AD rules aim to ensure equal opportunity for workers who are the same in experience, ability, education.
HE is intuitive but has limited applicability to redistributive design since it concerns only identical individuals.

VE requires that those in a better position to pay should pay more (progressive taxation).
The challenge is defining the proper measure of ability to pay (tax base).

Ability to pay can be measured by well-being or earning capacity.
Both approaches are difficult due to informational asymmetries; income/wealth is a common proxy with possible adjustments (e.g., health cost deductions for the handicapped).

If two individuals have the same earning ability but different willingness to work, income-based taxation may unfairly tax the career-oriented individual more.
Additional fairness concerns: a low-income person may voluntarily work less; potential labeling as ‘lazy’ and undeserving.

Designing an optimal tax/policy requires balancing efficiency and equity; a universal lump-sum tax that minimizes distortions is highly regressive and raises inequality.
Okun’s leaky bucket metaphor captures the trade-off between leakage (inefficiency) and access to water (equity).

Policies are evaluated using a social welfare function that aggregates individual utilities:
- Social welfare aggregates utilities, so allocations on the same indifference curve are socially equivalent.
The welfare function provides a framework to compare policy outcomes.

Non-paternalistic (individualistic): policy relevance only insofar as it affects individuals’ well-being (rational, consenting adults).
Paternalism is relevant in debates (e.g., tax benefits for retirement savings; sin taxes on fatty foods).

Social welfare function with weight on B: $\Psi = (1 - m) UA + m UB$ with $m \in [0.5, 1]$ , where larger m = stronger redistributive preference towards B.
When m = 0.5, equal weight on both individuals; effectively maximizes the sum of utilities (cake size).

Given the example utilities, the condition for intervention to be socially desirable is:
60m + 80(1 - m) > 50m + 100(1 - m).
Solving yields:
m > \frac{2}{3}.
Therefore, if inequality aversion exceeds 2/3, the redistributive policy is preferred under these numbers.
For values of m between 0.5 and 2/3, some less distortionary interventions might be desirable, though not explicitly analyzed here.

Efficiency and equity often conflict; the social planner must trade off distortions against redistribution.
Lump-sum taxes are ideal for efficiency but hard to implement; Pigouvian taxes address externalities.
A simple two-person example shows how changing weights on utilities shifts the desirability of intervention.
The threshold m > 2/3 provides a concrete criterion for when a redistributive policy is preferred given the specified initial utilities.