Bergson–Samuelson social welfare function

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The Bergson–Samuelson social welfare function is a formal tool in welfare economics that aggregates individual utilities into a single measure of social welfare to evaluate and compare economic states or policies.

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Predicate Object
instanceOf concept in welfare economics
normative economic concept
social welfare function
allows ranking of social states
welfare comparisons under different allocations of resources
assumes complete social preference ordering over feasible allocations
transitive social preferences
basedOn individualistic social welfare ethics
canRepresent different ethical systems depending on its functional form
category economic theory concept
social choice theory concept
characteristic allows interpersonal comparisons of utility via social value judgments
normative value judgments are embedded in its functional form
ordinally invariant with respect to individual utilities
contrastsWith purely Paretian welfare analysis without explicit social welfare function
developedBy Paul A. Samuelson NERFINISHED
field microeconomics
welfare economics
formalizedIn Bergson’s 1938 paper "A Reformulation of Certain Aspects of Welfare Economics" NERFINISHED
Samuelson’s subsequent works on welfare economics
generalizationOf utilitarian welfare aggregation
hasInput individual utility levels
hasOutput scalar measure of social welfare
influenced cost–benefit analysis
modern optimal taxation theory
public economics
theory of second-best
introducedBy Abram Bergson NERFINISHED
mathematicalForm real-valued function of individual utilities W(u1, u2, …, un)
mayBe increasing in each individual’s utility
symmetric with respect to individuals
namedAfter Abram Bergson NERFINISHED
Paul A. Samuelson NERFINISHED
purpose aggregate individual utilities into a measure of social welfare
evaluate and compare economic policies
evaluate and compare economic states
relatedTo Arrow’s impossibility theorem NERFINISHED
Pareto criterion NERFINISHED
Rawlsian maximin social welfare function
utilitarian social welfare function
requires explicit specification of social value judgments
timePeriod 20th century
usedFor analyzing optimal policy interventions
deriving conditions for Pareto efficiency
formalizing social choice in economic models

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welfare economics usesConcept Bergson–Samuelson social welfare function