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The social welfare function could then be specified in a substantively individualistic sense to derive Pareto efficiency (optimality). Paul Samuelson (2004, p. 26) notes that Bergson's function "could derive Pareto optimality conditions as necessary but not sufficient for defining
In a 1938 paper Bergson defined and discussed the notion of an individualistic social welfare function. The paper delineated necessary marginal conditions for economic efficiency, relative to: real-valued ordinal utility functions of individuals (illustrated by indifference-curve maps) for commodities; labor supplied; other resource constraints.
This debate seemed to have been addressed by Abram Bergson's seminal paper in 1938, "A Reformulation of Certain Aspects of Welfare Economics." Bergson demonstrated that economic efficiency conditions could be precisely formulated without fully specifying the underlying social welfare function.
Following Abram Bergson, whose formulation of a social welfare function launched ordinalist welfare economics, [1] Arrow avoids locating a social good as independent of individual values. Rather, social values inhere in actions from social-decision rules (hypostatized as constitutional conditions ) using individual values as input.
He follows Lange in deriving a set of equations which are necessary for Pareto optimality, and then considers what additional constraints arise if the economy is required to satisfy a genuine social welfare function, finding a further set of equations from which it follows 'that all of the action necessary to achieve a given ethical desideratum ...
Chapter VIII on welfare economics is described as an attempt "to give a brief but fairly complete survey of the whole field of welfare economics" (p. 252). This Samuelson does in 51 pages, including his exposition of what became known as the Bergson–Samuelson social welfare function. Theorems derived in welfare economics, he notes, are ...
Social choice theory is the study of theoretical and practical methods to aggregate or combine individual preferences into a collective social welfare function. The field generally assumes that individuals have preferences , and it follows that they can be modeled using utility functions , by the VNM theorem .
The chapter on welfare economics "attempt(s) to give a brief but fairly complete survey of the whole field of welfare economics" (Samuelson, 1947, p. 252). It also exposits on and develops what became commonly called the Bergson–Samuelson social welfare function. It shows how to represent (in the maximization calculus) all real-valued ...