The Keynesian System

In October 1942, Samuelson received a letter from a former MIT student, Arthur Ashbrook, who described himself as “a hireling in OPA's iron and steel branch” in Washington, but who thought that he would be in the armed forces before the end of the year.^q Ashbrook told Samuelson that, being unable to suppress “some of my more pernicious vices acquired at MIT,” he had been reading the General Theory.⁴⁴ “Horrible doubt” had crept into his mind, for it seemed to him that Keynes's argument about why there would not be full employment was confused.

Involuntary unemployment should be linked with frictional and voluntary unemployment as qualifications of the classical concept of full employment. When we talk of “millions of unemployed,” we are speaking principally not about a lack of full employment in the strict sense, but of a low MPC and a low MEC, coupled with an I [interest rate] that because of institutional factors will not fall below a rate substantially above 0. In other words, we always have full employ­ment to a first approximation; what our real goal is statistical full employment.^r

He asked Samuelson whether he “would be willing to restore my faith in the bible” by pointing to some articles that explained why unemployment could remain high even when supply and demand for labor were high. After all, it was “all right to doubt that Joshua stopped the sun in its course, but when one begins to doubt that man was born sinful....”

Samuelson replied that he was uncertain about whether he could restore Ashbrook's faith. “You must remember,” he wrote, “that not all the books of the Bible are to be given the same weight” and he had “always thought that Keynes['s] discussion of involuntary unemployment was the weakest part of the book.”⁴⁵ He conceded that if all markets were frictionless and competitive, it was hard to see why wages would not fall.

q. The OPA was the Office of Price Administration. Ashbrook was to complete his PhD, under Samuelson's supervision, in 1947.

r. Full employment as measured by unemployment statistics. point, he questioned the usefulness of Ashbrook’s definition of the term “full employment”:

It conceals more problems than it illuminates. In particular it does not explain the huge swings in effective demand which determine how far from what you call “statistical” full employment the system’s actual full employment will be.

Unemployment was not explained just by the structure of wages. The labor market was highly imperfect, in that people were often unable to sell their labor whatever the wage they were willing to accept. This was the reality irrespective of any theoretical justification for it.

If you don’t believe this, just wait until the next depression. Try chain­ing yourself to the desk of the personnel officer of a huge company brandishing evidence of your high IQ and the fact that your family is starving. For a thousand and one reasons the employer cannot take advantage of your offer to work for less, even if he should want to... and if he were a man of good will he would not want to since he him­self believes in a fair minimum wage, regardless as to whether or not this belief is well founded.

Samuelson went on to explain that belief in a fair wage, and that cutting wages would not help, were important.

In explaining the unwillingness of workers to cut wage rates when their families are almost starving, we must appeal to the same vague beliefs in a fair wage, to this intuitive notion that this will not help, to their group and class sympathies.

All in all it is only too easy to explain why wage rates are stick­ing. Keynes should have let it go at that, pointing out that frictions explain the rigidity of wage rates but not unemployment.

Drawing on points that Keynes had made, Samuelson challenged Ashbrook’s assumption that a man could get work if his wage were less than the marginal product of labor; even if true for an individual, it was not true for large groups. Ashbrook was only partly convinced, reply­ing to Samuelson in a long letter in which he defended his position that it would make more sense to work simultaneously with more than one concept of full employment.^46,8 Unfortunately, we do not have Samuelson’s reρly.^t

Samuelson’s opinion that Keynes’s discussion of involuntary unemploy­ment was the weakest part of the General Theory is significant, given that this was to prove the Achilles’ heel of Keynesian economics.⁴⁷ When Ashbrook, drawing on standard supply and demand theory, confronted Samuelson with what he believed were theoretical inconsistencies in Keynes’s treatment of involuntary unemployment, Samuelson did not respond by defending Keynes’s reasoning; he appealed to the reality of involuntary unemployment, saying that though such explanations were not part of the theory, it was easy to explain why wages would not bring labor markets into equilibrium. This meant that even in the absence of a formal theoretical justification, it made good sense to talk about there being involuntary unemployment, rather than fit the analysis into categories that kept it closer to traditional price the­ory. Samuelson’s response also makes clear the importance of dynamics. As Keynes had realized and, as Samuelson had pointed out in an earlier paper, he took seriously Keynes’s belief that cuts in wages might be destabilizing.

Ashbrook was not the only economist to contact Samuelson seeking expla­nations of the new theory. Hans Neisser, also working at the OPA, had writ­ten in July to point out that if there were no lag between the receipt of income and spending on consumption, the multiplier-accelerator model would not produce a cycle, merely exponential growth.⁴⁸ He wrote again in November, having read Samuelson’s “Fiscal Policy and Income Determination.”⁴⁹ After a point about investment that Samuelson was able to dismiss as a misunder­standing, Neisser questioned whether a rise in the propensity to consume would necessarily conduce to full employment.

s. The letter is fascinating because of the picture he gives of life inside the OPA. He writes of a “price-fixers’ school” in which staff members had the opportunity to listen to big shots “sounding off about prices and the state of the union.” Galbraith had explained that, though most economists thought price control naive, the OPA had taken actions that either emptied the shelves in stores or led to rationing. The only “dynamite” in the meetings was criticism of other agencies. Seymour Harris, as chairman, had been peculiarly gauche, and though he was apparently a hard worker, “could best use his time for some concentrated thought on various subjects, not excluding economics.” Gilbert had made a good impression and Clark (Ashbrook wrote J. B. but must have meant

J. M.) came across as very modest.

t. Ashbrook was called up, and his next appearance in Samuelson’s papers is after the war, when he returned to MIT to complete his PhD.

correctly, as well as the point that full employment might require a reduced standard of living. This elicited from Samuelson a clear statement about the assumptions he was making about the supply side.

Your second point, which I did not get into, was whether or not an increase in effective demand can result in extra employment only by reducing the real wage. I do not think that Keynes would agree with this—I know that I should not. It would depend upon the exact nature of the loss of returns, external and internal, and upon the degree of monopoly.⁵⁰

The effect of a rise in the propensity to consume would depend on the degree of monopoly power and cost conditions facing companies, about which he and Neisser were making different assumptions.

I should say that we differ in our emphasis upon the importance of limited capital as a bottleneck causing an increase in effective demand to dissipate itself in an incipient inflation, short of full employment.

In response to this, Neisser replied that costs could be constant “only over a limited range” and that there was no reason to believe that the point at which costs began to rise would be full employment.⁵¹ In other words, he was sug­gesting that there might not be sufficient productive capacity to employ the entire labor force without a fall in real wages. This elicited a further clarifica­tion from Samuelson.

I agree that the full employment point need not coincide with the bottleneck point at which capacity gives out—nor, for that matter, with the point at which workers will begin to push up money wages. After a period of long stagnation the bottleneck point is certain to be considerably below the full employment point so that there is a [serious] problem of an upward price spiral even though people are still unemployed. On the other hand, after a boom period the reverse could conceivably be true and I am not sure that after 1929 this was not the case. Of course certain assumptions with respect to monopoly, expectations etc. would be involved in any explanation of this fact.⁵² This shows that Samuelson was well aware of capacity issues and the need to consider the supply side. His argument that capacity would fall during a long period of stagnation no doubt reflects the experience of 1937, when recovery stopped well short of full employment. It is also worth noting his repeated emphasis on monopoly and expectations.

A point Samuelson found more difficult to answer, and more interesting, was an argument Neisser made about whether there was a point at which a rising propensity to consume would lower investment, a point Lange had also made.

The end result of their correspondence was to reduce their disagreements considerably. Neisser explained that he had viewed Samuelson as one of the “mature economy” theorists who “deny the necessity of net savings in the present stage of capitalist development,” but that he had been wrong to do so. He excused his misunderstanding because he though Samuelson had talked about “taxing away saving” in a misleading way. “You should explain,” he wrote, “how a tax system would look which reduces savings and raises con­sumption as long as utilization and income does not exceed, say, the level of 1939 but does not reduce to the same extent the marginal propensity to save for higher incomes. Our present system of graduated income taxes seems to have the opposite effect.”⁵⁴

Samuelson shared Hansen's view that there might be a shortage of invest­ment opportunities, but was distancing himself from more radical posi­tions. Neisser drew a clear distinction between Samuelson's view and that of Keynes, suggesting that this might reflect differences between the European and American situations.

As to the problem of the mature economy, I should like to point out that the impossibility of sufficient investment is not proved at all for the European economies, and is in particular disproved for Germany by the experience up till 1929 and for England by the experience after 1933. It is this experience which presumably led Keynes to take a different view from the mature economy theorists, viz., that it is not the absence of investment opportunities (the inelasticity of the mar­ginal efficiency function), but the inelasticity of the money supply which was mainly responsible for the English unemployment situa­tion before 1930.

Neisser agreed that there was no shortage of investment opportunities in Europe—how could there be, given the contrast with the situation in America during the 1920s—though he did not accept that Britain's problem had been an inelastic money supply. On the other hand, though there was more evidence to support the mature economy thesis in relation to America, he opined that “no conclusive proof ever has been tried. And the great obsta­cles our tax system and other institutions put in the way of investment make such a proof rather difficult.”

In this correspondence with Neisser, not only do we see Samuelson dis­cussing the new economics in relation to what had been experienced over the previous decade, debating its relevance as much as its logical consistency, but we also see him explaining results about which he was confident because he had proved them mathematically. Neisser could follow his mathematics—he had read and appears to have understood at least one of Samuelson's very technical articles on the stability of equilibrium—and he was sympathetic to the ideas Samuelson was proposing.⁵⁵ His problems arose in relating results from simple mathematical models to the world they saw around them. The exchange also shows the way in which Keynesian ideas were being used by two economists who did not completely accept them.

The merits of Keynesian ways of thinking about employment were also raised by an exchange that Samuelson had with Abba Lerner in the same month. Lerner tried to persuade him that it was possible to conduct the analysis in terms of the supply and demand for saving, thereby relating the Keynesian theory to older theories that ran in terms of supply and demand for loanable funds.⁵⁶ While Samuelson contended that Lerner's argument was wrong, suggesting an alternative way of deriving such curves, he disputed that this had anything to do with the old theories.⁵⁷ Lerner was trying to find a way to reduce the problem to a two-dimensional diagram involving famil­iar ideas such as supply and demand. Samuelson's letter showed him finding fault with Keynesians, as well as with the anti-Keynesians.

[T]he Keynesians have sinned grievously in not understanding their own system. I believe this to be true of Harrod, Joan Robinson,

Kalecki, and that at one time even Lange was confused as to whether the marginal propensity to save and to invest had to be equal. Keynes himself is a split personality on these subjects. In fact it can be shown that in the Treatise and in his earlier writings he made similar blunders by not recognizing the senses in which things are equal at the intersec­tions of schedules, but “virtually” away from the intersections.... In the Keynesian system for the first time the non-mathematical econo­mist has had to work with many dimensional relationships. It is not surprising but it is nevertheless deplorable that the confusions of a century ago with respect to the equality of supply and demand should rise once again to plague and confuse us.⁵8

Using appropriate mathematical analysis was vital, because the Keynesian system was multidimensional. Yet despite this, Samuelson persisted with trying to help Lerner understand it by arguing in terms of two-dimensional diagrams. If he had constructed an algebraic model that could capture all dimensions of the problem, Samuelson did not reveal it.

Samuelson also pointed out the benefits of using mathematical reasoning to analyze the multiplier in print. When reviewing a book by Fritz Machlup in early 1943, he found a long list of points where he believed Machlup had made mistakes, and claimed that Machlup's 200-page book could have been compressed into a single mathematical article.⁵⁹ His belief that the use of mathematics simplified arguments was made even explicit when he argued that Machlup's more technical chapters were the easiest to understand. In these, Machlup had used mathematics to analyze the working out of the multiplier in systems of international trade: analyzing the effects of a shift in demand from domestic to foreign products, and the effect on one country of an increase in investment in another country. The multiplier was being used increasingly widely.

However, despite all the attention paid to the multiplier, there remained unanswered questions. Samuelson discovered one of these while working on some numerical examples where he suspected a computational error.⁶⁰ Samuelson noticed that, though the multiplier was used in two different ways, no one, including himself, had proved they were the same. One was the case in which there is a one-time increase in spending, and the other was one in which spending rises to a new level, at which it remains con­stant. In the first case, the multiplier gives the cumulative rise in income; in the second, it gives the higher level of income in every period. He sought to show that these two multipliers were the same, over whatever period the multiplier was calculated.⁶¹ He extended his analysis to multi-country multipliers and applied to it techniques learned from studying problems related to engineering.⁶²

Samuelson’s notion of a “truncated” multiplier—a multiplier calculated over a finite number of periods—was taken up by Oskar Lange, who gener­alized his result, allowing for changes in spending in every period.⁶³ Lange stepped up the mathematical analysis, drawing on a number of techniques Samuelson did not understand, and in April 1944, Samuelson wrote to him asking for some references and questioning some of his results.⁶⁴ He sug­gested that one of the problems might be the way one represented a one­time expenditure increase in continuous-time models—a single impulse of spending would have to be represented as “a momentary impulse of infinite magnitude—i.e., like an improper Dirac function.”⁶⁵ The multiplier might appear to be a simple concept, but it raised difficult mathematical problems that few economists were able to handle properly.