The purpose of this paper is to propose a new concept of the welfare judgement, named the marginal substitution rate of distribution, and to consider some problems related to this concept.
We sometimes say one dollar for a certain individual is equivalent from the social welfare view point to two dollars for another individual. In this case, one dollar transfer from the second individual to the first increases the “social welfare”. This statement, of course, involves a value judgement. The marginal substitution rate of distribution is the rigorous formulation of this value judgement. That is, when one marginal dollar for an individual is judged to be equivalent from the social welfare judgement, to
w marginal dollars for another individual, then the marginal substitution rate of distribution between the latter and the former is defined as
w.
We first discuss the relationship between this concept and the Bergson-Samuelson welfare function. For, the latter is the most generally and exactly formulated one among the formulations of welfare judgements ever appeared in the economic sciences. We will show our concept to the Eergson-Samuelson welfare function is the same as the marginal rate of substitution between commodities to the utility index. That is, our concept is a localized one of the Bergson-Samuelson welfare function which is an expression of a global value judgement.
As mentioned above, the concept is the same type of concept as that of the marginal rate of substitution between commodities for an individual. We, therefore, have the same kind of problems as those related to the latter. That is; the problem of the integrability. Since the marginal substitution rate is a “local” concept, it is quite natural that the “global” consistency does not necessarily hold. We also discuss the relationship between the integrability problem for the marginal substitution rate of distribution and the imposibility theorem of the social welfare function by K. J. Arrow.
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