Paul Anthony Samuelson (1915-2009)

Life

Paul Anthony Samuelson was born in Gary, a steel town near Chicago, on 15 May 1915. His father ran a small pharmacy. During his childhood, Samuelson saw the plight of the workers labouring in the steel works without any welfare provision whatsoever.

Among Samuelson’s teachers at Harvard University were the economists Alvin Hansen, Wassily Leontief and Joseph Schumpeter, as well as the mathematician and physicist Edwin Bidwell Wilson. Abram Bergson, Lloyd Metzler and James Tobin were among his fellow students. Despite his brilliance, which was obvious to all, he found it difficult to pursue a career at Harvard University, an institution that, like all Ivy League universities at the time, was tainted by strong anti-Jewish prejudice (on this, see Samuelson 2002). He therefore decided to accept a position at the nearby Massachusetts Institute of Technology (MIT), a university to which he remained faith­ful until his death in 2009.

The publication of his Foundations soon established Samuelson as one of the leading mathematical economists of his generation (Samuelson 1947). Ralph Freeman, the chairman of his department at MIT, dispensed with some of Samuelson’s teaching duties after the war, requesting him to write a modern introductory textbook. This textbook, given the title Economics, was published in 1948 and very quickly became a bestseller and a model for the entire textbook literature in economics. On the one hand, the book is imbued with the new Keynesian spirit; on the other, there is a neoclassi­cal approach in modernized form, developed by Samuelson himself. Since the book dispenses with mathematical derivations and is written in an extremely skilful didactic manner, it very soon made known all over the world the idea of “neoclassical synthe­sis”, that is, the concept of integrating the Keynesian macroeconomic revolution into neoclassicism.

In the social sciences, as far as I can tell, this textbook is a unique experience: Samuelson, belonging to a younger generation, knew exactly how to change pro­foundly, and in a very short period of time, the broad effect of an entire field. Perhaps there was a renewed sense, following the Depression, of orthodox teaching absorbing Keynesian thought. However, the fact that this neoclassical synthesis was able to spread so smoothly is due in no small part to Samuelson’s textbook. Despite its accessibility, it avoided misleading simplifications, introducing students to economic thinking in such a convincing way as to show them just how all this could be useful to economic policy.

As mentioned before, Samuelson remained faithful to MIT, arguably making its Economics Department the leading department in the world, alongside his colleagues. One crucial reason for this was that he produced a string of scientific publications that developed, improved and even revolutionized the standard of knowledge in several branches of economics.

Two characteristics are central to Samuelson’s research. First, the rigorousness of his argumentation; and secondly, the embedding of specific results in a greater context. The combination of these two characteristics makes Samuelson distinguishable from most of his peers. There are certainly some economists, including important ones, who retain a sense of the greater picture, although most of them lack the rigorous argumentation based on the mathematical model. On the other hand, there are scores of economists who will develop and publish innumerable mathematical models, albeit without displaying any sense of the greater picture. Samuelson’s way of working also means he cannot be pigeonholed as either a “market disciple” or a “state disciple”. In his work, Samuelson is able to demonstrate in crystal-clear fashion what market processes and competition can do in different contexts; at the same time, however, he uses the same methods to point out the limits of the market principle - limits that call for the state to make adjustments. Perhaps, therefore, Samuelson may be regarded, more than any other economist, as a theorist of the “mixed economy”. The neoclassical synthesis between Keynes and a mod­ernized neoclassicism is only one example for this. Analogous examples can be found in his ground-breaking work on welfare economics, on international trade theory, on risk and financial economics or on the theory of public goods.

In this sense, he is quite different from his long-time rival Milton Friedman, the intellectual leader of the Chicago School and a fervent critic of state activity and of Keynesianism. Samuelson frequently accused Friedman of oversimplification.

Despite his huge public impact and his influence on economic policy, in particular that of the Democratic Party and its presidential candidates, Samuelson’s political influ­ence rests mainly on his teaching and research. Part of this is due to the broad effect of his textbook that was emulated in one form or another by those who came after him. A much larger part is due to his teaching, and that of his colleagues at the MIT Economics Department. There, graduate and doctoral students learned how to combine rigorous theory with empirical relevance in economics. They were introduced to an incentive structure that proved particularly conducive to research. Samuelson spread a spirit in the department, so that all graduate students could expect their own original research results to be appreciated and to have a positive effect on furthering their careers. The MIT would become able to choose the cream of the crop for its own graduate school, but even for young people who are above average it is certainly a stroke of good fortune to become involved, on the one hand, in the strict discipline of rigorous theoretical derivations and, on the other, to experience a stimulating discussion environment in which new ideas are appreciated and not stifled.

The spirit that reigned at the MIT Economics Department may be illustrated by a Samuelson anecdote, of which there are many. This anecdote was told by Cary Brown and Robert Solow in their preface to a Festschrift for Samuelson dating back to 1983 (Brown and Solow 1983b). In the mid-1950s, Seymour Harris, who was then chairman of the Harvard Economics Department, had organized a nationwide survey among the economics departments in order to establish what people thought about the quality of their departments. Harvard ended up in first place, while MIT scored a place in the upper third of the list.

In the 1950s and 1960s, the Economics Lunch Table at the MIT Faculty Club (located in the same building as the Economics Department) was renowned. Every day, the subject and its current condition would be debated at a big round table, without a for­mally elected chair, albeit under Samuelson’s informal guidance. Subjects for debates would include current controversies within economics or in the economic policy of the day, questions of methodology or content, the scene in the United States and the rest of the world, with a particularly critical glance towards England (especially Cambridge) and the famous neighbour, Harvard, and the intellectual opposition in Chicago. Samuelson’s encyclopaedic knowledge, his capacity to follow other people’s thought processes, his unsurpassed memory for anecdotes and stories, his quick-wittedness and sense of humour that bristled with self-mockery all made these intellectual forays at lunchtime extremely gratifying. At the same time, they were also intensive courses in which one could learn - by speed-listening, as it were - outside of the dry old system. This laughing lunch table, lasting about an hour or an hour and a half, was very close to Humboldt’s ideal for university life, at least with regard to the field of economics (on this see Brown and Solow 1983: xif.).

Thus, the MIT School produced a large number of important economists and advisers to governments and international organizations. Today’s apparent obsession to evalu­ate everything means that we also look at the number of Nobel laureates connected with a particular institution. Well, there is no doubt that among the more recent Sveriges Riksbank Prizes in Economic Sciences in Memory of Alfred Nobel, the share of MIT PhDs, and professors is larger than at any other school.

Work

The Foundations

Shortly after World War II, in 1947, Samuelson published his Foundations. The work would become the most important reference, in the years following publication, for any research in theoretical economics. It was certainly not the first book on mathematical economics, but it is no exaggeration to say that it revolutionized the way in which eco­nomic theory was conducted. It was this book that laid the foundation for the axiomatic method that became the dominant method of economic theory during the following decades and to this day. This book is a classic. It became a model for how an economic theorist should conduct research. Nowadays, it is generally referred to as Foundations, abbreviated in the same way that the titles of Adam Smith’s Wealth of Nations and Keynes’ General Theory are shortened.

The epigraph Samuelson used for Foundations is a quote from the American physicist Willard Gibbs, “Mathematics is a language”, and there is no doubt that Samuelson saw the increasing reliance of theoretical physics on mathematics and wished to apply this model to economics. The first part of the book takes up 70 per cent of its entire volume. It is dedicated to themes that the field of economics has since then been referring to as comparative statics. The second, shorter part deals with themes related to dynamics. However, it is primarily the first part that forms the basis for the way in which economic theory, particularly microeconomics, develops models.

Two relatively abstract terms are central to the first part of Foundations: maximization and equilibrium. Of course, neither term was new to economic theorists. Yet, they were primarily applied in concrete contexts; the field had not yet recognized what the various cases in which they were used had in common. Samuelson brought the theories of utility maximization and profit maximization or cost minimization together to show the formal characteristics they have in common, namely, those resulting from the principle of maxi­mization itself. He views the term equilibrium in a similar vein, namely, as a solution to a system of equations, only to discover then what statements can be derived at the abstract level about the relation between the exogenously given parameters (describing, for instance, the available production technology) and the values of the variables, deter­mined endogenously in equilibrium (for example, the quantities produced).

Samuelson understands his theory as empirically refutable: by deriving certain conclu­sions from the theoretical approach, for example, the hypothesis of utility maximization, on the relation between variables and parameters, or on different variables among each other, these results may be compared to empirical findings. If these contradict the theo­retical information, then the basic hypotheses have not passed the empirical test. From this point of view, it was also wrong to refer to this axiomatic approach as “modelling Platonism”, as was done later.

One of the central results of Samuelson’s approach is a proposition he himself refers to as the “Le Chatelier principle”, thereby indicating the close proximity to findings in theoretical physics. In the mathematical model, this Le Chatelier principle proves an insight that had already been intuitively grasped by economic theorists since the time of Alfred Marshall. At the same time, this insight is substantially generalized, so that this already known insight turns out to be a special case of a general principle. Since Alfred Marshall’s studies, the following empirically rather robust statement has been known: reaction elasticities are higher in the long term than in the short term. An example for this lies in the price elasticity of demand: in case of a change in price, the demanded amount declines less dramatically in the short term than in the long term. The Samuelson-Le Chatelier principle now says the following: we assume a maximiza­tion task in several variables with additional constraints. We examine how the optimal values react to parameter changes. We look at one point that maximizes the target with and without a particular additional constraint. Then, in the case when the constraint ceases to apply, reaction elasticity to a parameter change is higher than when the con­straint applies. This mathematical statement, which can also be generalized, has multiple applications in economics. One of these is the relation of the long-term to the short-term marginal cost curve. Similar results are reached in consumer theory. The fact that it makes sense, in time of war, to ration food consumption - without deducing from this that the same makes sense in normal times - can also be ascribed to the insight that adap­tive reactions require time. Samuelson’s Le Chatelier principle provides these intuitions with a general structural theory that can be used as a basis for all economic contexts. On the Samuelson-Le Chatelier principle, see Milgrom (2006). On the principle of maximization or minimization in economics and physics, see Samuelson’s Nobel lecture (Samuelson 1971a).

There is not enough room here to analyse the individual chapters of Samuelson’s Foundations in depth. I shall highlight merely one further chapter, on “welfare economics”. On the one hand, it is a masterpiece of “Dogmengeschichte” (history of thought) from the beginnings of this field with Bentham and Adam Smith up to the current state of knowledge before Samuelson himself contributed his work. At the same time, Samuelson’s work successfully brings a much-needed clarity to an area that had hitherto fallen victim to a host of misunderstandings. The “social welfare function” he develops here is the point of departure of a continued development and application of welfare economics in the post-war world. Even today, it remains the theoretical founda­tion for the efficiency criterion, which is almost universally used in applied economics, be it in a cost-benefit analysis or in modern industrial economics. We should, however, not fail to mention that this theoretical foundation is not very solid. The limits to a “new welfare economics” that wants to do without an interpersonal benefit comparison were quite clearly outlined by Samuelson. In practice, they are mostly forgotten nowadays, or even consciously ignored. One of Samuelson’s important later contributions to welfare economics is Samuelson (1956).

In the following, I discuss selectively a few of Samuelson’s contributions, published mainly in scholarly journals over the course of several decades.

Revealed preference

Even before World War II, Samuelson developed the seminal idea of “revealed prefer­ence”. In economic theory, we take the axiom as given that people act rationally in the sense that the actions they select orient themselves along the principle of achieving as far as possible most of the goals they have set for themselves. Then, however, it should be possible in principle to draw conclusions from individuals’ observed actions to their goals or preferences. Samuelson and later Houthakker were able to show that complete knowledge of an individual’s demand curve allows us to unlock that individual’s com­plete preference order if a particular rationality axiom, the strong axiom of revealed preference, can be assumed.

In a similar vein to the Samuelson-Le Chatelier principle, the Samuelson-Houthakker theory of revealed preference confirms a long-existing intuition: liberal social philosophy always knew that a society of free human beings can only remain stable if the conse­quences of a citizen’s actions, resulting from his or her own free will, are ascribed to a substantial degree to that individual. Let us call this the principle of responsibility. Now, what exactly does this principle mean? What is the exact content of the term “private autonomy”? Even today, we have no clear answer to this yet. However, in its axioma- tization undertaken by Samuelson and continued by others, the revealed preference principle is the beginning of the answer: the consequences of his or her actions may be attributed to the acting individual, as an expression of the individual’s preferences, which are assumed to remain consistent; preferences thus deduced can serve as a benchmark for benefit and cost of a public investment project or changes to legislation or a particular external trade policy (see Samuelson 1938, 1948a; Houthakker 1950).

The concept of revealed preference has not been without criticism from within the field. Consider Hayek’s fundamental critique of the “constructivism” of all welfare- economic approaches, as criticism “from the right”, as it were (Hayek 1974); or, on the “left”, Amartya Sen’s relativization of the idea in the context of his reference to the ori­entation of behaviour along norms that limit purely preference-oriented decisions (Sen 1977). Revealed preference nonetheless remains an innovation of theoretical thought on the possibilities of the coexistence of free citizens. At its core, it remains indispensable to a modern society.

On Marx

Only a handful of great researchers in economics have studied intensively the work of their predecessors. Among these we must certainly count George Stigler. However, it is perhaps Samuelson who can lay claim to have tried, more than anyone else, to understand and honour his predecessors. This is expressed by the string of names that can be found in his work, referring to certain earlier findings and their advancement in the field. Almost every work of Samuelson’s is imbued with references to the achieve­ments of earlier scholars; and perhaps some readers of Samuelson’s works have only truly appreciated the importance of certain earlier scholars after reading Samuelson. Without Samuelson’s influence, I for one would never have grasped the significance of Knut Wicksell or Alfred Marshall.

Apart from the references to heroes of the past, Samuelson also dealt extensively with theories of the past. Such articles were very often written with the express purpose of engaging in “Dogmengeschichte” and concern, for instance, such figures as David Ricardo and Karl Marx. The following paragraphs focus only on Karl Marx.

Among sensible people, the significance of Karl Marx as a social theorist, an econo­mist, a philosopher and a person who influenced the course of mankind like barely anyone else is undisputed. However, his works on economic theory (in the sense of an understanding of economic theory as developed by “bourgeois” economics) have always been controversial. One important early critic of Karl Marx’s theoretical approach was Eugen von Bohm-Bawerk. Over the course of time, there have been numerous debates between Marxist theorists and those stemming from the “bourgeois” camp.

In an article he published in 1957, Samuelson developed a new analytical set of tools, particularly the wage-interest curve, in order to conclude logically that three different statements made by Marx in his work are contradictory. The statements in question are (1) in capitalism, there is constant technical progress (the Marxist production of relative surplus value); (2) in capitalism, the real wage does not rise, but instead always remains near the margin of subsistence; and (3) in the long term, the profit rate falls in capitalism (Samuelson 1957). Technical progress means that, as Marx himself stressed, the “degree of exploitation” and the profit rate rise. Thus, it is impossible for the real wage to remain stagnant, or even fall, and for the profit rate to fall at the same time.

Since each of these three statements are indispensable for a complete analysis of capitalism in Marxist theory, Samuelson’s proof of their inconsistency constitutes a blow to the Marxist worldview. It was this essay by Samuelson that so concisely managed to condense the contradictory nature of the Marxist theoretical approach. I consider this essay one of the high points of the debate between traditional bourgeois economics and Marxism.

When the essay appeared in 1957, Marxism had not yet experienced its renaissance in the intellectual debate. In the western world, this only happened in the 1960s in particu­lar. That probably prompted Samuelson to engage with Marxism once again at a later stage, in particular in the context of the famous transformation problem and, in the same context, the study of the labour theory of value. These further essays also demonstrate Samuelson’s willingness to deal in depth with Marx’s extensive “sociological” analyses (see Samuelson 1971b).

International trade theory

Samuelson contributed to international trade theory for seven decades. Not long ago, he published an essay that was subject to much public debate; however, his first analytical approaches to international trade theory date back to the 1930s. In the following, I wish merely to refer to two of these contributions, one very early and another very recent. It can be stated quite generally that the theory of foreign trade was one of Samuelson’s favourite fields. For him, it was particularly fertile ground, enabling him to approach the more abstract theory of welfare economics and thereby influencing his own welfare- economic way of thinking.

The best-known work is probably his joint work with Wolfgang Stolper, which was published in 1941 under the heading “Protection and real wages” (Samuelson and Stolper 1941). Using analytical methods that were fairly new at the time, the authors show in this article that certain perceptions on the effect of foreign trade on wage dis­tribution were not correct. They use a two-country model in which there are two goods and two production factors (for example, labour and capital). The production functions exhibit constant returns to scale and - apart from one proportionality factor - are the same for both countries. Factor inputs are different for the two goods. The two countries differ in terms of their domestic supply of the two production factors. With these hypoth­eses, it is possible to show that, after a transition from a state without external trade to a regime of free trade, real wages of that production factor fall which is scarcer at home than abroad. Thus, despite the overall economy profiting from the introduction of free trade, the production factor that is scarcer at home than abroad suffers.

The Samuelson-Stolper theorem became a milestone in the advancement of foreign trade theory. It showed that more care had to be taken when deriving the advantages of a system of free trade, as most economists do, than had traditionally been the case. Incidentally, Samuelson never used this theorem to defect to the protectionist camp. The specific assumptions of the model are not meant to mirror reality, merely serving instead to demonstrate that distribution effects of foreign trade play a significant role. At the same time, they can also serve to understand which groups in a country support protectionism.

It is worth keeping in mind that Samuelson attracted much attention with another article he wrote on international trade, aged 89 (Samuelson 2004). This article appeared at the height of the controversial discussion on globalization, in 2004. Samuelson was then seen by many media as a critic of free international trade. However, this is not correct. What Samuelson was absolutely right to note was that the advantages of inter­national trade, for example, between two countries such as the United States and China, can diminish over time if the production technologies at the disposal of both countries gradually reach the same level. This is obviously the case, as China’s productivity in industrial production is making huge progress and, in this sense, is approaching the level of the United States. However, it is quite natural for the advantage of international trade - which rests on the effect of comparative advantage - to decline over time, if this effect can be traced back to the difference in the technologies at the disposal of both countries. Put simply, the advantage of cheap textiles from China diminishes for the American consumer if wages rise in China. Samuelson’s entire contribution to interna­tional trade theory is well appreciated by Jones (1983).

Public-goods theory

As in so many other cases, Samuelson was just as adept in public-goods theory at formulating a problem as clearly as possible. The renowned public-finance scholar Richard Musgrave wrote in a Festschrift for Samuelson in 1983: “The modern theory of public goods may be dated from June 1954, when Samuelson’s ‘Pure theory of public expenditures’ appeared. Never have three pages had so great an impact on the theory of public finance” (Musgrave 1983: 139-56).

In these three pages, Samuelson develops the mathematical structure of the optimal provision of a public good; this structure made its way into all public-finance and eco­nomics textbooks that followed. Even today, it remains the reference point for innumer­able articles on public-goods theory. Samuelson also demonstrates here why the invisible hand of the market fails in providing public goods (Samuelson 1954).

The overlapping generations (OLG) model

In 1958, Samuelson published the essay entitled “An exact consumption-loan model of interest with or without the social contrivance of money” (Samuelson 1958). In this article he develops a model in which it is possible, without physically creating capital, to optimize inter-temporal consumer decisions. The “trick” here is the introduction of a model in which a new generation emerges in each period. Each generation lives for three periods, each individual working in the first two of these periods, albeit wishing to consume in all three periods. Samuelson now shows how a quasi-credit system makes saving for the third period individually possible without the economy requiring physi­cal capital. Different institutional arrangements are examined, and it is demonstrated that they influence the result. The fundamental insight, however, is that the process of saving, conducted by one generation, can be synchronized with the process of dissaving, conducted by the other generation. This allows every generation to substitute and opti­mize inter-temporally, even though an inter-temporal substitution is not possible in the economy as a whole. On Samuelson’s model from today’s perspective, see Solow (2006) and Kotlikoff (2006).

Perhaps the true significance of this work of Samuelson’s lies not so much in his answering the specific question that had initially been his reason for developing the OLG model. Rather, I believe that the idea of the model as such is the truly seminal part. It took some time before economic theory realized the true potential of this OLG concept. Only in the late 1970s, and then increasingly in the 1980s and 1990s and up until today, have innumerable works using that idea been written.

Risk and capital-market theory

In his later years, Samuelson dealt intensively with the stochastics of markets that redistribute risks, that is, with the financial markets. We cannot go into the details here. However, just as in welfare economics, where he warned of over-simplistic recipes - such as the term consumer surplus - he also warned of simplifications here, such as the idea of maximizing the expected value of a logarithm of a portfolio in a multi-period model being an investment strategy that should be recommended at all times. He is also a pioneer of the option pricing theory, which led to the famous Black-Scholes-Merton formula in the early 1970s. The tempestuous growth of the markets for financial deriva­tives goes back to the existence of this formula. Samuelson devoted intensive and math­ematically highly complex work to the “efficient market hypothesis” in its various guises. Samuelson is one of the fathers, if not the father, of modern finance as an academic field (see Samuelson 1965a, 1965b, 1971c). An excellent appraisal of Samuelson’s contribu­tions to this prospering field was written by one of his students, Sveriges Riksbank Prize laureate Robert Merton (2006).

Further contributions

It is impossible to sketch Samuelson’s extensive scientific research work here in its entirety. Contributions to the following further fields are therefore merely mentioned: stability theory of market processes, induced technical progress, neoclassical capital theory, in particular his part in the famous Cambridge-Cambridge controversy, the non-substitution theorem, the turnpike theorem, consumer and utility theory, theory of index numbers, the relation of linear programming and economic theory, multiplier and acceleration theory, Say’s law, fiscal policy, the theory of money, methodology, in particular on the role of mathematics in economics, population theory and mathematical models of biology.

Impact

Every analysis of impact or effect is a search for causes. With innovations in economic or scientific areas, there is always the difficulty of not knowing whether the concrete creator made something that might have been created by others at a later stage, had the creator not got there first. In a sense, thus, the attribution of discoveries to a single discoverer - as has been the routine in the history of science - overestimates somewhat that single person’s significance for the progress of science. On the other hand, the indirect effect of the eminent researcher is often underestimated when his or her successes are depicted. This indirect effect lies in the fact that later research results, obtained by later research­ers, could not have been achieved had it not been for the earlier researcher achieving the earlier results.

Like barely anyone else, Samuelson always explicitly acknowledged the previous work of others who either made his own research results possible or else merely kindled in him an interest in a problem. If his successors in the field - in other words, virtually every economist working since World War II - all documented their debt to earlier sci­entists, as Samuelson did, then it would become instantaneously obvious to all just how immense the indirect effect of Samuelson’s output is. We may surmise that it is much larger than any potential downgrading of his significance or stature, which may occur if we consider that others could have made the same discoveries later. Perhaps that is a characteristic of the truly great in a field; that their overall effect is underestimated if their direct research results, first and foremost, are attributed to them. In that sense, Samuelson is a truly great scientist. On the other hand, the significance of performances by lesser men and women is overrated if we attribute their direct research results to them and forget that most of what they have been researching would most likely have been researched by others, albeit later, even if they had not done their work. Thus, there is a kind of “re-distribution” from the top to the bottom, if we measure the importance of a researcher by the number of works published, as is commonly done nowadays in the ubiquitous evaluation campaigns.

Carl Christian von Weizsacker

See also:

Kenneth Joseph Arrow (I); Abram Bergson [Abram Burk] (I); Growth (III); John Richard Hicks (I); Income distribution (III); International trade (III); John Maynard Keynes (I); Keynesianism (II); Macroeconomics (III); Public economics (III); Frank Plumpton Ramsey (I); David Ricardo (I); Adam Smith (I); Robert Merton Solow (I); Piero Sraffa (I); Welfare economics (III).

References and further reading

Brown, E.C. and R.M. Solow (eds) (1983a), Paul Samuelson and Modern Economic Theory, New York: McGraw Hill.

Brown, E.C. and R.M. Solow (1983b), ‘Preface’, in E.C. Brown and R.M. Solow (eds), Paul Samuelson and Modern Economic Theory, New York: McGraw Hill, pp. ix-xiii.

Hayek, F.A. von (1974), ‘The pretence of knowledge’, Nobel Lecture, 11 December, Stockholm. Houthakker, H.S. (1950), ‘Revealed preference and the utility function’, Economica, 17 (66), 159-74.

Jones, R.W. (1983), ‘International trade theory’, in E.C. Brown and R.M. Solow (eds), Paul Samuelson and Modern Economic Theory, New York: McGraw Hill, pp. 69-103.

Kotlikoff, L.J. (2006), ‘Paul Samuelson’s amazing intergenerational transfer’, in M. Szenberg, L. Ramrattan and A. Gottesman (eds), Samuelsonian Economics and the Twenty-First Century, Oxford, Oxford University Press, pp. 42-53.

Merton, R.C. (2006), ‘Paul Samuelson and financial economics’, in M. Szenberg, L. Ramrattan and A. Gottesman (eds), Samuelsonian Economics and the Twenty-First Century, Oxford, Oxford University Press, pp. 262-300.

Milgrom, P. (2006), ‘Multipliers and the Le Chatelier principle’, in M. Szenberg, L. Ramrattan and A. Gottesman (eds), Samuelsonian Economics and the Twenty-First Century, Oxford, Oxford University Press, pp. 303-10.

Musgrave, R.A. (1983), ‘Public goods’, in E.C. Brown and R.M. Solow (eds), Paul Samuelson and Modern Economic Theory, New York: McGraw Hill, pp. 139-56.

Samuelson, P.A. (1938), ‘A note on the pure theory of consumer behaviour’, Economica, 5 (17), 61-71, adden­dum 353-4; also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 1, ed. J.E. Stiglitz, Cambridge, MA: MIT Press, paper no. 1.

Samuelson, P.A. (1947), Foundations of Economic Analysis, Cambridge, MA: Harvard University Press, enlarged edn 1983.

Samuelson, P.A. (1948a), ‘Consumption theory in terms of revealed preference’, Economica, 15 (36), 243-53, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 1, ed. J.E. Stiglitz, Cambridge, MA: MIT Press, paper no. 9.

Samuelson, P.A. (1948b), Economics, New York: McGraw-Hill, and P.A. Samuelson and W. Nordhaus (2004), Economics, 18th edn, New York: McGraw Hill.

Samuelson, P.A. (1954), ‘The pure theory of public expenditure’, Review of Economics and Statistics, 36 (4), 387-9, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 2, ed. J.E. Stiglitz, Cambridge, MA: MIT Press, paper no. 92.

Samuelson, P.A. (1956), ‘Social indifference curves’, Quarterly Journal of Economics, 70 (1), 1-22, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 2, ed. J.E. Stiglitz, Cambridge, MA: MIT Press, paper no. 78.

Samuelson, P.A. (1957), ‘Wages and interest: a modern dissection of Marxian economic models’, American Economic Review, 47 (December), 884 912, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 1, ed. J.E. Stiglitz, Cambridge, MA: MIT Press, paper no. 29.

Samuelson, P.A. (1958), ‘An exact consumption loan model of interest with or without the social contrivance of money’, Journal of Political Economy, 66 (6), 467-82, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 1, ed. J.E. Stiglitz, Cambridge, MA: MIT Press, paper no. 21.

Samuelson, P.A. (1965a), ‘Proof that properly anticipated prices fluctuate randomly’, Industrial Management Review, 6 (2), 41-9, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 3, ed. R.C. Merton, Cambridge, MA: MIT Press, paper no. 198.

Samuelson, P.A. (1965b), ‘Rational theory of warrant pricing’, Industrial Management Review, 6 (2), 13-39, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 3, ed. R.C. Merton, Cambridge, MA: MIT Press, paper no. 199.

Samuelson, P.A. (1966-86), The Collected Scientific Papers of Paul A. Samuelson, 5 vols, vols 1-2 (1966) ed.

J. E. Stiglitz, vol. 3 (1972) ed. R.C. Merton, vol. 4 (1977) eds H. Nagatani and K. Crowley, vol. 5 (1986) ed.

K. Crowley, Cambridge, MA: MIT Press.

Samuelson, P.A. (1971a), ‘Maximum principles in analytical economics’, in Les Prix Nobel en 1970, Stockholm: Nobel Foundation, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 3, ed. R.C. Merton, Cambridge, MA: MIT Press, paper no. 130.

Samuelson, P.A. (1971b), ‘Understanding the Marxian notion of exploitation: a summary of the so-called transformation problem between Marxian values and competitive prices’, Journal of Economic Literature, 9 (2), 399-431 also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 3, ed. R.C. Merton, Cambridge, MA: MIT Press, paper no. 153.

Samuelson, P.A. (1971c), ‘The “fallacy” of maximizing the geometric mean in long sequences of investing or gambling’, Proceedings of the National Academy of Sciences, 68 (10), 2493-6, also in P.A. Samuelson (1966), Collected Scientific Papers, vol. 3, ed. R.C. Merton, Cambridge, MA: MIT Press, paper no. 207.

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