Static Economic Theory
Only after these methodological and mathematical preliminaries, explaining how economics should be done, which filled almost half the thesis, did Samuelson turn to substantive economic problems.
The first of these was “A Comprehensive Restatement of the Theory of Cost and Production.” This was, presumably, a development of the paper on the theory of production that had failed to impress the audience at the American Economic Association when he presented it in December 1938.23 Perhaps it was in reaction to that experience that he began by explaining the significance of what he was doing in relation to existing economic theory. “Economic theory as taught in the textbooks,” Samuelson claimed, “has often become segmentalized into loosely integrated components, such as production, value, and distribution.”24 While this might be pedagogically useful, it obscured the fact that these were all aspects of the same problem. Given the technical conditions of production (the relationship between inputs and outputs), it was possible to analyze the activities of the profitmaximizing company as a single problem, covering the demand for factors of production (labor, land, capital goods) and sales of goods and services.Brushing aside the issues over which economists had argued endlessly since Marshall’s death, and which were of particular concern to his teacher Chamberlin, Samuelson noted that most of his results held irrespective of whether competition was “impure” or “pure.” His method could cope with any number of factors of production, and he had attempted to derive “all possible operationally meaningful theorems” relating to the theory of the firm and production.
Though they may have been struck by the bravado in this claim, for most economists the main novelty in Samuelson’s argument would have been the routine use of matrices and determinants, probably learned from Margarete Wolf in Madison in the summer of 1936.
One of the most significant passages, echoing the point made in his chapter 2 about the importance of considering finite changes, was the following:It is curious to see the logical confusion into which many economists have fallen. The primary end of economic analysis is to explain a position of minimum (or maximum) where it does not pay to make a finite movement in any direction. Now in the case that all functions are continuous, it is possible as a means towards this end to state certain equalities on differential coefficients which will (together with appropriate secondary conditions) insure that certain inequalities will hold for finite movements. It is no exaggeration to say that infinitesimal analysis was developed with just such finite applications in view.25
Economic theory was replete with marginal conditions—so much so that they could be taken almost to define the content of the discipline—but economists had lost sight of their main goal. Propositions such as that the wage rate must equal the marginal product of labor, or that the company must produce to the point where price equals marginal cost, applied only in a world where functions were continuous. The general case involved inequalities, of which the equalities of traditional theory formed a special case. Aside from dismissing most previous theorizing as missing the big picture, Samuelson showed this formulation had the merit of encompassing not only traditional theory but also the input-output modeling of Wassily Leontief, from whom he had initially learned much of the economic theory he was analyzing.
In his three chapters on the theory of consumer behavior, which drew heavily on his published articles on the subject, Samuelson was even more critical of the existing literature, very little of which, he claimed, clarified the important issues. “Nowhere in the literature” was there “an adequate account of the theory” that made clear what content consumer theory had.26 There had been progress, in that consumer theory had moved progressively away from making ethical judgments, as in the utilitarian theories of Jeremy Bentham, Henry Sidgwick, and Francis Edgeworth; and along with this change there had been a move away from seeing consumer behavior as having a psychological or even physiological basis.
Citing Alan Sweezy, as he had done in his earlier article, Samuelson argued that many economists had jumped to the conclusion that the whole theory was based on circular reasoning: behavior is explained by preferences, which are defined by behavior. This was wrong, because the theory did have implications: “modern utility theory with all its qualifications is not in a technical sense meaningless. It is an hypothesis which places definite restrictions upon demand functions and price-quantity data; these could be refuted or verified under ideal observational conditions.” He continued with a strong criticism of previous writers,One should have thought that these empirical implications would have been the sole end of the theorists who concerned themselves with these matters. Strangely enough, means and ends have been so confused that only a small fraction of the literature has been concerned with this problem even indirectly; moreover, in this there are not half a dozen papers in which valid demand restrictions have been developed.27
Given that he presumably included some his own papers in this “not half a dozen,” this amounted to a very strong criticism of his elders.j
When Samuelson turned to “Progression in Mathematical Thought,” his story was one of increasing generality of the functional forms used for utility functions and to the recognition, by Pareto, that there was no need for cardinal utility functions. From here he went on to the device of indifference curves used by John Hicks and Roy Allen, arguing that there was no reason why these would be integrable into utility functions. Even the notion of an ordinal utility function was stronger than necessary. This led to the conclusion that it was sufficient to assume individuals select the most preferred combination of goods from those they can afford. All meaningful results could be derived from this. He pointed out that this did not imply anything about the way consumers thought or that they were rational in any other sense.
Samuelson then proceeded to derive concrete results. As in his earlier papers, he emphasized that one equation contained all of the valid, meaningful results found in previous work on consumer theory.j. He had by then published six papers on the theory of demand.
In two further chapters, drawing on his articles and the chapter written for the Schultz volume, he moved into a discussion of special topics, including cardinal utility functions and functions where the utility of each good depended only on consumption of that good; complementarity between goods; constancy of marginal utility of income; and consumer’s surplus (a measure of the change in utility caused by a change in the constraints faced by a consumer). These chapters, relentlessly critical of previous economists, could be seen as exercises that demonstrated the value of the methods he was propounding by cutting through seemingly complex theoretical problems.k