BERGSON-SAMUELSON SOCIAL WELFARE FUNCTIONS AND THE WELFARE EVALUATION OF THE DISTRIBUTION OF INCOME

ALAN DAVID SLIVINSKI, Purdue University

Abstract

The thesis develops an approach to the Bergson-Samuelson Social Welfare Function (BS-SWF) which distinguishes it from both the Arrow formulation and the welfare information formulation of Sen. This is to consider the BS-SWF as the real-valued representation of a social ordering over some appropriate set. It is argued that this is more relevant to the fundamental reasons for utilizing a social welfare function--the definition and clarification of value judgments to be used in policy analysis. The first problem investigated is the relationship between the classic BS-SWF functional form and the Pareto Principle. It is shown that a representable social ordering extends the Pareto ordering and its asymmetric part extends the strict Pareto ordering if and only if every representation of it is a BS-SWF. An analogous result is proved for indirect social orderings defined on price-income space. This leads to an investigation of the question of imposing value judgements (i.e., restricting the class of admissible social orderings) on Pareto-consistent orderings by placing conditions on their BS-SWF representations. It is demonstrated that conditions placed on the individual utility representation used in a BS-SWF are never value judgments, while conditions imposed on the aggregator function can be. Then a class of aggregators, the generalized quasi-linear (g.q.l.) functions, is shown to be equivalent to a value judgment relating to how sub-groups of individuals are dealt with by the ordering. Still another ethical judgement is then shown to be implied by a boundedness property of g.q.l. aggregators. The second major problem to be considered is that of the welfare evaluation of income distributions via the 'indirect' BS-SWF. Particular attention is paid to the case of homothetic individual direct preferences. The concept of y-separability is developed to rationalize the welfare evaluation of income distributions in a world of more than one commodity, and for the homothetic case, y-separability is shown to imply that the BS-SWF aggregator must be g.q.l. The results of the research point strongly to the fact that if the BS-SWF is to be a useful tool for welfare analysis, a good deal more research is needed on aggregator functions as value judgements, and on the value judgements which can be developed through the interaction of aggregators and individual utility functions. Also, there appears to be some reason to believe that the techniques used in the analysis of y-separability above will be useful in such investigations.

Degree

Ph.D.

Subject Area

Education

COinS