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A significant part of economics as we know it today is the outcome of battles that took place in the post-war years between Keynesians and monetarists. In the US, the focus of these battles was often between the neo-Keynesians at the Massachusetts Institute of Technology (MIT) and the Chicago monetarists. The undisputed leader of the MIT Keynesians was Paul A. Samuelson, one of the most influential economists of the 20th century and arguably of all time. Samuelson’s output covered a vast number of subjects within economics, the quality of theseoften pioneering contributions unmatched in the modern era.
The volume focuses both on how Samuelson’s work has been developed by others and on how that work fits into subsequent developments in the various fields of speciality within which Samuelson operated.



Chapter 1. Introduction

Paul Samuelson was a scientist, MIT professor, and the pre-eminent economist of the twentieth century. An undergraduate at the University of Chicago from 1932 to 1935 and a graduate student at Harvard from 1935 to 1940, Samuelson described economic science during the 1930s as interesting, easy and (well suited to his talents) poised to become mathematical. His Harvard dissertation, published in 1947 as Foundations of Economic Analysis, revolutionized economic analysis. He described his career as bringing mathematics to every slice of the economics pie.
Richard G. Anderson

Samuelson’s Contribution to Economics: Methodology and Mathematics


Chapter 2. Paul Samuelson’s Ideology and Scientific Economics

Joseph Schumpeter defined ideology as a scientist’s prescientific vision from which scientific work proceeds. He argued that Keynes’s General Theory was the product of a long struggle to make his ideological vision of economic stagnation analytically operative. We apply Schumpeter’s definition of ideology to his student Paul Samuelson, whose vision we identify in two parts: Keynesian stagnation and mathematical economics. We identify similarities in how Keynes and Samuelson each viewed himself and his role in history. In addition, we see how in Keynes and Samuelson the modern Rationalist conception of science restricted the scope of economists’ contributions to public discourse.
J. Daniel Hammond

Chapter 3. Re-examining Samuelson’s Operationalist Methodology

During the heyday of discussion about Milton Friedman’s 1953 methodology paper, Samuelson’s operationalism was often discussed as the primary competitor to Friedman’s position. Although Friedman’s paper continues to be discussed—albeit at a steadily decreasing rate—Samuelson’s account of economic methodology has all but disappeared from the literature. This paper offers a re-examination of Samuelson’s account. Why a re-examination now? There are many reasons, but I will focus on just two. The first is that the historical research on Samuelson has exploded since his death in 2009, primarily because of the extensive archival material he left behind. The second is Samuelson’s revealed preference theory; it is methodologically relevant because Samuelson insisted it was an exemplar of his operationalist approach.
D. Wade Hands

Chapter 4. The Young Paul Samuelson: Mathematics as a Language, the Operational Attitude, and Systems in Equilibrium

In his Foundations of Economic Analysis, which was an extension of his dissertation defended in 1940 at Harvard University, the young Paul Samuelson argued that he was providing economics with new scientific foundations. In these texts, believing that “Mathematics is a Language,” Samuelson connected mathematics and economics while adopting an operational attitude and treating the individual and aggregate levels of the economy as systems in stable equilibrium. His work resonated with the work of preeminent Harvard figures of the 1930s, particularly the physicist Percy Bridgman’s operationalism and the physiologist Lawrence Henderson’s ideas about systems in equilibrium. However, the connection between Samuelson and these figures still remains opaque. In this chapter, it is noted that Samuelson wrote his dissertation and Foundations under the significant influence of his professor of mathematical economics at Harvard, Edwin Bidwell Wilson, who defined mathematics as a language. I argue that Wilson acted as a mediator between his Harvard colleagues and Samuelson.
Juan Carvajalino

Chapter 5. Paul Samuelson and My Intellectual Development

This chapter covers three topics: (1) the influence of Paul Samuelson on the author’s intellectual development when the author was an undergraduate before meeting Samuelson; (2) the influence of Samuelson when the author was a junior faculty member at MIT; and (3) exchanges between Samuelson and the author on the method of dynamic optimization.
Gregory C. Chow

Chapter 6. Some Correspondence with Paul Samuelson on Economic Theory: An Intimate Memoir

This memoir presents some extracts from the correspondence and conversations between Paul Samuelson and me about topics in economic theory over a period of fifty-three years. It is an informal intellectual biography, not a research paper. It is of interest because it presents previously unpublished comments that Samuelson made on major questions that arose in the course of the development of economic theory during his lifetime. His letters illuminate those questions with scientific analyses and enliven his treatment of them with frank expression of opinions about the work and personalities of many leading economists. The memoir also reveals the personal qualities that he had to an extraordinary degree: steadfastness of friendship, intellectual integrity, graciousness, receptivity, and generosity.
Donald A. Walker

Chapter 7. Some Correspondence with Paul Samuelson on the History of Economic Thought: An Intimate Memoir

This memoir provides information about Paul A. Samuelson’s ideas on the history of economic thought that is not to be found in published documents. That is done in two ways. First, the memoir presents pertinent extracts from correspondence between Samuelson and me, and from some of the notes I made of our telephone conversations. Samuelson’s communications are of interest because they have analytical content, are enriched by perceptive commentaries and interesting facts, and have a freshness, spontaneity, and frankness of expression that derive from the circumstance that they were created in the intimacy of discourse with a friend. Second, the memoir presents the list of Samuelson’s essays on the history of economic thought that he preferred, circa 2000–2003, to be reprinted in a dedicated volume, and some discussions related to the process of choosing those essays.
Donald A. Walker

Chapter 8. The Samuelson Revolution in Australia

Paul Samuelson’s classic textbook, Economics: An Introductory Analysis, had a major bearing in shaping the education of a generation of Australian economics students in the 1970s and beyond. However, in order to be the success that it was, it had to have a masterful adaption undertaken by two Australian economists. When the textbook was launched in 1970 it was, in itself, notable for being one of the first overseas social science texts to be adapted to local conditions. Its success preceded the arrival by Samuelson himself in Australia in 1973. This was at a time when visit by eminent economists to Australia was considered newsworthy. For the most part, Samuelson was given a rapturous reception, but his guest lecture at the University of Sydney on an ill-chosen subject merely fanned the flames of rebellion by students wanting an alternative to mainstream economics.
Alex Millmow

Samuelson’s Contribution to Economics: Microeconomics and Finance


Chapter 9. Samuelson’s Approach to Revealed Preference Theory: Some Recent Advances

Since Paul Samuelson introduced the theory of revealed preference, it has become one of the most important concepts in economics. This chapter surveys some recent contributions in the revealed preference literature. We depart from Afriat’s theorem, which provides the conditions for a data set to be consistent with the utility maximization hypothesis. We provide and motivate a new condition, which we call the Varian inequalities. The advantage of the Varian inequalities is that they can be formulated as a set of mixed integer linear inequalities, which are linear in the quantity and price data. We show how the Varian inequalities can be used to derive revealed preference tests for weak separability and show how they can be used to formulate tests of the collective household model. Finally, we discuss measurement errors in the observed data and measures of goodness-of-fit, power, and predictive success.
Thomas Demuynck, Per Hjertstrand

Chapter 10. Paul Samuelson and the Economics of Pass-Through and the Envelope Theorem

The revealed-preference proof of non-negative pass-through by a profit-maximizing firm is discussed and modestly extended. A revealed-preference proof of a “bounds” version of the envelope theorem is discussed. The relationship between the envelope theorem, pass-through, and total incidence of a cost increase (with and without perfect competition) is analyzed. Much of this is, or risks becoming, folk theorems, absent from graduate textbooks despite its basic nature.
Joseph Farrell

Chapter 11. Not a Behaviorist: Samuelson’s Contributions to Utility Theory in the Harvard Years, 1936–1940

In this chapter, I review the contributions to utility theory that Paul Samuelson made when he was a Ph.D. student at Harvard, from the first scientific papers he began writing in 1936 to the dissertation he submitted in November 1940. Based on this review, I make three points: (1) After exploring contrasting research paths during the years 1936–1937, Samuelson’s stance on utility analysis quickly stabilized and, from around mid-1938, he became an advocate of an ordinal utility approach to choice theory; (2) accordingly, the widespread image of the young Samuelson as a committed behaviorist who wanted to free economic analysis from the utility concept is misleading; and (3) the so-called Das Paul Samuelson Problem, that is, the question of whether Samuelson changed his mind on utility analysis between 1938 and 1948–1950, has either a negative answer or is ill-posed.
Ivan Moscati

Chapter 12. A Short History of the Bergson–Samuelson Social Welfare Function

The so-called Bergson–Samuelson social welfare function was first introduced in 1938 by Abram Bergson, and subsequently developed by Paul Samuelson in his 1947 Foundations of Economic Analysis. However, the very existence of the social welfare function was called into question by Arrow’s (1951) landmark impossibility theorem, which states that under a set of reasonable conditions, the social welfare function can be shown not to exist. Yet social welfare functions are today still widely used in a range of fields in order to formulate policy ends. It thus seems that the use of such functions has flourished independently of the theoretical debate about their existence. The objective of this chapter is to offer a short history of the social welfare function, from its origins in the late 1930s up to the present day.
Herrade Igersheim

Chapter 13. Climbing Mount Everest: Paul Samuelson on Financial Theory and Practice

Paul Samuelson regarded finance as the “Mount Everest” of economic pursuits. He proved that informationally efficient markets implied random price behavior and believed that very few investors could “beat the market.” Motivated by his study of the dismal performance of “managed money,” Samuelson was the first to advocate the creation of a low-cost stock index fund and his writings spurred Jack Bogle to create the S&P 500 Index Trust. His work on option theory brought him to the verge of the Black–Scholes formula, but the final equation eluded him. Samuelson warned investors that the Law of Large Numbers did not imply that investors with longer horizons should put a greater proportion of their portfolio in stocks but demonstrated that mean reversion of equity prices coupled with sufficient risk aversion would imply that strategy.
Jeremy J. Siegel

Chapter 14. Paul Samuelson: Three Key Contributions to Finance

This chapter explores three key contributions that Paul Samuelson made to the specialism of finance. The first is his demonstration that in well-informed and competitive speculative markets, asset prices will be random; Samuelson’s proof of this has been crucial to the development of the so-called efficient markets hypothesis. Secondly, his work on the pricing of options, and particularly the demonstration that the value of an option cannot be unbounded, set the foundations for the industry benchmark Black–Scholes pricing formula. Finally, Samuelson addressed key fallacies in portfolio theory, such as the view that long-horizon portfolios are riskless; his contributions in this area still resonate strongly today.
Ronald MacDonald

Samuelson’s Contribution to Economics: Macroeconomics, International Trade and Development


Chapter 15. Paul Samuelson and Macroeconomics

This chapter considers a restricted field to which Paul Samuelson contributed, across almost the whole of his astonishingly productive academic years: macroeconomics—more often considered as macrodynamics. The restriction is further confined to his pioneering and fundamental contribution to the multiplier-accelerator model of macrodynamic fluctuations. In this, he was influenced by his friend and mentor, Alvin Hansen—the American Keynesian—which led him to develop a distinct brand of Keynesianism. The Correspondence principle, linking comparative statics and the stability of dynamical systems, is the guiding light; maximization and equilibrium, including expectational and monetary macrodynamics, among other important macroeconomic factors, are ignored. It is also necessary to set aside the neoclassical synthesis and, thereby also the IS/LM mechanism, augmented by the Phillips curve. The emphasis, throughout, is also the classical logic that was used in formulating what Samuelson called meaningful theorems. The concluding section suggests how or what is the desired way one can extend the Samuelsonian framework.
K. Vela Vellupillai

Chapter 16. Keynesian Uncertainty: The Great Divide Between Joan Robinson and Paul Samuelson in Their Correspondence and Public Exchanges

Joan Robinson and Paul Samuelson found little to agree upon in a correspondence which began in 1946, shortly after the death of Keynes, and ended a year prior to Robinson’s death in 1983. One way to read the correspondence is to keep in mind that Keynesian uncertainty was central to Robinson’s understanding of how capitalist economies function. Samuelson, never impressed by Keynes’s handling of uncertainty, understood capital theory—if not capitalism—in terms of dynamic programming, with its perfect foresight entailments. This is evident throughout his letters to Robinson, although rarely acknowledged in a straightforward way, particularly during the period from 1971 until 1975 when their disagreements came to a head. On several occasions, Robinson despaired of making any progress in getting Samuelson to acknowledge the importance of her questions. Unfailingly polite to her, he granted only in a letter to Solow that, “She is on to a real problem…”.
Harvey Gram

Chapter 17. Paul Samuelson, Government, and Monetary Policy: Some Evidence from the Archives

Discussions about Paul Samuelson’s involvement in the US government usually centre on his relationship with John F. Kennedy, this beginning when Kennedy was a senator, candidate for president, president-elect and continuing when he became president. However, evidence from Samuelson’s personal papers demonstrates that he gave economic advice to various presidential candidates and presidents. A potted history of the economic advice Samuelson gave to the Democratic Party is presented in this chapter, delineating the approaches that he took in order to get his hands dirty in the world of public policymaking. This together with some of his views on monetary policy suggests a much wider and richer contribution than has been previously assumed.
Robert A. Cord

Chapter 18. Paul A. Samuelson and the Foundation of International Economics

The bell is still tolling for Samuelson’s works on trade theory. This chapter looks at some models he presented that are still relevant for global trade driven by communication and digital technologies. The models rest on a sound general equilibrium base, for which Samuelson used theoretical and operational perspectives. The models invoke free trade, which bequeaths potential gains for all players. In today’s world of increasing productivity for many underdeveloped economies, the Stolper–Samuelson theorem points to the idea that rich nations which lose comparative advantages may suffer lower wages and lower net gains from trade. An allied theorem relates to factor price equalization where competition in final products can cause convergence in factor prices. This chapter presents Samuelson’s fundamental contributions to international trade theory, including his contribution to the transfer problem, which constituted the main research programs in the last half-century or more in this field of economics, and are still the paradigms for future research.
Lall Ramrattan, Michael Szenberg

Chapter 19. Samuelson’s Contributions to Population Theory and Overlapping Generations in Economics

Paul Samuelson made a series of important contributions to population theory for humans and other species, evolutionary theory, and the theory of age-structured life cycles in economic equilibrium and growth. The work is highly abstract but much of it was intended to illuminate issues of compelling policy importance, such as declining fertility and population aging. While his work in population economics has been very influential, his work in population and evolution appears to have been largely overlooked, perhaps because he seldom published in demographic journals or went to population meetings. Here, I discuss his many contributions in all these areas, but give particular attention to demographic aspects of his famous work on overlapping generation models, social security systems, and population growth.
Ronald Lee

Chapter 20. Paul Samuelson’s Contributions to Public Economics

This chapter provides an impressionistic review of Paul Samuelson’s enduring contributions to the field of public economics. It focuses on his main foundational methods widely used in public finance and their important applications, elaborations, clarifications and caveats to his conclusions. The chapter discusses the pathbreaking use of mathematics to clarify assumptions and make testable predictions more precise, from constrained choice optimization models to revealed preference theory to the overlapping generations model to integrating microeconomic foundations into macroeconomics. It then focuses on his primary contributions to public economics: the theory of public goods. From the characteristics of the goods as non-rival and non-excludable to the free rider preference revelation problem to the summation of individual marginal valuations to derive the efficiency conditions to their interaction with the income distribution, it is all there in just three pages. We then look at the extensions and caveats it inspired. Finally, the chapter discusses Samuelson’s primary contribution to tax theory, his analysis of economic depreciation. The influence of his prolific publications, textbook, public intellectual writing and advising, and teaching on and by his numerous students who became important economists and policy makers, has been and continues to be profound. That places Samuelson high in the pantheon of great economists of the twentieth century and, indeed, in the history of economic thought, which, given his love of that subject, no doubt would have delighted him.
Michael J. Boskin

Chapter 21. Samuelson on Ricardo and on Technical Change

This chapter deals with Samuelson’s view of the role of technical change, in particular that contained in Ricardo’s chapter in the third edition of the Principles, “On Machinery”. Samuelson argued that Ricardo was right in his analysis. The author takes a different view by stressing the character of technical change involved, labour- or capital-saving, and other characteristics of technical change, implied or assumed.
Arnold Heertje

Chapter 22. Divergence and Convergence: Paul Samuelson on Economic Development

The theory of economic development was an exception to Paul Samuelson’s claim of being a “generalist” in economics. It was a hard subject to tackle analytically because of the intrinsic difficulty of some of the concepts involved, such as increasing returns and long-term economic evolution. Nevertheless, Samuelson was aware of the utmost practical relevance of the topic, and discussed at length, sometimes critically, the empirics of development and the theories and policies put forward by development economists, particularly in connection with market failures that could help to explain underdevelopment phenomena. Moreover, he paid more attention than most development economists to the Malthusian demographic dimension of poverty. On the other hand, development planners made use of Samuelson’s turnpike theorems of growth theory, and reacted, mostly critically, to his factor price equalization (FPE) theorem of international trade and its apparent conflict with income divergence between developed and underdeveloped economies.
Mauro Boianovsky


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