Becoming a Mathematical Economist

In the spring quarter, 1934, immediately after the Labor Problems course, Samuelson took Math 104, Elementary Mathematical Analysis, a course also taken by freshmen. In later life he claimed to have signed up for this course immediately after encountering Cassel's theory of general equilibrium in Director's introductory economics course, but this memory is problematic.^e It seems much more likely that he conflated the two courses he took with Director and that it was in Labor Problems that he took the decision to take the mathematics course.

e. See chapter 2 this volume. been too great. It might have been in Labor Problems that Director exposed Samuelson to Cassel, or it could have been something else in the course that prompted his decision to study mathematics systematically.

One of the freshmen taking elementary mathematics was Norman Davidson, another graduate of Hyde Park School taught by Beulah Shoesmith, who was on his way to being a chemistry major and whose later research on DNA would become important for molecular biology and genetics. In 1996, Samuelson and Davidson were both awarded the Presidential Medal of Science by President Clinton and would meet in the Rose Garden. This prompted an exchange of letters. Samuelson, who had been out of touch with Davidson, aside from some interaction with him through the National Science Foundation, opened the correspondence by recalling their high school years: “I see that two of Beulah Shoesmith’s pupils at Hyde Park High School are to receive the Medal of Science this year. And why not?”²¹ Davidson had not remembered this, but recalled that they were classmates at the university.

What I do have a very strong impression of is you as an Econ major and I as a Chem major were in the same introductory calculus class at Chicago, probably in 1933—1934, which was my first year and you had become convinced that the future of Economics would depend on mathematical analyses and formulations. Is this correct?²²

Samuelson replied by explaining how he had come to see the importance of mathematics for economics.

Since I am a grandson of Willard Gibbs—through my Harvard men­tor Edwin Bidwell Wilson, who was Gibbs’ last (and maybe essen­tially only) protege at Yale—I am considered in economics to be a physicist manque. You know the brutal truth: that, late in life as an aging wunderkind, a good fairy whispered to me that math was a skel­eton key to solve age old problems in economics. This must explain why I as a junior was in Professor Bliss’s calculus class with you as a freshman. (Or was it Professor Barnard? When I went to him to show how I solved a famous problem in duopoly (two monopolized sellers), he said: “Oh, you could have used Lagrange multipliers.” And presto, all mystery evaporated. I knew I wanted more of that good stuff. And like Oliver Twist, always it was a case of MORE.^23,f

f. Elsewhere he recognizes that Irving Fisher was also a protege of Gibbs, but he overlooks this here.

It is not clear whether this refers to the same incident as when he recalled dis­covering some results on asymmetric oligopoly, in ignorance of what econo­mists had already done.^24,g

If this memory is correct, it was a mathematician, Gilbert Bliss, chair of Chicago's mathematics department, who persuaded Samuelson to become a mathematical economist. If that is the case, the sequence of events seems to have been that attending Director's Labor Problems course in the winter quarter of 1934 made him realize the need to learn some mathematics, and so he took a course involving calculus in the spring. During that quarter he had the exchange he reported to Davidson, where their mathematics teacher put him on to the use of Lagrange multipliers, and he realized that he needed to know more mathematics, and thereafter he took as many mathematics courses as he could.

In the spring of 1934, Samuelson wrote a paper, “The Relationship Between Changes in Exchange Rates and General Prices,” the only other surviving paper from his undergraduate years.²⁶ While it could have been written for Douglas's course in economic theory, it is also possible that it was written for the otherwise undocumented course Undergraduate Research. The context for the paper was Roosevelt's attempts, early in the New Deal, to combat the Depression by trying to raise prices, the devaluation of the dol­lar in January 1934 being one of the ways by which this would be achieved. Samuelson sought to establish whether devaluation would in fact raise domestic prices.

Samuelson tackled this problem using the theory of purchasing power parity, associated with the Swedish economist Gustav Cassel (to whose account of general equilibrium Director had previously introduced him).

g. Oligopoly is a situation where there is a small number of sellers in an industry, each of whom has to take account of how others will respond to his or her own actions.

According to this theory, exchange rate must equal the ratio of domestic to overseas prices, implying that devaluation must raise domestic prices by the same proportion. Samuelson explained the theory carefully before explaining that, though it held for internationally traded commodities, it was not true of goods that did not enter international trade, such as housing.

One of the interesting features about the essay is that it supports the argu­ment with long quotations from Keynes's Treatise on Money (1971b). In these, Keynes denied that there was any justification for assuming that the cost of living in one country depended on the exchange rate, and any appearance to the contrary arose because wholesale price index numbers were biased toward internationally traded commodities. Samuelson also argued that the theory assumed all prices moved together, something that was not true. A good many problems, he wrote, “arise because of short-run deviations from long- run generalizations,” supporting this with Keynes's famous remark, “long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous sea­sons they can only tell us when the storm is long past, the ocean is flat again.” This remark was taken not from the Treatise but from the Tract on Monetary Reform (1971a), suggesting that Samuelson had been reading significant parts of Keynes's work.^27,h Given that Lloyd Mints used Keynes's Treatise on Money for his graduate teaching, it is tempting to speculate that he might have been the teacher for whom this essay was written, perhaps for the Undergraduate Research course.²⁸

Given that Samuelson later believed that his Chicago teachers had no theory to explain how an increase in the money supply would stimulate the economy,²⁹ it is interesting to note what Samuelson himself wrote about this question while he was still under their influence.

Moreover, it does not necessarily follow that the new equilibrium [fol­lowing a change in the money supply] will be the same as the old one. It is an over-simplification to think that a monetary change moves all prices equally, just as the movement of the world leaves all places on the earth in the same relationships to each other. For monetary changes often initiate non-monetary changes.

Furthermore, we must examine the mechanism by which price lev­els diffuse.

h. Nowadays Keynes's words are known by virtue of frequently being quoted, but in 1934 it would have been unlikely that Samuelson had picked it up from other sources. The Tract would have been a natural work for his teachers to recommend. group of commodities affect the prices of other commodities: first, by changing the demand for the other commodities; secondly, by chang­ing the supplies of the other commodities.³⁰

He went on to explain how differences in elasticities of demand would cause prices of different commodities to change by different amounts; and how, on the supply side, “idle reserves of factors of production” and “immobility and ‘unsubstitutability’ of productive resources between various industries” would have similar effects. The result was that a new equilibrium might be “long delayed” and might be different from the original one. If Chicago monetary theory were as bad as Samuelson made out, then he knew things that his teachers did not.

Samuelson came closer to a quantity theory analysis when he allowed for the possibility that foreign prices would not remain constant in the face of a dollar devaluation: there would likely be retaliation, rendering any advan­tages only short term. There would be a rise in world prices only if devaluing the dollar increased the means of payment. The 40 percent devaluation that had taken place in January would not affect the world’s money supply very much. However, by allowing a given quantity of gold to support a larger money supply, it raised the possibility of inflation:

Perhaps the important thing about devaluation is that it permits a higher pyramid of money on a smaller base. In other words, it raises the lid on inflation, whether this is desirable or not, but it is not in itself inflationary. For just as the mythical Greek king could not stop the tide merely by command, so cannot the government merely by exhortation lift the price level.³¹

Samuelson thus concluded that though devaluation would not raise the price level much, it would “permit greater inflation in the future.”³²

From here, Samuelson’s academic career was laid out, as shown in table 4.1.

table 4.1 Final Year Program, 1934—35

to weekend in a shack that Director owned, with Knight, in the Indiana dunes and to meet his dog, Jude the Obscure.³³ As be became committed to economics, the other students in the department grew more prominent in his life. These included Jacob Mosak, his rival for prizes; Gregg Lewis, who graduated a year later; and graduate students Martin Bronfenbrenner, George Stigler, Allen Wallis, Albert Hart, and Milton Friedman. He cited two ways in which he got to know the graduate students. One was through his performance in the graduate theory course, alternately taught by Viner and Knight. This course was notorious as the hurdle students had to clear to progress through the graduate program. Viner was incisive and organized, Rose Friedman later wrote, whereas Knight was more philosophical, with the result that some students took the course from both of them. Samuelson took Viner's course for credit, but given that he states he did attend some lectures by Knight, it is possible that he also audited the course when Knight was teaching it.

In addition, employment elsewhere being impossible in the midst of the Depression, Samuelson was given work in the Economics Department:

As I performed various make-work tasks for the department—dusting off the pictures of Bohm-Bawerk, Menger, and Mill in the departmen­tal storage room which Stigler and Wallis had squatted in—we would gossip for hours over the inadequacies of our betters and the follies of princes who try to set right the evils of the marketplace.³⁴

Stigler claimed that it was he who had introduced Samuelson to the joys of large determinants, showing him the notes he had taken in the course by Henry Schultz, and that Samuelson had told the story of how it was he (Stigler) and Wallis who had persuaded him to take advanced mathematics and become a mathematical economist.³⁵ Whether it was his fellow students or his math­ematics teacher who persuaded him, Samuelson proceeded to take as much mathematics as he could fit into the final year of his program, with the courses in algebra, geometry, and calculus listed in table 4.1. After graduating he took a summer course in Differential Equations. He would leave Chicago having taken more mathematics courses than any other economics student.

Stigler and Wallis were also responsible for telling Samuelson that the American Economic Association was meeting in Palmer Hall, in Chicago, in December 1934 and that he should, as he put it, “pay the zoo a visit.”³⁶ This was his first exposure to Joseph Schumpeter, who was to become important for him when he arrived at Harvard. Samuelson remembered Schumpeter, intro­duced by Arthur Marget, as speaking incomprehensibly in his German accent about business cycles in ways he had never encountered. “It was not love at first sight,” Samuelson remembered, “but he did capture my interest.”³⁷’’ Whatever the topic, Stigler was clearly not impressed, for Samuelson’s account elicited the reply, “Isn’t he the nut who believes the rate of interest to be zero in the station­ary state?”—an idea that went against the claims of their hero, Knight. More revealing of the way Samuelson’s interests were developing, he appears to have attended a session on statistical techniques, and when Stigler and Wallis asked him what he had learned, he was able to reply, “Harry Carver from Michigan Math Department suggested, ‘to avoid the sample assumption of normality, permute the sample’s measured properties with that universe’s means proper­ties,’ ” to which Wallis replied that it was the silliest idea he had ever heard.³⁸ This story, told against Wallis, who later made use of such methods, was likely embroidered with hindsight, for there was no Harry Carver on the program, though there was a session on sampling techniques and statistical methods.