Social Welfare Function

• The concept of Social Welfare Function (SWF) was propounded by A. Bergson in his 1938 article A Reformulation of Certain Aspects of Welfare Economics as an attempt to solve the long-standing problems of maximisation and measurement of social welfare that earlier welfare theories had failed to resolve.

• Earlier approaches to social welfare included:

  • Bentham’s idea of welfare as the “greatest happiness of the greatest number”.

  • Neo-classical welfare economics, which analysed welfare through cardinal utility measurement and interpersonal comparison of utility.

  • Pareto optimality analysis, which sought to maximise social welfare through satisfaction of marginal conditions relating to production, distribution, and resource allocation among products.

• The practical limitations of Pareto optimality were:

  • Required marginal conditions are often not fulfilled because of market imperfections and externalities.

  • It cannot evaluate welfare changes arising from situations where some individuals gain while others lose from an economic change.

• The Kaldor-Hicks-Scitovsky Compensation Principle attempted to overcome this limitation by measuring welfare changes through hypothetical compensating payments in situations where economic changes benefit some groups and harm others.

• Compensation theorists claimed to provide a value-free and objective criterion based on the ordinal utility approach, but the principle:

  • Actually rests on implicit value judgements.

  • Fails to provide a fully satisfactory evaluation of changes in social welfare.

• Bergson and Samuelson, through the concept of Social Welfare Function, introduced a new approach that sought to rehabilitate welfare economics and provide a more satisfactory framework for welfare analysis.

• Their Social Welfare Function:

  • Is based only on the ordinal preferences of individuals.

  • Accepts Robbins’ argument that interpersonal utility comparisons necessarily involve value judgements.

  • Maintains that economists cannot evaluate the welfare effects of policy changes without making value judgements.

• According to Bergson and Samuelson:

  • Welfare economics cannot be separated from value judgements.

  • Welfare economics is fundamentally a normative discipline.

  • Even though value judgements are unavoidable, the study of welfare economics should be conducted through a scientific approach.

Bergson-Samuelson Social Welfare Function

• Social Welfare Function (SWF) is an ordinal index of society’s welfare and is expressed as a function of the utility levels of all individuals in society: W = W(U₁, U₂, U₃, … Uₙ), where W denotes social welfare and U₁, U₂, U₃…Uₙ represent the ordinal utility indices of different individuals.

• The ordinal utility index of an individual depends on:

  • The goods and services consumed by him.

  • The magnitude and nature of the work he performs.

• A fundamental feature of the Bergson-Samuelson Social Welfare Function is the incorporation of explicit value judgements in its construction.

  • These value judgements determine the specific form of the SWF.

  • A different set of value judgements would generate a different social welfare function.

  • Value judgements are essentially ethical notions introduced from outside economics.

• The value judgements required for constructing the SWF may arise:

  • Through a democratic process based on voting by individuals.

  • Through dictatorial imposition on society.

  • In either case, the form of the SWF reflects the value judgements of those who determine them, since it embodies their views regarding how the utility level of each individual contributes to overall social welfare.

• According to Scitovsky, the social welfare function can be viewed as a function of each individual’s welfare, which depends not only on his personal well-being but also on his assessment of the distribution of welfare among all members of the community.

• Since the value judgements used in constructing the SWF are not those of the economist and are introduced from outside economics:

  • They are not derived through scientific methods.

  • The economist is relieved from making personal value judgements regarding what constitutes a desirable distribution of welfare.

• The SWF is claimed to have solved a basic problem of welfare economics because:

  • Economists no longer need to decide themselves which distribution of welfare among individuals is most desirable.

  • They can treat the relevant value judgements regarding distribution as externally given data and proceed with welfare analysis on that basis.

• Bergson’s Social Welfare Function is assumed to depend on changes in economic events that directly affect individual welfare.

• The ordinal utility level of an individual is determined by:

  • His own consumption of goods and services.

  • Not by the consumption of others.

• Individual utility also depends on the person’s own value judgements, tastes, and preferences regarding the composition of goods and services consumed.

  • Different individuals derive different levels of satisfaction from the same commodity.

  • For example, one individual may derive substantial utility from consuming liquor, whereas another may derive only negligible utility or none at all from it.