Production and the Rate of Interest

Samuelson was also trying to clarify the other side of the theory of supply and demand—the theory of the firm and production. In December 1938, he had presented a paper on the theory of production at a meeting of the American Economic Association, despite Schumpeter’s arguing that the paper was too short.^z According to the abstract Samuelson wrote for the published sum­mary of the session, he criticized economists for failing to provide a clear and correct account of the relationship between the production function and the cost curve, and for not deriving results of operational significance.

A year earlier, in December 1937, Samuelson had written to Knight, enclosing a paper he had written on what determined the rate of interest— a topic on which Knight had taken a strong stand.⁶⁰ Samuelson began by pointing out that when discussing competitive markets, economists usually

y. The first definition of a constant marginal utility of income (that the marginal utility of income would not change when the price of a good changed) was Marshall’s. The second was that the marginal utility of some good—the good in terms of which other prices were measured, usually called “money”—was constant. Using each definition, along with other commonly made assumptions, Samuelson was able to derive unexpected and unwarranted implications, such as that the shares of income spent on each good never changed.

z. See chapter 7 this volume.

started by analyzing how individuals would behave, given the market price (the essence of a competitive market is that an individual has no power to influence the market price). Only after that did they analyze how the actions of all individuals taken together determined market price. He proposed to apply the same method to the theory of the rate of interest, bringing mathe­matics into a discussion of a controversial topic to which much of the previous literature employed purely verbal reasoning. However, although Samuelson had hoped that the paper would interest him, Knight was not impressed. Echoing the comments Viner had made six months earlier in relation to a different paper, Knight took the view that although the mathematics was correct, it added nothing significant to what was already known:

Anyhow, the fact is that your paper rather leaves me cold! In consider­able part... it impresses me as symbolic restatements of fairly obvi­ous relations always do; I find it “sound,” and admit that symbolic formulations have some value in the way of definiteness and precision. But I can't see that the paper makes any important “contribution.”⁶¹

Knight argued that “the high intellectual quality” of Samuelson's work was all the more reason for developing his ideas “to a point where they do achieve clarity and make a real contribution.” For example, he thought Samuelson had not been clear where he referred to “total asset holdings” as a variable that adjusted so as to bring the system into equilibrium. Knight consid­ered this misleading, because the sum of total assets was the outcome of the processes involving investment, disinvestment, and asset revaluation that he was analyzing, and should not be seen as a variable in the system. He wanted an approach that focused more on the actions of individuals and less on aggregates.

The one aspect of the paper that Knight liked was Samuelson's criticism of Keynes. Samuelson revised the paper and it was eventually published in February 1939 as “The Rate of Interest Under Ideal Conditions.”⁶² “Ideal conditions” meant the absence of any uncertainty.

Samuelson then turned to consumers. He justified considering indi­viduals and families separately, on grounds that in modern specialized life, thought patterns tended to be compartmentalized: “the same man thinks differently as an entrepreneur and [as] a consumer.”⁶⁶ There was justification for this in that the existence of financial markets meant that, if entrepre­neurs maximized the present value of their assets, this sum could then be spent in whatever way the individuals preferred. Samuelson rejected hedo­nistic theories that explained saving in terms of the disutility of abstaining from consumption, or in terms of the utility of consumption over time—a view that, originating in the early nineteenth century, had dominated eco­nomic thinking for a long time. He even argued that because, as Knight had pointed out, revenues from personal services cannot be capitalized and sold (people cannot sell themselves into slavery), “it serves no purpose to consider each family as owning its future discounted earnings.”⁶⁷ The result was that consumption was determined by factors that were very different from those determining investment.^bb That is, it depended primarily on the age struc­ture of the population.

Starting from a few elemental facts concerning our civilization, it is clear that individuals are born into families and remain dependent for a number of years. There follows a period of earning power during which income may be rising, falling, or remaining constant, and usu­ally a twilight period of decreased earnings or even no earnings.... Because of the break between generations and the growing tendency for each generation to keep its own books, except in the case of bring­ing up children, there is a considerable holding of assets by individuals in anticipation of a period of dependency.⁶⁸

The purchase and liquidation of financial assets would not cancel each other out, and as a result there would be a need for families to hold a large quan­tity of assets, including life insurance policies, pension funds, and savings

aa. His argument was that it was not a true marginal concept. This was the second occasion when his publication was critical of Keynes. His position in relation to Keynes will be discussed in subsequent chapters.

bb. Note that Samuelson is assuming that people cannot borrow against their anticipated future earnings, something that would now be considered normal (think of student loans or, in a sense, a mortgage on a house).

accounts. The volume of asset holding would depend on the distribution of income. It was “probable” that the rate of interest—the factor tradition­ally thought to determine asset holding—was “only a minor element among many” in determining a demand for assets: “The cultural values of modern society are such that there would presumably be asset accumulation at any rate of interest.”⁶⁹ People might, Samuelson argued, accumulate assets even if the rate of interest were negative. To explain how the behavior of entre­preneurs and consumers determined the rate of interest, Samuelson argued in terms of discrete periods, his exposition perhaps reflecting the approach adopted by John Hicks in his very recently published book Value and Capital (1939b), or his own reading of Swedish economists such as Erik Lindahl and Bertil Ohlin.

I break time up into discrete periods and discuss the determination of the rate of interest in each.

In a footnote, he worked out the continuous-time case.

The discussion is interesting because it contains many ideas that were to become central to postwar economics: the “life-cycle” theory accord­ing to which households save to provide consumption in old age, and the idea Samuelson himself was to popularize as the overlapping-generations or consumption-loan model.⁷¹ And yet, despite the presence of these ideas, he refused to accept some of the presuppositions of later theories, in that he rejected the idea of consumption being based on discounted future earnings and questioned whether households could be seen as maximizers. Rather than being an application of the theory of utility maximizing households, as was the case in his later work on the consumption-loan model, his anal­ysis of overlapping generations was intended as an alternative to that the­ory. The paper provides evidence of the way his thinking was still framed, very strongly, by the views of his teachers—Knight as much as Wilson and Schumpeter. He was also, like his teachers, critical of Keynes. He went along with Keynes in arguing that the rate of interest would adjust so that people wanted to hold the stock of assets existing in each period, and in denying that equality of saving and investment could determine the rate of interest (saving and investment must be equal).^cc However, beyond that, their theories were very different.

Samuelson adopted an explicitly dynamic framework; he abstracted from uncertainty; he focused on the total stock of assets rather than just money.

In this paper, as in his earlier paper on investment, Samuelson was using his mathematics to cut through the confusions that he thought abounded in less rigorous theorizing. The theory of capital was a major area of confu­sion, but by focusing on the value of assets, he believed that he had man­aged to build a theory in which investment was the outcome of maximizing behavior without defining anything called the “quantity of capital.” The literature on measuring capital had, he claimed, concealed the difference between rising asset values and the real physical investment—something to which his analysis drew attention. However, as he was unwilling to make the assumptions necessary to model consumption formally (for example, as the solution to a maximization problem), his analysis of that side of the model remained purely verbal, and as a result the conclusions he could draw were limited.

Samuelson never wavered in his belief that, in all the areas of economics he was investigating, mathematics could be used to cut through confusions in the previous literature. He explained his position to his friend Tsuru:

I think it is like trying to cut with a small knife through the brambles of a wood that have overgrown to the extent that one cannot move, in order to make a path big enough for people to pass. Economics is inundated with categories and system with complexity in direct proportion to the multiplying number of economists, but in the end, when the general notion and the reasoning are clarified and a thorough investigation is carried out, the theoretical framework is revealed as quite simple and has common features.⁷³

cc. In itself this suggests that, like many economists at the time, he had not properly understood the General Theory, in which although realized saving and investment must be equal, planned saving and planned investment need not be.

dd.It is not clear that Samuelson’s analogy makes sense here.

Samuelson’s work on consumption and production was to be central to his doctoral thesis and a major part of his Foundations of Economic Analysis, the book that cemented his authority as a mathematical economist. However, though he was simplifying economic theory, cutting through the complica­tions that others had introduced, these early papers reveal a young economist still finding his way, containing many remarks that imply skepticism of ideas that would later become standard assumptions in economic theory.

His first article showed that if individuals maximized the discounted sum of utilities, it would be possible to measure utility—but he went on to question the relevance of this, given evidence on actual behavior. His arti­cle on the rate of interest provided reasons for skepticism of using a theory based on utility maximization for analyzing what might be thought the natural subject matter for such a theory—saving and the rate of interest. He even added a footnote dismissing his earlier paper, describing it as “an intellectual curiosity, which served to treat to my own satisfaction the arbi­trariness of the assumptions and the barrenness of the results.”⁷⁴ He showed that utility analysis had empirical implications even though in another paper he had argued that these implications were of no consequence. The term “revealed preference,” which came to define his approach to consumer theory, was introduced only in what was effectively an addendum to his earlier paper in Economica, where the main ideas had been presented in a form that turned out to be more complicated than strictly necessary. His approach to capital theory was conceived in terms that fitted with the work of Knight and Schumpeter. In short, he may have been simplifying the previous literature, but he had not yet cut free of the way questions were formulated in that literature.

There are also suggestions that his methodological position was still evolving. His first paper in Economica toyed with a traditional defense of his assumptions as indisputable, whereas a few months later he turned to opera- tionalism—but he interpreted it in a way that echoed the Vienna Circle ideas with which two of his friends, Alan Sweezy and Quine, were engaging. His work in this period contained ideas that were to be of lifelong concern— operationalism, revealed preference, overlapping generations, and concep­tions of capital—but his thinking about them was evolving as he turned out paper after paper.

There is no question that he was ambitious, very confident, and filled with a belief that the use of mathematics could dramatically change economic theory. A young scholar in a hurry, he was receiving the mes­sage consistently from his teachers, including Wilson, Schumpeter, and Knight, that he should take more time to present his ideas in such a way that more notice would be taken of them. On August 4, 1939, he acquired a further reason to be in a hurry when his father died, at age fifty-six. Samuelson was then only twenty-four, but having been living with the knowledge of his hypertension since his student days, and having had his activities restricted on account of this, he became anxious that he did not have long to live.