A General Theory of Welfare Economics
Samuelson’s PhD thesis (Samuelson, 1940), written in 1940 after he had left the Society of Fellows and was now free to work toward a higher degree, and examined in February 1941, contained material on the measurement of marginal utility, but did not discuss welfare.
The fifty-page chapter on welfare included in Foundations of Economic Analysis (1947) was written later. It began with what was effectively a long defense of the historical claim he had made in his Econometrica article about the process whereby ethical and, later, psychological elements had been removed from consumer theory.Economics had, Samuelson claimed, always been associated with the notion that “in some sense perfect competition represented an optimal situation,” albeit expressed in different ways (Samuelson, 1947, p. 203). It was exemplified by the case for free trade. This clearly normative idea was bound up with teleology, whether ideas of natural rights, natural selection or the Malthusian doctrine that competition was necessary to bring out the best in people. But though these were generally conservative ideas, used to defend the status quo, Samuelson noted that arguments about perfect competition could also be used to challenge the status quo, as when they were used to justify anti-monopoly legislation.
More convincing were arguments that did not depend on teleology. The argument that some trade was better than no trade could easily (albeit illegitimately) become an argument for free trade. This was reinforced by the argument that in an equilibrium every agent is doing the best they can for themselves. So by the end of the nineteenth century, economists, including Walras, Jevons, Launhardt, Wicksell and Marshall, were in a position to construct proofs that competitive equilibrium was optimal. Some went further, trying to argue that the distribution of income produced under competition was optimal and though John Bates Clark's (1899) view that people were morally entitled to their own marginal product was attractive to many in a frontier society, such notions were inconsistent with widely held ethical views.
Generally, economists concluded that, subject to some caveats, perfect competition was optimal provided that the distribution of income was appropriate. However, Samuelson did not find any of their arguments convincing. For example, Walras barely went beyond the assertion that people did what was best for themselves, Jevons assumed he could add up utilities and Marshall made the mistake of assuming that he could measure utility with consumers' surplus, an idea Samuelson discussed at length because Hicks had recently sought to revive it.The economist who went further was Pareto, who argued that competition produced “a maximum d’utilite collective regardless of the distribution of income, and indeed even if the utilities of different individuals were not considered to be comparable” (Samuelson, 1947, p. 212). This maximum position “was defined by the requirement that there should not exist any possible variation or movement which would make everybody better off” (p. 212). Pareto's exposition was not ideal, partly because he worked with infinitesimal changes - one of the main features of Samuelson's dissertation was that he also analyzed finite changes - but the main defect in his exposition was that he failed to make it clear that the optimum he had defined was not unique. What remained was to work out the conditions that it implied, a process that writers from Barone to Lerner and Hotelling had undertaken. This development culminated in the work of Bergson.
The last writer to be mentioned is Professor A. Bergson. He is the first who understands the contributions of all previous contributors, and who is able to form a synthesis of them. In addition, he is the first to develop explicitly the notion of an ordinal social welfare function in terms of which all the various schools of thought can be interpreted, and in terms of which they for the first time assume significance. (Samuelson, 1947, p. 219)
The stage was thus set to introduce the idea of the social welfare function, which Samuelson was adopting as his own approach to the problem.
Samuelson’s defense of the notion of a social welfare function began with the charge made by Lionel Robbins (Robbins, 1932) that value judgments had no place in scientific analysis. However, whilst such a view was useful in culling bad reasoning, it went too far. “It is a legitimate exercise of economic analysis to examine the consequences of various value judgments, whether or not they are shared by the theorist, just as the study of comparative ethics is itself a science like any other branch of anthropology” (Samuelson, 1947, p. 220). Contrary to Robbins and many proponents of the new welfare economics, Samuelson contended that even propositions that rely on interpersonal utility comparisons have “real content and interest for the scientific analyst” even though the economist may not wish to deduce or verify the ethical judgments on which they rest, “except on the anthropological level.” He summed this up when he explained his use of a social welfare function.
Without inquiring into its origins, we take as a starting point for our discussion a function of all the economic magnitudes of a system which is supposed to characterize some ethical belief - that of a benevolent despot, or a complete egoist, or “all men of good will,” a misanthrope, the state, race, or group mind, God, etc. Any possible opinion is admissible, including my own, although it is best in the first instance, in view of human frailty where one’s own beliefs are involved, to omit the latter. (Samuelson, 1947, p. 221)
All he assumed about such ethical beliefs was that they provided an ordering of possible states of the world and that they were transitive (that if A was better than B, and B better than C, then A was better than C).
At this point, even though Samuelson’s position might be read into Bergson’s formulation of the problem, he was, as Suzumura (Chapter 7,
this volume) has noted, taking a more radical stance. Where Bergson assumed that his EWF reflected the consensus of the relevant community, other functions not being relevant, Samuelson argued that the economist could analyze any set of ethical judgments, completely separating the problem from that of discerning the views of the community whose welfare was being analyzed.
To this point, Samuelson’s analysis led up to Bergson's formulation of the problem of welfare, though he provided a more substantial historical context and he cut the analysis free from the tangled debates of the 1930s. This freedom from engaging closely with the terms in which welfare had been discussed in the 1930s meant that Samuelson could outline, far more clearly than Bergson had done, various ethical judgments that might be used to give structure to the social welfare function and make it possible to derive substantial results. His starting point was a function that was even more general, and with less content, than Bergson’s, for it simply stated that social welfare, w = w(z1, z2,...) where the z’s are variables that are thought relevant to social welfare. This formalized the problem but added no content whatsoever, because nothing was said about either the z's or the form of the function W. Anything more specific than this involved making ethical judgments.
After observing that the z's were not normally taken to include prices (itself a value judgment) he explained that many of the variables would be specific to individual households. It mattered what different households consumed, and the services different households provided were not interchangeable. The crucial assumption was, however, the fifth, that individuals’ preferences “count.” Yet, important as this assumption was, and though it was, in the context of the 1940s, ideologically charged as Samuelson implicitly noted when he referred to the attitude of the “soap box speaker” who said, “When the revolution comes, you will eat strawberries and cream, and like it!” (Samuelson, 1947, p. 224),6 there were still objections that could be raised to it. One of these was handled by a further assumption that individuals’ preferences were to depend only on their own consumption and not that of others, so as to rule out Veblenian conspicuous consumption, envy and related phenomena.
Samuelson contended that the ethical judgments he had made up to this point were held by most economists. He then explored more controversial ones: that the social welfare function be nearly symmetric with respect to
The importance of individual rationality as a distinction between the United States and the Soviet Union has been discussed by Amadae (2003).
the consumption of all individuals (that everyone counts for approximately the same); and that welfare was the sum of individuals’ cardinally measurable utilities. These involved judgments about the distribution of resources. It is important to note that Samuelson was not arguing about the merits of such judgments: his claim was merely that they did involve value judgments even though they might appear to be mere technical assumptions.
Samuelson then turned to the mathematical analysis of welfare, using this list of value judgments first to narrow down the z’s to quantities of commodities and productive services, to render the social welfare function as w = w(U1(.), U2(.),...) - that social welfare is a function of the utilities of all the individuals in the society - from which he could derive the now-familiar conditions relating to production and exchange. More unusually, given subsequent developments, he had a section discussing interpersonal optimum conditions. The point here is that he did not claim that interpersonal comparisons could not be the subject of scientific analysis. His first point was that the previously derived optimum conditions defined an infinite number of points: to use Ian Little’s terminology, there was an infinite number of Pareto optima. All that the production and exchange conditions could do was to establish that there was an equation relating the well-being of different people in the system, 0 = P(U1(.), U2(.),... Un(.)): a utility possibility function. Using this device, he proceeded to make sense of the concepts of marginal social costs and benefits that Pigou (Pigou, 1932) had used to construct a case for government intervention.
Samuelson used this to mount a brief discussion of public policy, noting that the lump-sum taxes and subsidies, favored by some economists as a way to separate issues of resource allocation from issues of distribution, might not always work. For example, we might wish everyone to have a minimum income, but such a policy could easily provide an incentive not to work. His own view, which took him away from welfarism, was that it might be possible to avoid this problem by creating new motivations for work. “However,” he continued, “this will not provide comfort to those who wish to utilize a parametric pricing system with algebraic lump-sum allowances, since these same considerations undermine the ‘individualistic’ assumptions upon which their analysis is based.” The issues of resource allocation and distribution could not be separated: “from a consistent ethical point of view decisions should be made concerning the welfare function itself. Beliefs concerning the distribution of income are derivative rather than fundamental” (Samuelson, 1947, p. 248).
8.6