Social Welfare Function | Economics Optional Notes for UPSC PDF Download

Introduction

• In the previous unit, we explored the neo-classical and new welfare economics approaches to efficient resource allocation.
• Now, we will examine the role of value judgment in analyzing welfare issues and identify areas for development and refinement.
• We will discuss the ethical and social foundations of the welfare function and the compensation principle.
• The compensation principle plays a crucial role in achieving optimum welfare.
• Additionally, we will evaluate whether the compensation principle represents an improvement over earlier methods.

Value Judgment

Value judgment refers to the beliefs or conceptions of people about what is good or bad or simply what is desirable or not from the point of view of the well being of the society. These conceptions or perceptions of the people in society are based on ethical, political, philosophical and religious beliefs of the people and are not based on any scientific logic or law.

In a broader sense, 'any statement which implies a recommendation of any kind is a value judgment'. This definition covers all ethical judgments as well as statements, which might appear to be merely descriptive, but are in certain contexts recommendatory, persuasive or influential.

Examples of Value Judgments
1. "A country grows faster if profits are taxed lightly."
2. "Honesty is the best policy."
3. "Monopolies need to be controlled."
4. "An essential aim of public policy anywhere is a reduction in the inequalities of incomes."

Value Judgments in Welfare Economics

1. Role of Value Judgments

• Welfare economics involves making propositions about the welfare of individuals in a group.
• Since welfare is an ethical concept, any theorem using the term "welfare" is inherently ethical and based on value judgments.

2. Prescriptive Nature

• Welfare economics is seen as a part of economics that studies policy prescriptions.
• Any prescription requires a notion of what is desirable or good, which is a value judgment.

3. Formulating Objectives

• Objectives and questions of desirability cannot be settled without assuming value judgments, either explicitly or implicitly.

Controversies and Developments

1. Criticism by Lionel Robbins

• Economist Lionel Robbins criticized the use of value judgments in welfare economics, arguing for a more objective analysis.
• He suggested that value judgments should be treated as descriptive data reflecting the community's values.

2. New Welfare Economics

• In response to criticisms, economists like Kaldor and Hicks sought to develop a value-free core of welfare economics, leading to the concept of "New Welfare Economics."

3. Compensation Principle

• The Compensation Principle emerged from New Welfare Economics, aiming to assess welfare changes without explicit value judgments.

4. Economic Welfare Function

• Abram Bergson introduced the Economic Welfare Function to address the role of value judgments in welfare economics.
• This concept allowed for the formalization of value assumptions within welfare analysis and their implications.

5. Value Judgments in Welfare Studies

• Value judgments in welfare studies are determined by their alignment with the prevailing community values.
• For example, assumptions about non-labor resources, consumer sovereignty, and equal distribution of shares reflect community values.

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Illustrative Value Judgments

1. Non-Labor Resources

• A shift in any non-labor factor of production from one unit to another does not affect economic welfare, assuming other welfare elements remain constant.
• For instance, factors like "factory smoke" are considered neutral in terms of social welfare impact.

2. Consumer Sovereignty

• Individual preferences are prioritized in welfare assessments.
• Changes that make everyone indifferent have the same social welfare level, while improvements or declines for individuals affect social welfare differently.

3. Equal Distribution of Shares

• Equal shares among individuals are crucial for social welfare.
• Transfers between individuals that restore equal shares do not impact welfare, while deviations from equality decrease welfare.

Furthermore, Professor S.K. Nath, in his 1969 book "A Reappraisal of Welfare Economics," points out certain value judgments inherent in Paretian welfare economics. He argues that the Paretian economic-welfare theory of allocation is based on value judgments because it makes propositions about resource allocation that are meant to be suitable, good, or optimal. The Paretian value judgments identified by Nath are as follows:

1. Focus on Individual Welfare: The concern should be with the welfare of all individuals in society, rather than with a fictional entity called 'society' or 'state,' or with a specific group or class.

2. Ignoring Non-Economic Factors: Non-economic factors affecting an individual's welfare can be disregarded.

3. Complete Consumer Sovereignty: An individual is the best judge of their economic welfare and, therefore, their overall welfare. This value judgment is known as 'complete consumer sovereignty.'

4. Resource Allocation and Social Welfare: If a change in resource allocation increases the income and leisure of everyone or at least one person (or one household) without reducing those of others, then the change is considered to have increased social welfare.

Value Judgments in Welfare Economics

• Inescapable Role of Value Judgments: Welfare economics is inherently tied to value judgments. The field has evolved to make policy recommendations for enhancing social welfare, which necessitates the introduction of ethical norms or value judgments.
• I.M.D. Little's Perspective: In his 1957 book "A Critique of Welfare Economics," I.M.D. Little emphasizes the inseparability of welfare economics and ethics. He argues that welfare terminology is value-laden, and eliminating value judgments would undermine the subject. Welfare economics is fundamentally about moral interests in welfare and happiness.
• Scientific Approach Despite Value Judgments: The explicit inclusion of value judgments does not render welfare economics unscientific. Economists can still adopt a scientific approach by deducing welfare propositions from given value judgments. The analysis remains scientific even with the introduction of ethical considerations.

Social Welfare Function

Classical Welfare Function

• The classical welfare function, known as the "Benthamite welfare function," was proposed by thinkers like Jeremy Bentham and Alfred Marshall. According to this view, social welfare is the sum of the cardinal utilities of all individuals in society.
• The goal is to maximize social welfare by equalizing the marginal utility of income across individuals. This perspective emphasizes that maximum social welfare is achieved through equal income distribution.
• Mathematically, it can be represented as: W = U₁ + U₂ + ... + U_n where W is social welfare and U_i represents the cardinal utility of individual i.

Rawlsian Welfare Function

• Philosopher John Rawls introduced an alternative welfare function by considering a hypothetical initial position where individuals must choose a welfare criterion without knowing how it will affect their utility.
• Rawls argued that individuals, being risk-averse, would choose a criterion that allows for deviations from perfect equality only if it benefits the worst-off individual.
• This can be expressed as: W(U₁, U₂, U₃, ..., U_n) = min(U₁, U₂, U₃, ..., U_n) where W represents social welfare and U_i denotes the utility of individual i.

Bergson-Samuelson Social Welfare Function

• The Bergson-Samuelson SWF is an ordinal index of societal welfare based on the utility levels of all individuals in society. It is expressed as: W = W(U₁, U₂, ..., U_H) where W is society's welfare, and U_i represents the ordinal utility index of individual i.
• The ordinal utility index reflects the goods and services consumed, the type and amount of work done, and the leisure enjoyed by individuals.

Social Welfare Function (SWF) and Its Implications
The Social Welfare Function (SWF) represents the welfare of society based on the individual utility levels of its members. The functional form of the SWF is given by:

w = ∑ (I_h (U_h)^a )

where:

• w = social welfare
• I_h = income of household h
• U_h = utility of household h
• a = weight assigned to household h

The SWF yields convex social indifference curves and is sometimes referred to as a "Bernoulli-Nash" social welfare function.

The slope of the social indifference curves is equal to the negative of the marginal rate of social substitution (MRSS) between consumers, which is the ratio of the marginal utilities of income for households A and B. The tangency condition for the Generalized Utility Possibility Frontier (GUPF) is that the MRSS is equal across households.

Alternative Welfare Functions

• w = ∑ (U_h )

This welfare function maximizes the weighted sum of individual utilities and yields linear social indifference curves.

2. Bergson-Samuelson Welfare Function
The Bergson-Samuelson welfare function states the conditions for social justice by equating the marginal rate of social substitution between households A and B to the ratio of their marginal rates of substitution. This implies that the allocation of goods should be compatible with the "worthiness" of individuals according to the social welfare function.

3. Income-Based Welfare Function
The income-based welfare function expresses social welfare as a function of the total income of individuals in society:

• W = ∑_h=1^Hα^hU^h

where Y_i is the income of each individual i in society. Maximizing this function means maximizing total income without regard to distribution.

4. Max-Min Utility Function
The Max-Min utility function relates social welfare to the income of the poorest person in society:

• W = min (Y₁ , Y₂ , ..., Y_n )

where Y_i is the income of each individual i in society. Maximizing this function means maximizing the income of the poorest person without regard for others.

5. Political Economy and Social Welfare Functions
The choice of social welfare function is often considered part of political economy and reflects societal preferences and tolerances. It is related to the broader question of how wealth relates to the ability to live as desired. Modern human development theory emphasizes the need for direct measures of well-being beyond total incomes or GDP.

6. Amartya Sen's Perspective
Amartya Sen highlights the importance of understanding the relationship between wealth and the ability to live as desired. Without addressing this question, income and welfare remain indirectly related. This perspective underscores the need for a uniform social welfare function across society to achieve balanced growth.

Compensation Principle

The Pareto criterion suggests that if an economic change harms no one and benefits at least one person, it increases social welfare. However, this criterion does not apply to situations where some people are harmed, and others are benefited. In the context of the Edgeworth Box diagram, the Pareto criterion fails to determine whether social welfare increases when moving along the contract curve because it rejects the idea of comparing utility between individuals. There are many Pareto optimum points on the contract curve, leading to uncertainty. Economists like Kaldor, Hicks, and Scitovsky have developed the Compensation Principle to evaluate changes in social welfare when some are harmed and others benefited. This principle is based on several assumptions:

• Individual Satisfaction: An individual's satisfaction is not dependent on others, and they are the best judge of their own welfare.
• No Externalities: There are no externalities in consumption and production.
• Constant Tastes: Individual preferences remain constant over time.
• Separation of Issues: The problems of production and exchange can be addressed separately from those of distribution.
• Ordinal Measurement of Utility: Utility can be measured in an ordinal manner, and it is not possible to compare utilities between individuals.

Given these assumptions, Kaldor, Hicks, and Scitovsky aim to create an objective criterion for measuring changes in social welfare using the concept of compensating payments.

Kaldor-Hicks Criteria

 Nicholas Kaldor proposed an alternative criterion for judging allocations in his 1939 article. According to Kaldor, if a change benefits some people and harms others, it increases social welfare if those who benefit could compensate the losers and still be better off. In other words, an allocation is preferred if the gainer can compensate the loser and still gain utility. 

•  Hicks expressed a similar idea, stating that if a gainer could compensate a loser and still have a surplus, the reorganization is an improvement. 
•  Kaldor's criterion focuses on the gainer's perspective, while Hicks emphasizes the loser's view. Despite this difference, the criteria are essentially the same and are collectively referred to as the 'Kaldor-Hicks Compensation Criteria.' 

 When considering the move from allocation E to C, individual A gains utility, while individual B loses. This indicates that E and C are not Pareto-comparable. However, by moving to allocation C, individual A can compensate individual B to maintain her old utility level. For instance, A can pay B a portion of her gains, allowing A to move to point F. This demonstrates that A's utility at allocation F is greater than at E, making the move to C and compensation to B worthwhile. 

 If the Kaldor compensation criteria merely suggested moving from E to F, it would not improve upon the Pareto criterion since F is clearly Pareto-superior to E. Kaldor's contribution lies in proposing that allocation C is superior to E because A can compensate B and still be better off. The key point is the possibility of compensation, not the actual compensation. Therefore, the move from E to C is real, while the move from C to F is hypothetical. Kaldor's idea allows for comparing Pareto-incomparable points through the "hypothetical compensation" test. In summary, an allocation is preferable if it is possible to hypothetically redistribute goods to achieve a Pareto improvement. 

Kaldor-Hicks Criteria in Production Economy

• Strong Kaldor Criteria: Compensation must be a lump-sum transfer within a given Utility Possibility Frontier (UPF). Production cannot change as part of the compensation.
• Weak Kaldor Criteria: Production can change as part of the compensation, allowing for comparisons across the entire Generalized Utility Possibility Frontier (GUPF).
• Comparison of Allocations: An allocation is considered superior if it is possible for the winners to compensate the losers for moving to the former (Kaldor) or if the losers can bribe the winners not to move to the former (Hicks).

Comparability Issues

• Strong Kaldor Criteria: Can lead to inconsistent comparisons between allocations. For example, moving from point E to G may be considered superior, but moving from G to E may also be deemed superior, creating a paradox.
• Weak Kaldor Criteria: Faces challenges in comparing welfare under different types of change. The Scitovsky reversal paradox highlights this issue, where position B may be preferred over A, but A could also be preferred over B under the same criterion, leading to inconsistent results.

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Scitovsky Reversal Paradox

• Identified by Tibor Scitovsky, this paradox reveals a drawback of the weak Kaldor criterion.
• It suggests that if position B is preferred over A based on the Kaldor-Hicks criterion, it should not be possible for A to be preferred over B using the same criterion.

Implication:

• To achieve consistent results, the preference order between positions must remain stable when using a welfare criterion.
• This ensures that if position B is deemed better than A, A cannot be simultaneously considered better than B using the same standard.

Conclusion:

• The Kaldor-Hicks criteria, both strong and weak, have their limitations in comparing welfare under different allocations and changes.
• The Scitovsky reversal paradox highlights the need for consistent preference ordering when using welfare criteria to evaluate different positions.

Scitovsky Reversal: Explanation: When production conditions improve due to technological advancements, the production possibility frontier (PPF) shifts from PPFp to PPF+. To assess whether this change enhances welfare, we compare the Pareto-optimal points D and F, where the community indifference curves (CIC) are tangent to the respective PPFs. 

Key Observations: Intersection of CICs: 

• Utility Levels: The intersection of CICp and CIC+ indicates a Pareto improvement, meaning F is better than E and D represent the same level of aggregate utility, allowing for a hypothetical Pareto improvement from D. 
• Weak Kaldor Criteria: According to this criterion, situation F is better than D. However, the movement from PPF+ to PPFp makes D better than G, where G and F have the same aggregate utility level. 
• Reversal Paradox: The rankings of D and F reverse, highlighting a paradox where F is better than D, and vice versa. 
• Resolution: Scitovsky proposed combining the Hicks and Kaldor criteria to resolve this paradox. The double criteria suggest that an allocation is preferred if it meets both Kaldor and Hicks criteria, eliminating Scitovsky reversals. 
• Non-Intersecting Utility Possibility Curves: When the utility possibility curves do not intersect, and the change involves moving from a lower to a higher utility possibility curve, social welfare increases based on the Kaldor-Hicks-Scitovsky criterion. This typically occurs with an increase in aggregate output or real income.

William Gorman's Intransitivity Problem

• Introduction: William Gorman highlighted a limitation of the Scitovsky double criteria in resolving ranking reversals by demonstrating the possibility of intransitive chains. 
• Intransitive Chains Explained: An intransitive chain occurs when: Allocation G is preferred to allocation D. Allocation D is preferred to allocation F. Allocation F is not preferred to allocation G. 
• Illustration in Figure 15.6: In a hypothetical scenario with three PPFs (PPFo, PPF+, and PPFg) and corresponding CICs: Allocation D on CICp is considered superior to allocation F by the Scitovsky double criteria. Allocation G on PPFg is preferred to allocation D because CICp intersects PPFo, while CICa does not. However, G and D do not fulfill the double criteria, leading to an intransitive ranking. 

Conclusion: The Scitovsky double criteria eliminates ranking reversals but does not prevent intransitive chains, as demonstrated by the example where G is preferred to D, D to F, and F not preferred to G.

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Samuelson's Criteria

• Introduction: Paul Samuelson proposed a solution to Gorman's intransitivity problem through the Samuelson Criteria. This criterion suggests a preference for allocation G over D based on hypothetical redistributions of utility. 
• Key Aspects of the Samuelson Criteria: Utility Superiority: Allocation G is preferred to D if all hypothetical redistributions from G result in utility allocations better than some redistributions from D. Utility Attainability: No hypothetical redistribution from D should yield utility allocations that cannot be achieved through redistributions from G. 
• Utility Space Requirement: The utility space must lie above UPFp, indicating superior utility allocations from G compared to D. Production Space Requirement: In production space, PPFg should intersect the interiors of CICp and any other CIC tangent to PPFp, ensuring G's superiority over D. 
• Implications of the Samuelson Criteria: Avoidance of Reversals and Intransitivities: By dealing exclusively with PPFs that meet the criteria, neither Scitovsky reversals nor Gorman intransitivities occur. Restrictive Nature: The criteria are restrictive as they exclude reasonable scenarios where PPFs do not meet the specified conditions. 

Conclusion: Samuelson's Criteria offer a way to address Gorman's intransitivity problem by establishing clear preferences based on hypothetical redistributions of utility, ensuring avoidance of ranking paradoxes.

An Appraisal of the Compensation Principle

The Samuelson criterion is more stringent than the Kaldor, Hicks, or Scitovsky double criteria. However, it is essential to question whether the Kaldor, Hicks, and Scitovsky criteria are objectively valid. The Kaldor criterion is ethically contentious because it is based on what could happen, not what would or should happen. Critics like M.D. Little argue that it is unlikely for a change that makes the rich much richer, even if they could overcompensate the poor, to increase overall community wealth. This view is supported by contemporary economists like Baumol, Reder, and Samuelson.

Advocates of the compensation principle offer three lines of defense:

• Transforming "Could" into "Would": This approach suggests that winners should actually compensate losers, leading to some improvement. However, the practical challenge is that once a new allocation is established, winners are unlikely to give up any of their gains.
• Long-Term Benefits: Proposed by Hicks in 1941, this argument posits that even if losers are not compensated immediately, they may benefit in the long run if society consistently follows the Kaldor-Hicks criteria. This idea aligns with "trickle-down" theories and the notion of free trade, where short-term losses are believed to lead to long-term gains for everyone. However, this assumption is purely hypothetical, as there is no guarantee that initial losers will eventually become winners.
• Economic Possibility versus Policy Judgment: This defense argues that the Kaldor-Hicks criteria outline what is economically feasible, leaving it to policymakers to decide based on their value judgments whether to force compensation for losers. This perspective emphasizes that the criteria present options, not prescriptions, and that ethical, philosophical, and political considerations play a crucial role in decision-making.

Conclusion

Value judgments are essential in welfare analysis, and they cannot be eliminated from it. However, even with the explicit inclusion of value judgments, the economist's approach can still be scientific. This is because welfare propositions can be scientifically deduced from the value judgments embedded in the welfare analysis. Value judgments play a crucial role in formulating the social welfare function (SWF), which measures the social welfare of society. There are different types of SWFs:

• The classical or Benthamite SWF and the Rawlsian ethical SWF emphasize a cardinal approach.
• The Bergson-Samuelson SWF is based on an ordinal approach, making it more scientific.

However, the construction of the SWF is ultimately a matter of political economy.

The compensation principle is an improvement over Paretian optimality because it evaluates changes in social welfare resulting from economic reorganization that harms some individuals while benefiting others. This aspect is neglected by the indeterminate Paretian optimality analysis. Kaldor and Hicks offer different perspectives on Pareto optimality, focusing on the viewpoints of gainers and losers, respectively. The Scitovsky reversal criteria and Gorman's problem of intransitivity are also examined, with Samuelson's criterion providing a potential solution. In conclusion, despite the inherent problems in these criteria, the ethical implications are important. Kaldor's criterion, in particular, can be disputed as it represents a "could" rather than a "would" or "should" perspective.