Measuring Utility
It was during Samuelson’s second year at Harvard that he made the transition from writing papers solely for his teachers to writing for publication: in February 1937, he had an article published in the British journal The Review of Economic Studies and in May, another in Harvard’s Quarterly Journal of Economics.
However, though he had passed his generals, he was still taking courses when he wrote these articles. Two courses he took that year, International Trade with Haberler, and Business Cycles and Economic Forecasting, which comprised lectures by Schumpeter in the first term and a seminar run jointly by Schumpeter and Haberler in the second term, introduced him to fields that were eventually to be transformed by his work. Public Finance with Burbank, which he described as a course against public finance rather than on it, and Recent Economic History, where recent meant since 1450, taught by Usher, were presumably taken solely to meet his course requirements.’The first of the two articles Samuelson wrote was “A Note on the Measurement of Utility.”7 He probably wrote this during the summer, after his generals and after attending summer school in Madison, making final revisions in the fall of 1936. It was well known that it is not generally possible to derive a unique measure of utility.k In this paper, Samuelson showed that if one considered an individual deciding how to spend money over time, and if one made some seemingly natural assumptions about behavior, it was possible to derive a unique measure of utility. He simplified the problem by considering an individual who starts with a given amount of money. The individual thus has to choose how much money to spend at each moment in time. Samuelson assumed that utility at any moment depends on consumption at that moment, and that future utility is discounted with a constant discount rate, reflecting the assumption that future consumption is less valuable than present consumption.
Samuelson showed that, given this set of assumptions, if we know the time path of consumption chosen by the individual, it is possible to calculate what the utility function must ܺ.[19] [20]However, though Samuelson showed that utility could be measured, he went on to point out that this measure of utility was subject to “serious limitations” that “almost certainly vitiate it even from a theoretical point of view.”8 His result rests on very special assumptions about utility—namely, that utility at any moment depends on consumption at that moment, and not on the whole time path of consumption. This was the “independence assumption” for which Wilson had criticized Pareto: it was completely arbitrary. Samuelson claimed that it would be more general to assume that utility depended on the time path of consumption throughout the individual’s life, but such an assumption was not specific enough to lead anywhere useful: there were no a priori grounds for saying anything about how utility related to the time path of consumption, and given that it relied on more advanced mathematics, it was hardly a convenient simplification of the standard theory.9
Samuelson’s mathematical analysis stopped abruptly at this point, and he adduced evidence that people do not behave in this way. As time passes, people typically change their spending decisions, and recognizing that they may be tempted to spend rashly, they do things like set up irrevocable trusts and commit themselves to saving through life-insurance schemes. He claimed that the time path of consumption would depend on “socially determined” parameters: desire for prestige, life expectancy, the “life cycle of individual economic activity,” and the institutional structure of industry and finance. His conclusion was that the entire analysis was inappropriate:
Even to generalise concerning these can only be done in terms of a theory of “history” (in itself almost a contradiction in terms).
In any case, this would seem to lie in the region which Marshall termed Economic Biology, where the powerful tools of mathematical abstraction will little serve our turn, and direct study of such institutional data would seem in order.10This reference to “economic biology” is one that Schumpeter and Wilson would both have approved. However, this did not deter Samuelson from concluding that his mathematical analysis was useful and that utility could be measured. What he had shown is that utility measurement requires “Pareto's Postulate Two”—namely, that the individual can compare differences in utility—a corollary of his assumption that total utility was obtained by adding up utilities obtained at different points in time. This was precisely the issue that had concerned Wilson two years earlier, though he had tackled it in the context of demand for different commodities at a particular point in time.11
In the last paragraph of the article, Samuelson explained that the utility he was measuring did not measure the individual's welfare.
In conclusion, any connection between utility as discussed here and any welfare concept is disavowed. The idea that the results of such a statistical investigation could have any influence upon ethical judgments of policy is one which deserves the impatience of modern economists.12
Given that he had not previously mentioned the problem of welfare, this short paragraph appears almost as an afterthought; perhaps it was added at the last minute when he realized that his paper might cause a misunderstanding without it, and it was too late to modify the main text. Despite the brevity with which it is expressed here, this point was one to which Samuelson attached great importance, for it was central to the approach to welfare economics he was to propose in Foundations (1947a) and to which he held throughout his career.