Wassily Leontief

It might appear that there would have been considerable overlap between Chamberlin’s course on Monopolistic Competition and Associated

o. Samuelson was later to describe Chamberlin as one of the most anti-Semitic members of the department, raising the question of whether Chamberlin’s grading of his work contributed to this view.

Problems in Value Theory and a seminar titled Price Theory and Price Analysis (Ec. 18) that Samuelson also attended in 1935—36, seemingly not for credit.^p This course had been established by Schumpeter soon after his arrival, to remedy the deficiency in Harvard's teaching of math­ematical economics. However, Schumpeter was not a sufficiently good mathematician to be a success in teaching this course, and in 1935 it was taken over by a young assistant professor, Wassily Leontief, whose math­ematical credentials were much stronger than Schumpeter's. Leontief's offering this course was no doubt also a result of Schumpeter's having to take over the main theory course that Taussig had taught for the previ­ous half-century, and the extensive reallocations of teaching necessitated by the retirements of Carver and Bullock. This was not the first occa­sion that Samuelson had seen Leontief, for he remembered seeing him at the American Economic Association meeting in Chicago the year before (though there is no suggestion that they spoke on that occasion).

Quite understandably, reconstructions of Leontief's career normally focus on input—output analysis, which became the focus of his life's work. Its origins can be traced back to his youthful publication, “The Balance of the Economy of the USSR: A Methodological Analysis of the Work of the Central Statistical Administration.”⁴⁶ The idea for examining the relations between different sectors of the economy can in turn be traced back to the linear models employed by Karl Marx, and from there to Quesnay's Tableau economique.

National income analysis had gone part of the way toward filling this gap, but it remained at a highly aggregative level. Analyzing national income, treating the economy as a whole, lost an enormous amount of information, for

p. It is not clear exactly when he took this, for it is listed as being available in either term. His comment about its preparing him for Wilson's expositions of thermodynamics suggests it might have been in the fall of 1935. This might help account for the facility with which he used mathematics in his second paper for Chamberlin, discussed earlier. it could say nothing about the relationships between industries. Leontief's first step was essentially a generalization of the national accounts to repre­sent production and income for every sector of the economy. Of course, that raised the problem of how sectors should be defined, but in principle they should comprise businesses that produce similar outputs in similar ways. This required that the national accounts become a matrix, listing every sector's purchases from and sales to every other sector of the economy. The input-output coefficients that formed the heart of his system were the ratios of inputs to output in each sector.

For example, the production of $1 of steel required purchases of 43d from coal industry, iod from the railways, and so on.

However, for the first decade of his career Leontief's work had not been so specialized as it later became, and he had worked on a variety of problems in economic theory.⁴⁹ Russian by birth, Leontief escaped from the USSR after graduating from the University of Leningrad, to spend three years studying for his PhD in Berlin, followed by three years at the University of Kiel (with a year advising the Ministry of Railways in China). In 1931, he moved to the United States, where, after a year at the National Bureau of Economic Research, he took up an instructorship at Harvard. In 1933 he was promoted to assistant professor. In the years before Samuelson's arrival, he was prolific, producing a string of papers linked by little more than their use of math­ematical economic theory.^q

In a paper published in May 1935, just before Samuelson's arrival, he turned to the business cycle, examining the relations between prices and quantities of pig iron and cotton (typically taken to represent investment

q. While at Kiel, he had published papers on industrial concentration (1977, chapter 2 [1927]) and on the problem of identifying supply and demand curves from price and quantity data (1929). The latter took him into debate with Elmer Working (Leontief 1932) and Ragnar Frisch (Leontief 1934a, 1934b). He combined indifference curves with Gottfried Haberler's concept of the production possibility frontier to produce a theory of and consumption goods) over a series of business cycles.⁵⁰ Though a con­tribution toward understanding the mechanism of the business cycle, the analysis related to his earlier work on identifying demand and sup­ply curves for individual commodities.

What was common to all of this work was an interest in the interaction of economic theory and data. His 1925 article had been concerned with sta­tistical methods used in the USSR and the appropriateness of different ways of measuring concepts such as output and income, tackling problems such as gross and net income, value added, and the treatment of intermediate goods. Much of the theoretical analysis involved linear inequalities and indifference curves, then less widely used than they became after the papers by Hicks and Allen in 1934, and he engaged with those who were working on the problem of relating theory to price and quantity data. He tackled directly the problem of aggregation, deriving conditions under which rigorous aggregation over commodities was possible; however, when he applied indifference curves to the problem of international trade, he was not sufficiently familiar with these ideas to see that aggregation posed theoretical problems for the type of analy­sis he was constructing.

Samuelson wrote that although Leontief's course was “camouflaged” by the title “price analysis,” this did not fool him, and that it was a course in mathematical economics. “We were a small class,” he wrote, “Abe Bergson, then a third-year graduate student, was one attendee. Another was Harvard honors senior, Sidney Alexander [later a colleague at MIT]. Maybe Shigeto Tsuru and Philip Bradley were auditors, as was Schumpeter occasionally.”⁵¹ Tsuru did indeed attend the course, he and Samuelson getting to know each other well because it was one of three courses they were attending together (the others being Schumpeter's and Chamberlin's).⁵² As befitted

international trade (Leontief 1933), and he challenged the marginal productivity theory of wages proposed by Samuelson's Chicago teacher, Paul Douglas (1934), on the grounds that using a production function in which output depended solely on inputs of labor and capital did not make it possible to build a theory of the rate of interest, as well as the prices of individual capital goods (Leontief 1934c).

a seminar, the course was not based on a textbook or assigned reading, but on exercises. Given the importance Samuelson attached to the course, about which he wrote glowingly, it is worth noting in detail his memory of its contents, which would be familiar to any modern student who has covered consumer theory.¹

Samuelson wrote about the class discovering normal and inferior goods and then, “the Holy Grail at the North Pole,” the case of a so-called “Giffen good” where a rise in the price led to an increase in consumption, the oppo­site of the normal case.⁵³ Leontief made the students work these results out for themselves, using determinants: “We proved it by 2x2 determinants! Ah bliss.”^54,s Tsuru remembers that Samuelson achieved a particular rapport with Leontief:

Leontief, who wasn't particularly eloquent, started to explain by draw­ing a diagram on the blackboard. When Leontief said, “At this point where two lines cross.. ” and was thinking for a moment, Samuelson said “That's where.... ” Then, Leontief stopped him and said, “Yes, that's right, therefore.. ” Often, lectures continued in such a way. There was a tacit understanding between them; however, other stu­dents were often left bemused.⁵⁵

This is as much as we know about what Leontief taught in the year Samuelson took the course. However, we have more detailed evidence on what Leontief was teaching two years later, when Lloyd Metzler took it and made extensive notes.^56,t The first thing to stand out is that Metzler's handwritten notes open with a statement that the law of diminishing utility is nonoperational, a word that Metzler underlined suggesting that

r. “Here is what we learned from late September to almost November Thanksgiving. (a) Specified two-good indifference contours, non-intersecting and ‘convex to the origin.' (b) A negatively sloped budget line.

s. Many students recall their time studying such problems as anything but blissful.

t. It is possible that what Leontief covered in 1937 reflects included results derived by Samuelson, who was then starting to publish articles on the subject. However, even if this is the case, it provides evidence on the way Leontief was thinking.

Leontief may have stressed the point, on the grounds that it cannot be inferred from the actions of individuals:

Law of dim. utility is non operational (equil be inferred from actions of individuals. This law becomes operationally defined if we assume marg utility of one good (or of money) is constant. Thus an addi­tional assumption is necessary (this is the assumption of independent utilities).⁵⁷

If the marginal utility of one good can be assumed constant, or if the utilities of different goods were independent, Leontief continued, the theory became operational. In either case, an additional assumption was needed. This led into a discussion of the properties of demand functions: Would demand rise or fall when prices or income changed? Leontief stressed the difference between necessary and sufficient conditions, something that was important because it determined whether a point could be made by finding a single example or whether it required a general proof. Given that these notes were presumably made in the fall of 1937, they could well have reflected discus­sions in which Samuelson played a part and possibly a reading of Henry Schultz's work on demand.⁵⁸ However, the emphasis on the marginal util­ity of money and independence reflects what others, including Wilson, were doing before Samuelson's arrival. It establishes that Samuelson's early work on consumer theory had a very close fit with what his teachers were doing.

After starting with consumer theory, Leontief turned to problems of choice over time, time preference, and saving and investment, including Keynes and the classics (analyzed using a three-by-three matrix of coefficients). At this point, Leontief discussed alternative approaches to modeling, explaining that most empirical studies are of particular equilibrium, and that most general equilib­rium studies are “macro economic” (interesting as an early use of the term) and some are “macro dynamic.” Here, Leontief posed a choice. One option was to have a few variables and to model the dynamics. The other was to take account of many variables and to ignore problems related to time, such as lagged effects. Metzler then went on to make notes on Leontief's own approach, describing the input—output method. The two-by-two determinants that were such bliss for Samuelson were, at least in the year Metzler took the course, the prelude to ana­lyzing much larger input—output models, for by December they were analyzing saving and investment using n-by- m matrices.

What this evidence shows is that, although Leontief might not assign readings from Hicks and Allen—the economists responsible for the mod­ern theory of the consumer—the material was clearly up to date, in line with issues that were actively being discussed in the journals. It was a course in contemporary mathematical economics using what, by the standards of the time, were advanced mathematical techniques. Indifference curves were increasingly being used to analyze behavior without making the assump­tions necessary for the notion of utility to have operational significance. The stress on operationalism presumably reflected ideas that were being widely discussed at Harvard among Percy Bridgman’s colleagues, and it is notable that Leontief was using the term in precisely the sense that Samuelson was to use it in his discussions of revealed preference.

Thus, even though Samuelson could not have been exposed to all the ideas that Leontief included in his 1938 class (discussion of Keynes could not have been there), there is no reason to doubt his claim that Leontief prepared him for the lectures he was to take the following term from Wilson.

No other course I ever took so profoundly set me on the way of my life career. It was, so to speak, slow motion, and all the better for that. It prepared me to master Edwin Bidwell Wilson’s exposition of Willard Gibbs’ thermodynamic analysis.⁵⁹