UGC NET Economics Unit 1-Welfare Economics: Fundamental Theorems and Social Welfare Function

1. Introduction to Welfare Economics

Welfare Economics is a branch of microeconomics that studies how the allocation of resources affects social welfare — the collective well-being of society.

It tries to answer two essential questions:

1. Efficiency Question:
   How can resources be allocated to achieve maximum total output or satisfaction?
   (→ Efficiency analysis)

2. Equity Question:
   How should resources and welfare be distributed among individuals?
   (→ Distribution analysis)

Thus, welfare economics aims to design and evaluate economic policies that lead to the most efficient and just allocation of resources.

2. Objectives of Welfare Economics

1. To identify conditions for Pareto efficiency.

2. To analyze when market equilibrium is socially optimal.

3. To propose ways to improve social welfare through redistribution.

4. To develop a Social Welfare Function (SWF) to measure collective well-being.

3. Approaches to Welfare Economics

4. The Two Fundamental Theorems of Welfare Economics

These theorems link competitive market equilibrium and Pareto efficiency — forming the foundation of modern welfare economics.

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🧮 The First Fundamental Theorem of Welfare Economics

Statement:

“Every competitive equilibrium is Pareto efficient.”

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Meaning:

Under certain ideal conditions, free markets automatically lead to an efficient allocation of resources without any external intervention.

If all agents act competitively and markets are complete, the equilibrium achieved is Pareto Optimal — no one can be made better off without hurting someone else.

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Assumptions:

1. Perfect competition in all markets.

2. Rational consumers and firms (utility and profit maximization).

3. No externalities (production or consumption).

4. Perfect information (all agents fully informed).

5. Convex preferences and diminishing returns.

6. Complete markets for all goods and factors.

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Implications:

• Market mechanism ensures efficiency (allocative + productive).

• Justifies laissez-faire policy (minimum government interference).

• Explains why competitive markets are considered “efficient” systems.

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Limitations:

1. Does not guarantee equity or fairness — an efficient allocation may still be highly unequal.

2. Assumes ideal market conditions rarely found in reality.

3. Ignores externalities, public goods, and asymmetric information.

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⚖️ The Second Fundamental Theorem of Welfare Economics

Statement:

“Any Pareto efficient allocation can be achieved through competitive equilibrium, provided there is an appropriate redistribution of initial endowments.”

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Meaning:

Equity and efficiency can be separated.
👉 The government can redistribute wealth or resources (to ensure fairness) and then allow free markets to reach an efficient outcome.

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Assumptions:

1. Convex preferences and continuous utility functions.

2. Perfect competition in all markets.

3. Possibility of lump-sum redistribution (without distorting incentives).

4. No transaction costs or externalities.

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Implications:

• Efficiency and equity can be achieved simultaneously.

• Government’s role: redistribute income, not control prices.

• Establishes a normative policy framework — government adjusts endowments, markets ensure efficiency.

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Graphical Explanation:

• In an Edgeworth box, redistribution shifts the initial endowment point, leading to a new contract curveallocation.

• Each new endowment point represents a different Pareto efficient outcome achievable through market exchange.

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Limitations:

1. Lump-sum transfers are unrealistic (governments can’t perfectly redistribute).

2. Assumes perfect competition and no distortions.

3. Ignores transaction costs and political constraints.

4. Focuses only on efficiency — does not specify which allocation is “best” socially.

5. The Social Welfare Function (SWF)

Concept Origin:

Proposed by Abram Bergson (1938) and later refined by Paul A. Samuelson, the Social Welfare Function incorporates value judgments to evaluate alternative allocations.

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Definition:

“The Social Welfare Function (SWF) represents the welfare of society as a function of the welfare (utility) of all individuals.”

Formally:

$$W=f(U_1,U_2,U_3,\dots ,U_n)$$

Where:

• $W$ = Social welfare

• $U_i$ = Utility of individual i

• n = Number of individuals in society

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Assumptions:

1. Society’s welfare depends on individual utilities.

2. Interpersonal comparison of utilities is allowed (value judgment).

3. Welfare is an increasing function of individual utilities.

4. Government or planner defines ethical weights for individuals’ utilities.

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Interpretation:

Each point in the Utility Possibility Frontier (UPF) represents efficient allocations (Pareto Optimal).
The SWF identifies which point on the frontier maximizes overall social welfare.

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Graphical Explanation:

• Utility Possibility Frontier (UPF): All Pareto-efficient combinations of utilities of individuals A and B.

• Social Indifference Curves (SICs): Show combinations of $U_A$ and $U_B$ giving equal social welfare.

• The tangency between UPF and the highest SIC gives maximum social welfare.

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Types of Social Welfare Functions

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Role of Value Judgments

• Explicit value judgments are necessary to define social preferences (unlike Pareto).

• The SWF is normative, reflecting society’s ethical priorities.

• The choice of form (utilitarian, Rawlsian, etc.) determines the social goal — equality vs. efficiency trade-off.

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Limitations of SWF

1. Interpersonal utility comparisons are subjective.

2. Determining weights for individuals’ utilities is difficult.

3. Arrow’s Impossibility Theorem (Kenneth Arrow, 1951) — no social choice rule can convert individual preferences into a consistent collective ranking satisfying fairness axioms.

4. Ignores non-utility aspects like freedom, justice, or rights (as Amartya Sen emphasized).

6. Relationship Between Welfare Theorems and SWF

• First Theorem: Defines efficiency (Pareto optimality).

• Second Theorem: Describes how to reach efficiency with equity through redistribution.

• SWF: Selects the most desirable efficient allocation based on social value judgments.

Hence:

$$\text{Efficiency (Theorems)}+\text{Ethics (SWF)}=\text{Complete Welfare Economics}$$

7. Key Differences

8. Importance in Policy Making

1. Justifies market mechanism for efficiency (Theorem I).

2. Justifies redistribution policies for equity (Theorem II).

3. Provides analytical foundation for welfare states.

4. SWF helps evaluate alternative policies on ethical and distributive grounds.

9. Key Terms Summary

10. Summary

📖 11. Suggested Readings

1. A.P. Lerner – Economics of Control

2. D.N. Dwivedi – Microeconomics: Theory and Applications

3. Paul A. Samuelson – Foundations of Economic Analysis

4. Koutsoyiannis – Modern Microeconomics

5. Amartya Sen – Collective Choice and Social Welfare

6. Hal R. Varian – Intermediate Microeconomics