Cheryl Misak’s Ramsey: Notes on his association with Harrod, Dobb, and Sraffa

Frank Ramsey was in Cambridge at the same time as John Maynard Keynes, Arthur Pigou, and Piero Sraffa, some of the most influential economists of the twentieth century. Ramsey died on 19th’January 1930, six years before The General Theory of Employment, Interest and Money’(1936), ten years after The Economics of Welfare(1920), and around the same time as the central propositions in Production of Commodities by Means of Commodities’(PCMC) was worked out. While an earlier blog post had examined Ramsey’s views on the rate of interest, the present one narrates his intellectual association with Maurice Dobb, Roy Harrod, and Sraffa, and a forthcoming one will focus on his intellectual association with Pigou and Keynes. The present and future posts are primarily based on Cheryl Misak’s new biography of Ramsey (2020, Oxford University Press). This post supplements the observations found in Misak’s Ramseywith those found in the books on Harrod and Sraffa published as part of the Palgrave Macmillan ‘Great Thinkers in Economics’ series by Esteban P’rez Caldentey (2019) and Alessandro Roncaglia (2009) respectively and the book on Dobb by Timothy Shenk (2013) published as part of the ‘Palgrave Studies in the History of Economic Thought’ series.

HARROD

While Harrod today is probably most well-known for his contributions to growth theory, he made important contributions to the fields of trade cycle theory, imperfect competition, and international economics. While there are 14 references to Harrod in Misak’s Ramsey, there are only eight references to Ramsey in Caldentey’s Harrod’(2019). [If there are two or more mentions of Harrod in a single page, I treat that as one reference.]

Ramsey and Harrod were friends (p. xxxi). Ramsey had known him ‘since 1922, when Harrod spent part of the year at King’s. Frank had taken Harrod under his wing then, introducing him to [G. E.] Moore and others’ (p. 195). After Ramsey was elected a fellow of King’s College, Cambridge in 1924, he renewed his friendship with Harrod, ‘a young left-leaning economics don at Oxford ‘ and they travelled between Oxford and Cambridge for intellectually rich weekends’ (p. 195). Caldentey mentions Harrod experiencing ”tremendous stimuli” after meeting Ramsey in Cambridge as opposed to his ‘frustrating Oxford experience’ (p. 10).

Although Harrod’s paper on the concept of marginal revenue curve was eventually published in the Economic Journal’as ‘Notes on Supply‘ (1930), on Ramsey’s advice, its editor, Keynes, had initially rejected the article in 1928 and had asked for revisions on the treatment of cartels (p. 305). In the meantime, according to Harrod, others had ‘discovered’ his concept and therefore he failed to receive credit for inventing it. Caldentey informs us that Harrod’s initial paper submitted in 1928 was titled ‘Notes on Monopoly and Quasi-competition’ wherein ‘he derived the increment of aggregate demand curve which was later re-baptized, the marginal revenue curve by Joan Robinson’ (p. 18). Moreover, Caldentey notes that in the foreword to the first edition ofThe Economics of Imperfect Competition’(1933), Robinson acknowledges the following individuals for teaching her about the marginal revenue curve: C. H. P. Gifford, P. S. Sloan, and T. O. Yntema (p. 101, n. 30). Also see Caldentey (pp. 18-19, 100-1) for a recounting of the refereeing episode between Ramsey and Harrod, which also makes reference to the three-volume work, The Collected Interwar Papers and Correspondence of Roy Harrod’published by Edward Elgar in 2003 under the editorship of Daniele Besomi.

DOBB

Dobb’s contributions to Marxist economics are well established. I was introduced to his work during my Master’s in Economics at the University of Hyderabad where we read selected parts from Theories of Value and Distribution Since Adam Smith: Ideology and Economic Theory’(1973). His collaboration with Sraffa in editing and producing The Works and Correspondence of David Ricardo’has also been noteworthy. In Shenk’s Dobb, surprisingly, there is not even a single reference to Ramsey while there are 21 references to Dobb in Misak’s Ramsey.

Dobb was Ramsey’s friend from their undergraduate days (1920-3) at Cambridge (p. 94). They had started their degrees at the same time (p. 79); Ramsey enrolled for mathematics at Trinity College and Dobb for economics at Pembroke College. And during this time, ‘Dobb had considerable influence on Ramsey, both by engaging with him about the kind of socialism that would be best, and by introducing him to workers’ meetings’ (p. 299). While Ramsey was finishing his secondary education at Winchester in 1920, in addition to reading the economics books by Alfred Marshall and Keynes, he also read works by Karl Marx and V. I. Lenin (p. 47). However, according to Misak, it isn’t clear how much they associated with each other after completing their undergraduate studies (p. 87).

In his 1925 doctoral thesis, Dobb tried to bring Marx and Marshall together (p. 300). Shenk points out that Dobb had been trying to synthesize Marx and Marshall even before he started his PhD at the London School of Economics (LSE): ‘Dobb, too, sought to integrate marginalism with classical political economy, but with Marx substituting for Ricardo as the standard-bearer for political economy. ‘ In Dobb’s vision, Marx appears as a theorist of the social, Marshall of the economic’ (p. 36). Dobb’s PhD thesis was published in 1925 as Capitalist Enterprise and Social Progress, and Shenk provides us with its outline: ‘Dobb dedicated the first section to economic theory, the second to economic history, and the third to evaluating contemporary economic practices from the perspective developed over the course of the book’ (p. 38). Since Ramsey ‘was considered (and considered himself) a socialist’ (p. 301), Misak argues that Ramsey’s use of utility theory in his paper on optimal saving needs to be seen in the light of the synthesis Dobb had attempted between Marxism and marginalism (p. 302).

Ramsey’s view of the use of mathematics in economics was similar in spirit to that of Dobb (and Keynes): ‘Like Dobb, he thought that one ignores mathematics at one’s peril, for the mathematics has to be right in order for progress in the real world to be made. And some real-world issues are going to be solvable by doing the maths’witness Ramsey’s response to the Douglas Proposals. But he did not think that the mathematician could step in and solve all problems. He agreed with Keynes that we mustn’t be so taken with the precision of mathematics that we erase the outlines of the very thing we are examining. As Ramsey so often put it, one mustn’t be woolly, but one mustn’t be scholastic either’ (p. 326).

SRAFFA

Sraffa has made significant contributions to price theory and capital theory and deserves high praise for his editorship of the collected works and correspondence of Ricardo. I have written on Sraffa earlier.’ While there are only two references to Ramsey in Roncaglia’s Sraffa, there are 18 references to Sraffa in Misak’s Ramsey. Given this scant attention to Ramsey in Roncaglia’s Sraffa, I make use of Heinz Kurz and Neri Salvadori’s essay ‘Sraffa and the Mathematicians: Frank Ramsey and Alister Watson’ first published in 2000 in Piero Sraffa’s Political Economy: A Centenary Estimate, a volume edited by Terenzio Cozzi and Roberto Marchionatti (as republished in Classical Economics and Modern Theory: Studies in Long-Period Analysis, an edited volume by Kurz and Salvadori in 2003).

As Sraffa writes in the preface to his 1960 classic, ‘the central propositions had taken shape in the late 1920’s’ (p. vi). In the following paragraphs, he expresses his gratitude to Ramsey (along with Alister Watson) for ‘invaluable mathematical help’at different periods’, and his greatest debt is reserved for A. S. Besicovitch. Kurz and Salvadori examine Sraffa’s diaries to identify the number of his meetings with Ramsey; according to the dairy entries, they met twice in 1928 (28 June and 11 November) and thrice in 1929 (10 May, 30 May, and 29 November) (p. 190).

The main outcome of their first meeting is capably captured by the following excerpt from Kurz and Salvadori: ‘At first Sraffa appears not to have explicitly distinguished between the quantity and the price or value of a commodity, a fact to which Ramsey immediately seems to have objected. Sraffa then appears to have introduced the distinction during the conversation with Ramsey’. Ramsey then reformulated the system first by putting the system of homogeneous linear equations in its canonical form, then by setting the determinant of coefficients equal to zero in order to get a non-trivial solution’ (p. 197). The key aspects of this meeting are not as ably captured in Misak and it is also incorrectly stated that Sraffa’s famous work related to ‘the determination of prices and’outputs’ (p. 305; emphasis added) whereas the size and composition of output is a given in PCMC.

Ramsey died in the middle of writing his book on truth and probability. Misak draws attention to the fact that after his death the philosopher R. B. Braithwaite published some of Ramsey’s essays in 1931 under the title The Foundations of Mathematics and Other Logical Essays’(p. 273). According to Misak, John von Neumann and Oskar Morgenstern had reached very similar conclusions in their 1944 Theory of Games and Economic Behaviour’(p. 274). And Misak further notes that, the similarity was so striking that John Hicks went to the extent of writing to Sraffa on 3rd’September 1960 asking if Ramsey’s ideas were transmitted to von Neumann through him (and his ‘mathematical friends’) but Sraffa didn’t reply (p. 274; although a draft of Sraffa’s response is available, it is not clear whether he actually sent it to Hicks). However, after consulting the letter (available here), it is clear that Hicks is actually asking Sraffa how von Neumann arrived at a similar theoretical outlook as Sraffa; and it is not about the similarities between Ramsey and von Neumann as Misak claims.

ON VALUE THEORY

This blog post ends with some critical observations on Ramsey’s engagement with value theory. According to Misak, Ramsey ‘blended neo-classical economics and socialism’ (p. 303). Despite his ‘scepticism about the utility theory of value’, as Misak notes, ‘his two famous papers were written in the neo-classical framework of individuals maximizing utility’ (p. 302). The two important pieces of evidence Misak provides for the former are given in the following excerpt: ‘In his 1924 Apostles paper, he castigated Mill for putting all his eggs in the utilitarian basket. During 1927’28, when his two important papers in economics were written, he was also working on a book in which he hoped to carve out a subtle, naturalist theory of value’ (p. 302). Since this book was not completed, it is difficult to state whether Ramsey would have stood closer to the neoclassical or the classical theory of value. However, Sraffa’s position on the marginalist (or neoclassical) value theory is clear: it is futile. Therefore, unlike Misak, who writes that ‘It’s clear that Ramsey,’like’Dobb and Sraffa, had a complex, pluralistic, view of value’ (p. 302; emphasis added), I would be very reluctant to conjecture a similarity between Ramsey and Sraffa on the question of value theory.

 

Frank Ramsey and the Rate of Interest

I first came across Frank Ramsey in the preface to Piero Sraffa’s classic Production of Commodities by the Means of Commodities: Prelude to a Critique of Economic Theory (1960). My recent interest in Ramsey is primarily motivated by the following news. Cheryl Misak, a philosopher based at the University of Toronto has recently completed a biography of Ramsey. This blog post provides an introduction to Ramsey’s life and his contribution to the growth theory literature. [It was reassuring to notice that I first blogged about History of Economic Thought (HET) explicitly more than 10 years ago.]

Ramsey was born in 1903. In the year 1920, he read around 45 books, which included Karl Marx’s Capital, Sidney Webb and Beatrice Webb’s The History of Trade Unionism, J. A. Hobson’s The Industrial System, J. S. MiIl, and Alfred Marshall’s Industry and Trade. At the age of 19, he was commissioned to review Ludwig Wittgenstein’s Tractacus Logico-Philosophicus (1922), a significant treatise in philosophy, for the journal Mind; the review was published in 1923. Subsequently, he was commissioned to translate Wittgenstein’s work into English. In Wittgenstein’s later work, Philosophical Investigations, there is an explicit acknowledgement of Ramsey. He was acknowledged for his critique/interventions of Bertrand Russell’s and Alfred Whitehead’s Principia Mathematica in a new introduction by the authors. Sraffa, in his PCMC, had acknowledged Ramsey for mathematical help. In 1929-30, Ramsey met with J. M. Keynes, Sraffa, and Wittgenstein to discuss the theory of probability advanced by Keynes and Ramsey and also to discuss Freidrich Hayek’s theory of business cycles. Ramsey also had a close engagement with AC Pigou, a leading marginalist economist who was also the target of criticism in Keynes’s General Theory. Ramsey died in 1930.’

Under the patronage of Keynes, who was the editor of the’ Economic Journal, Ramsey published in it articles on the ‘theory of taxation’ (1927) and the ‘theory of saving’ (1928). In my 2019 article which critically evaluated the Nobel contributions of Paul Romer and Nordhaus, I had highlighted that Nordhaus employs a marginalist growth model drawing from Ramsey (without further comment). Ramsey’s question was the following: how much should a nation save today for future consumption tomorrow so as to maximise consumption across generations’ Nordhaus employs the optimal growth model with environmental protection as an important constraint. And, the rate of interest is seen as a price which equilibrates the society’s time preference. In other words, the rate of interest equilibrates the society’s preference for the future with that of the present. The policy implication when marginalist economists have a significant say in practical matters is as follows. Since the (actual) rate of interest captures the time preference of the society, this rate can be used to decide how much of current gross domestic product (GDP) should be devoted to environmental protection. In effect, not enough resources are being allocated to mitigate climate change and undertake environmental protection.’

Ramsey’s optimal growth theory also underlies Thomas Piketty’s position on economic growth. In his 2015 article in the American Economic Review, he writes that in the standard model ‘where each individual behaves as an infinitely lived family, the steady-state rate of return is well known to be given by the modified ‘golden rule’ r = + ‘ g (where is the rate of time preference and is the curvature of the utility function)’ (p. 2). The reciprocal of is the intertemporal elasticity of substitution which captures how much the representative family wishes to smoothen consumption over time. He uses this to point out that in general (marginalist) economic theory, we arrive at the r>g result–the focal argument in his book Capital in the Twenty First Century (2015; for a critical assessment see Thomas 2017). Furthermore, ‘in steady-state each family only needs to reinvest a fraction g/r of its capital income in order to ensure that its capital stock will grow at the same rate g as the size of the economy, and the family can then consume a fraction 1 ‘ g/r‘ (p. 3). To a marginalist (or neoclassical) economist, as Joseph Stiglitz wrote in an article in 1974, ‘interest rates are just intertemporal prices’ (p. 901).’

Therefore, for both Nordhaus and Piketty, interest rates are ‘intertemporal prices’ which allocate today’s income between today’s consumption and tomorrow’s consumption (today’s saving). As Ramsey (1928) writes, ‘The more we save the sooner we shall reach bliss, but the less enjoyment we shall have now, and we have to set the one against the other’ (p. 545). It is also interesting to note that their use of optimal growth models yields vastly different policy suggestions. While Nordhaus is conservative in his proposals for environmental protection, Piketty is progressive in his proposals to tax wealth.’

The rate of interest in Ramsey, as in Alfred Marshall, is a reward for waiting. Therefore, inequality in Ramsey necessarily arises from the heterogeneity of tastes or preferences; if a family is (relatively) more patient, it saves more than the (relatively) impatient one, and ends up owning all the capital stock (Attanasio 2015). How does this conception differ from the notions of interest rate found in Marx and Keynes’ For Marx, the rate of interest is the part of surplus value which is expropriated by the financial capitalist; the source of it is from the value added by labour. Keynes views the rate of interest as an expression of the preference for liquidity. To conclude, is the conception of the rate of interest found in Ramsey satisfactory for understanding a competitive economy’

REFERENCES

Attanasio, Orazio P.’ (2015), ‘Frank Ramsey’s Mathematical Theory of Saving’, The Economic Journal, 125 (March), pp. 269’294. https://doi.org/10.1111/ecoj.12229

Duarte, Pedro (2017), ‘Frank Ramsey’, In: Robert Cord (ed.) The Palgrave Companion to Cambridge Economics, Palgrave Macmillan, vol. 2, pp. 649’671.

Monk, Ray (1990), Ludwig Wittgenstein: The Duty of Genius, London: Vintage Books.’

Stiglitz, Joseph E. (1974), ‘The Cambridge-Cambridge Controversy in the Theory of Capital; A View from New Haven: A Review Article,’ Journal of Political Economy, vol. 82, no. 4, pp.’ 893903.

Further reading

Collard, David (2011), ‘Ramsey, saving and the generations’, Generations of Economists, London: Routledge.’

[Most of the contents of this post was informally discussed with my Economics colleagues at Azim Premji University on 19th February 2020.]