Statics—Welfare Economics

In his thesis, Samuelson had not tackled the problem of welfare economics, though he had worked closely with his fellow student, Abram Bergson, who had published a paper on the subject.’ Samuelson shared Bergson's views on how the subject should be tackled, but in his publications before Foundations his remarks were confined to noting, albeit emphatically, that the problem of welfare bore no relation to the concept of utility as that was understood in consumer theory.

Since Bergson's article, there had emerged a rapidly growing literature on the analysis of welfare, described by Hicks as “the new welfare economics.”⁵⁰ It was widely held that judgments of welfare were subjective—dependent on the values of the individuals making the judgments—and that nothing scientific could be said about them. “One's welfare economics will inevita­bly be different according as one is,” Hicks argued, “a liberal or a socialist, a nationalist or an internationalist, a Christian or a pagan,” something he found “rather a dreadful thing to have to accept.” The problem of welfare economics was to find a way out of this impasse—to find a way to analyze welfare scientifically. The standard method was represented by Marshall and Pigou, who had sought to ground welfare economics in utility theory. The problem was that this was conceptually flawed, the main problem being that it involved adding up the utilities of different individuals—something for which there was no basis.^k Fortunately, Hicks went on, recent work had pointed to ways of discussing the efficiency of the economic system without resorting to arbitrary subjective judgments about how one person's welfare should be valued against another's.

The first stage in Hicks's argument was to define an “optimum” as one in which everyone is as well off as he or she can be without making some­one else worse off (what later came to be called a “Pareto optimum”). In such an optimum, any change will make at least one person worse off. There might be many such optima. The second stage was to reduce the number of potential optima, considering as improvements those changes where those who gain can compensate the losers and still remain better off. Such a com­pensation test establishes, so Hicks and others argued, that an allocation is efficient. If compensation is not actually paid, it may not be possible to dem­onstrate that social welfare is higher—comparing the benefits to some people with losses experienced by others would require value judgments—but it establishes that the new allocation has the potential to make everyone better off. Compensation tests, therefore, so it was claimed, opened up the possi­bility of a scientific welfare economics that did not rest on subjective value judgments; it rested solely on individuals’ own judgments about their own welfare.

It seems likely that what prompted Samuelson to write his new chapter on welfare economics was the publication in the American Economic Review of a critique of the new welfare economics by his friend from his Chicago student days, George Stigler. We know that shortly after the exchange with Stigler, he decided to add significant new material to Foundations, and the chapter on welfare economics, which is very different in style from the rest of the book, could well be what he added. It is plausible that it was Stigler’s failure to understand the new welfare economics that made him realize there was a need to improve on Bergson’s exposition of the theory. In his article, Stigler claimed that the “new welfare economists” (in which he included Samuelson’s article on international trade) claimed that “many policies can be shown... to be good or bad without entering a dangerous quagmire of value judgments.”⁵¹ Claiming that the new theory, though usually presented using formidable mathematics, was simple enough to be summarized in half a page, he offered what he believed was a strong cri­tique: if the precepts of the new welfare economics were followed, thieves would be rewarded for their crimes and wars should be fought with check­books, a remark that had added significance, given that it was published in 1943.⁵² The problem with these arguments, Stigler contended, was that societies were concerned with more than maximizing national income.

Samuelson responded to Stigler by saying that he agreed with much of what Stigler was saying—economic welfare was not necessarily the main goal in society, and tastes would change—but Stigler had gotten the new welfare economics completely wrong.^[55] The new welfare economics was not intended to displace the old, but to derive necessary conditions for social welfare, basing them on the very mild assumptions that it is better to have more than to have less, and that “individual tastes are to ‘count’ in the sense that it is ‘better’ if all individuals are ‘better off.’ ”⁵³ In saying that the new welfare economics is no substitute for the old, he implied that stronger ethical judgments could and should be made, though this was not a point he chose to stress. The new chapter on welfare economics—a substantial chapter spanning fifty pages and with much less mathematics than other chapters—clarified the new wel­fare economics that Stigler had so badly misunderstood.

Samuelson approached the problem historically. Economics had, Samuelson claimed, always been associated with the notion that “in some sense perfect competition represented an optimal situation,” exemplified by the case for free trade.⁵⁴ The idea that competition was socially optimal had often been used to defend the status quo against arguments for government intervention, but Samuelson argued that it could also be a radical idea, used to challenge the status quo, as when it was used to justify anti-monopoly legislation. It had in the past been bound up with teleology—with argu­ments about natural rights, natural selection, or the Malthusian doctrine that competition was necessary to bring out the best in people—but there were also arguments that did not depend on teleology.

In the 1920s, economists had developed Pareto’s ideas and Samuelson claimed that this literature had culminated in the work of 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.⁵⁷

Bergson's paper introduced 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 that value judgments had no place in scientific analysis.⁵⁸ However, while 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.⁵⁹

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,” 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.⁶⁰

This made it clear that all the economist could do was examine the con­sequences of ethical beliefs: choose a different set of beliefs and a different evaluation of social welfare would follow. All he assumed about such ethi­cal beliefs was that they provided a consistent ordering of possible states of the world: that if A is considered better than B, and B better than C, then A must be better than C.^m

Though Samuelson followed Bergson in using what they both called a social welfare function, he cut his analysis free from the tangled debates of the 1930s in a way that Bergson had not. This is precisely what he had done with

m. This is the assumption of transitivity. the theory of the consumer: building on previous work, but presenting the theory in such a way that when one had read his account, it no longer seemed necessary to go back to the previous literature.

Samuelson did this by starting with a function that was even more general than Bergson's, and with less content, for it simply stated that social welfare was a function of all variables that are thought relevant to social welfare.ⁿ Indeed, it had no content at all. To give it content required making ethical judgments that restricted the form of the function. Its use lay in providing a framework both to analyze the implications of specific value judgments and to assess what value judgments were implicit in welfare criteria, such as Pareto optimality.

After observing that the variables in the social welfare function were not normally taken to include prices (itself a value judgment), he explained that many of the variables would be specific to individual households. The consumption of different households—who consumed what—did matter, and the services (including labor) provided by different households were not interchangeable. The crucial assumption, however, was that individu­als' preferences “count.” This assumption was far from ideologically neu­tral, for the essence of Nazi and communist “totalitarianism” was held to be that individuals' preferences did not count; but it was one that most American economists, who took for granted the importance of the individ­ual, could be assumed to find acceptable. Samuelson implicitly noted the ideological dimension of this assumption 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!”⁶¹ More serious were problems such as conspicuous consumption—enjoying something because others did not have it—and envy, but these could be minimized by assuming individuals' preferences were to depend only on their own consumption and not that of others.

Thus far, the ethical judgments made were, Samuelson contended—ones that most economists would accept. He then explored more controversial ones: that the social welfare function be nearly symmetric with respect to the consumption of all individuals (that everyone counts for approximately the

n. W = W⅛₁,^₂,∙ ∙∙), where the z^,s are any variables that are thought relevant to social welfare.

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 that such judgments were illegitimate; it was merely that they do 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 to reach two conclusions. The first was that the vari­ables in the social welfare function should include quantities of commodi­ties consumed and quantities of productive services provided, such as labor. The second was to argue that these would affect social welfare only if they affected the utilities of individuals.'’ Even with these restrictions, the social welfare function was still vague, but it was sufficient for Samuelson to derive conditions for a social optimum comparable with those derived by Hicks and others—the conditions that later came to be called the conditions for a Pareto optimum. He summed up what could be achieved by arguing that the optimum conditions he had derived defined what he called a “utility possi­bility function,” which stated that the maximum utility an individual could achieve given the utilities achieved by everyone else in the society. It made it clear that there was an infinite number of social optima and that choosing between them involved evaluating what some people gained against what others lost.

He then turned to the claim that any “individualistic” ethical optimum (that is, one of the optima defined by the conditions discussed in the previ­ous paragraph) could be a achieved by lump-sum taxes. The attraction of this theorem was that it made possible separating questions of resource allocation from questions of distribution between individuals. However, Samuelson contended that not only was it not a fundamental theorem in welfare eco­nomics, it was not even universally true.^p Among the reasons he cited were that people might have preferences that rendered the equilibrium unstable, that it would not hold if the optimum conditions were achieved through price discrimination (through different individuals being charged different prices), and that it was in practice very difficult to devise truly lump-sum taxes (taxes that did not depend in any way on an individual’s actions).

o. W = W(U₁Q,U₂Q,-Q, where the U^,s are the utility functions of the individuals in the society being evaluated.

p. It later came to be known as the second of two fundamental theorems of welfare economics: that any competitive equilibrium is Pareto efficient; and that any Pareto efficient allocation can be achieved as a competitive equilibrium by suitable redistribution of resources.

Perhaps echoing issues that he had been discussing in the National Resources Planning Board, which wanted to reduce income inequality, he noted that separating out the problem of income distribution simplified “the problem of formulating political slogans and beliefs which will command wide approbation.”⁶² However he claimed, without providing any explana­tion, that even if this was politically desirable, “it must never be forgot­ten that 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.” In a footnote, he implied that understanding the mathematics of the problem could shed light on the clash between equity and efficiency in capitalist economies; oversimplified analyses based on separating resource allocation from considerations of effi­ciency were misguided.

Whereas other economists were searching for a way of doing welfare eco­nomics that could stand independently of any ethical judgments, Samuelson denied that this was possible. The attempt to eliminate ethics from welfare economics was completely misconceived because welfare judgments were inherently ethical. The starting point for any welfare analysis had to be a set of ethical principles or value judgments. It also meant that if different people or different groups adhered to different ethical principles, the result would be different judgments about welfare. A social welfare function, therefore, had to reflect a particular set of ethical views; it could not be completely objective and independent of who was making the evaluation.

In taking this position, Samuelson was assuming the view of Frank Knight, under whose spell he had fallen while an undergraduate in Chicago.^q Though Samuelson was generally taking a very critical stance toward the mentor with whom he had once been besotted, there are clear parallels between Knight's views on the relationship between ethics and economics and Samuelson's welfare economics. The chapter on welfare economics refers to Knight four times, and in every case Samuelson is praising Knight.⁶³ Possibly his exchange with Stigler had prompted him not only to clarify his views on welfare economics but also to reread the work of the teacher in whose circle they had once both moved.

This analysis of welfare economics, Samuelson argued, completed his static analysis of maximization. In previous chapters, he had analyzed maxi­mization by companies and consumers, and in the chapter on welfare, he tackled the problem of maximizing social welfare. Because it was less clear

q. See chapter 5 this volume. what should be maximized, the nature of the discussion had to be very dif­ferent, focusing on more philosophical, conceptual problems, resulting in a chapter that had a balance of words and equations that would have pleased Wilson. Mathematics was, as in his other work, used to clarify his arguments, but in comparison with the mathematics used elsewhere in the book, it was comparatively simple. Samuelson’s chapter took up Robbins's challenge that value judgments should not be part of economic science. Scientific economic analysis might not be able to arbitrate between competing value judgments, but it could analyze the implications of different sets of values; Samuelson did not accept the view that economists, in their role as economists, could say nothing about interpersonal comparisons, and hence that welfare economics could not go beyond what became known as Pareto optimality."

Bergson and Samuelson took their analysis in a direction that was very different from that of the new welfare economics as defined by Hicks, in that instead of trying to do welfare economics without making any subjective value judgments, they placed ethical judgments at the center of the field. However, their work came to be seen as part of the New Welfare Economics. They were all agreed that utility could not be measured in the same way that, for example, temperature can be measured. In addition, they were prepared to make similar judgments—notably, that individual preferences counted. As economists came to accept that compensation tests were conceptually flawed, and as other approaches to welfare economics were developed, Samuelson’s approach appeared to have even more in common with that of Hicks.