Abstract
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…”.
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Notes
- 1.
Our main source of letters and other communications is Box 63 of the Paul A. Samuelson Papers, 1933–2010, located in the David M. Rubenstein Rare Book & Manuscript Library at Duke University. The Papers of Richard Ferdinand Kahn at King’s College Archive, Cambridge University, contain some of that same correspondence.
- 2.
For the long history behind this book, see Harcourt and Kerr (2013).
- 3.
Samuelson’s attitude toward Robinson prior to her visit was revealed in a letter (14 August 1957) to the Rockefeller Foundation (concerning another visitor to MIT). In a postscript, he noted that Richard Kahn, unable to spend the 1958–1959 academic year at MIT, had asked, “Why not invite Joan Robinson?” Samuelson described her as “a top-notch scholar … [A]lso controversial and would, I suppose, belong to the left wing of the labor party.” He then comes to the point: “But of this I am sure. An actual visit to America she needs very badly. Naturally she doesn’t know it. She can pontificate about the American peasant in a fashion that is often laughable. I think there is a sporting chance that a trip to this country might make a dent in her opinions, and since she is most definitely a leader of World opinion, this would be very much in our interest. Earlier I might have had some doubts whether it would [be] feasible for her to get a visa. Maybe such doubt still ought to prevail. I don’t imagine that she has ever been a member of the Communist party, but there is no doubt that she did go to the Moscow conference of 1952, etc.” He concludes, “From the standpoint of brain washing her, I think a stay at one place for some length of time is probably better than the quick tour, but naturally she would want to see the country in any case.” Robinson did visit a number of other universities (see Turner 1989: 170–184).
- 4.
In a letter (31 March 1961) to Kahn following the MIT seminar, Robinson remembered it this way: “He replied – you have a point there – I do not know the answer … [I]t seems he just was disconcerted … [A]ll very amiable tho’ hard hitting and plenty of good humoured banter.” In a follow-up (2 April 1961) to Kahn, she added: “[I]t is remarkable that he should never have asked himself this simple question before…and turn it to a joke against himself. But I wonder if the point will sink in.” Robinson’s doubts are recalled in her 1977 Reminiscences: “It was great fun to tease Samuelson, but this debate took attention away from the main issue” (Robinson 1978: xviii, cited in Turner 1989: 171–172). There, she reported that “the answer [Samuelson gave to the question] is that either you keep all physical inputs constant or you keep the rate of interest constant.” In the latter case, the main issue between them was what determined the rate of interest. For Samuelson, it was “the tradeoff twixt today’s and tomorrow’s consumption goods.” This would never satisfy Robinson because it only made sense in a world where output is continuously constrained by an economy’s production possibilities. She wanted a more general theory of the economy-wide rate of profits, such as she would offer in Robinson (1962a: 48–51). As for the short run, “keeping all physical inputs constant” was not the traditional basis upon which to define the marginal product of labor. Indeed, it was an old question, long discussed in Cambridge and elsewhere. Stigler (1952: 117, 1987: 136), echoing Robertson (1931: 48), found it reasonable to hold constant total expenditure on non-labor inputs while allowing their form to vary. Whether or not one accepts this way around the problem, estimates of, say, the marginal rate of substitution between more and less computer-literate workers—the ratio of their marginal products—would be quite meaningless without also knowing the prior level of investment in computer equipment (for empirical work, see Lichtenberg 1995).
- 5.
In her own theory of marginal productivity pricing, under conditions of imperfect competition, “the marginal net product of labour (after allowing for raw materials, power and maintenance of plant) is equal to the wage plus profit” (Robinson 1967: 77).
- 6.
The Editor of the Quarterly Journal of Economics, Richard Musgrave, wrote to Samuelson (3 July 1973), in reaction to Robinson’s submission: “We don’t think it very novel, but suppose that the prominence of the author suggests we take it in any case. We shall, of course, be glad to have a brief rejoinder by you, Bob [Solow] or, perhaps, the two of you jointly.”
- 7.
Karl Shell (1971: 1002) expressed the view of many: “Paul Samuelson’s (1958) paper on consumption loans is to my mind one of the most original and stimulating contributions to modern economic theory.” It has long since become standard textbook fare (e.g., Azariadis 1993) and remains a stimulus for research (e.g., Azariadis and Smith 1993; Azariadis and Lambertini 2003). Samuelson’s purpose, it should be recalled, was “to give a complete general equilibrium solution to the determination of the time-shape of interest rates [associated with] a rational consumer’s lifetime consumption-saving pattern … This sounds easy, but actually it is very hard, so hard that I shall have to make drastic simplifications in order to arrive at exact results” (Samuelson 1958: 219).
- 8.
There is a brief indication in an accompanying (undated) note that Robinson’s comment had been sent to the Journal of Political Economy. The note included a diagram, constructed with the help of Richard Kahn (as may be inferred from Kahn’s papers in the King’s College Archives), showing lending minus borrowing and income minus consumption as functions of the interest rate. It was not included in the final version which appeared only in Robinson’s Collected Economic Papers under the title “Saving Without Investment” (Robinson 1960).
- 9.
Robinson put it this way, focusing on the late stage of working life: “An elderly man cannot afford to borrow even at a negative rate, for he has little time left to repay and to save up for his retirement” (Robinson 1960: 192).
- 10.
For a summary of results for the consumption-loan model, see Azariadis (1993: 245–247).
- 11.
For further arguments along these lines, see Asimakopulos and Weldon (1968: 704, fn. 9) who wrote: “We have found the Lerner way of looking at the problem persuasive.”
- 12.
Samuelson (1958), it may be noted, is reprinted under “The Pure Theory of Capital and Growth” in his Collected Scientific Papers, rather than in the sections concerned with consumption theory .
- 13.
- 14.
Remarkably, Samuelson acknowledges that, “Up to any instant of time, the L-A [Lerner-Asimakopulos] state has produced more social utility than the S-D [Samuelson-Diamond] state. And departing from an ever-held S-D state in favor of an L-A state leads to an increase in social utility in every subsequent period” (Samuelson 1967a: 270, fn. 2; italics in original).
- 15.
Samuelson went on to outdo Lerner-Asimakopulos by proving a Catenary Turnpike Theorem. The most efficient path to a welfare-maximizing golden-rule equilibrium at some finite future date entails just such over-accumulation of capital as to bring the rate of interest down to zero for most of the path: “The optimum…presupposes direct intervention by the state to redistribute consumption by lump-sum taxation ”. (Samuelson 1967a: 279)
- 16.
- 17.
When the “parable” was published, Samuelson expressed his gratitude to Pierangelo Garegnani “for saving me from asserting the false conjecture that my extreme assumption of equi-proportional inputs in the consumption and machine trades could be lightened and still leave one with many of the surrogate propositions” (Samuelson 1962: 202, fn. 1). See also Asimakopulos and Harcourt (1974: 483), where it is pointed out that, “If there are many techniques, the differences in the value of output per head and the value of capital per man between adjacent points may be very small … These small differences in value may mask substantial differences in the types and composition of capital goods in each system. Hence, if an attempt were made to move from one long-period equilibrium position to another, much more than a marginal change in the capital goods would be required. The existing equilibrium would be ruptured, and there is no guarantee that the behavior of the individual decision-makers in the economy would be such as to enable the transition to the new equilibrium position to be made.” Robinson put it this way: “[T]he machines…may be completely different for each [technique]…[so that to] ‘change’ the technique in use…it would be necessary…to go back into the past and rewrite the history of the investment” (Robinson 1975a: 34, 53). Rewriting history is her way of ensuring equilibrium, but not, of course, Samuelson’s.
- 18.
In Dorfman et al. (1958: 321), capital-good prices at some terminal date must be set precisely—hence the “need for vision at a distance,” but a footnote states that setting initial prices correctly will do just as well.
- 19.
- 20.
Solow does not mince his words: “[T]he real difficulty…comes not from the physical diversity of capital goods. It comes from the intertwining of past, present and future, from the fact that while there is something foolish about a theory of capital built on the assumption of perfect foresight, we have no equally precise and definite assumption to take its place” (Solow 1955–1956: 102).
- 21.
Samuelson (1990) proves a theorem on the constancy of the capital-output ratio along an optimal path, where both prices and quantities of capital goods are changing continuously, i.e., along a non-steady-state path of accumulation. He then asks, recalling Robinson’s arguments: “Will these neoclassical results hold for a neo-classical model of Joan Robinson type, where marginal productivities in the form of partial derivatives are not definable because only a finite number of activities are technologically possible?” (ibid.: 58). His affirmative answer is qualified, and so “this law is not trivially true … I conclude that, at best, if discrete-time intervals can be taken so small that there is little error in approximating the system by a continuous-time model, we can hope to state an ‘almost-constancy’ of the capital-output ratio along any optimal path” (ibid.: 69). Champernowne (1953–1954) had also faced the problem of dealing with discrete versus smooth changes.
- 22.
A belief in the stabilizing role of speculators—neither backed up by an argument nor questioned in the way that Keynes (1936 [1973]) and Kaldor (1939) had done—informs Samuelson’s other published work with Solow: “This re-aiming is, so to speak, what an optimizing society is constantly doing” (Samuelson and Solow 1956: 548). How such “re-aiming” occurs and what damage is done before the ship is righted are, of course, the fundamental questions that Robinson wanted to discuss.
- 23.
The issues raised by Hahn recall the theoretical stance taken by Irving Fisher: “When prices find their normal level at which costs plus interest are covered, it is not because the past costs of production have determined prices in advance, but because the sellers have been good speculators as to what prices would be” (Fisher 1906: 188). “Thus Fisher shifted all economic reasoning to the future … It was a complete reversal of the classical causation, as Fisher himself put it” (Bharadwaj 1985: 18). Hahn found in this reversal a profound problem: “The fact that the description of the present involves the future in an essential way must bear the responsibility for the unsatisfactory behavior of the equilibrium path” (Hahn 1966: 645–646). Samuelson quickly realized the importance of Hahn’s argument, but nowhere is it mentioned in his correspondence with Robinson.
- 24.
In an addendum to an earlier letter (9 July 1973), Samuelson provides Solow with a list of eleven points he is considering in connection with a response to Robinson. There, he states categorically: “I doubt that she understands what a price-quantities warranted dynamic path is or that it is logically possible – albeit not always [if ever] realized in real life.” The eleven points, plus two more, are found in Samuelson (1976).
- 25.
“Conservation Laws ,” too, require the assumption of constant returns to scale (see Samuelson 1990).
- 26.
Samuelson also ignored Wicksell’s remarks on capital as a factor of production: “Whereas labour and land are measured each in terms of its own technical unit (e.g. working days or months, acre per annum), capital, on the other hand, as we have already shown, is reckoned, in common parlance, as a sum of exchange value – whether in money or as an average of products. In other words, each particular capital good is measured by a unit extraneous to itself. However good the practical reasons for this may be, it is a theoretical anomaly which disturbs the correspondence which would otherwise exist between all factors of production… If capital also were to be measured in technical units, the defect would be remedied and the correspondence would be complete. But, in that case, productive capital would have to be distributed into as many categories as there are kinds of tools, machinery, and materials etc., and a unified treatment of the role of capital would be impossible” (Wicksell (1934) [1977]: 149, cited by Eatwell 2012: 5, fn. 3).
- 27.
Samuelson wrote in the same vein to Solow in his letter of 19 July 1973 (underlining in original): “[R]eswitching and backward switching and all the important things that are possible in n-vector models but not in 1-vector models, do not provide a powerful test or refutation of ‘marginal-productivity income determination ’ or of what is even more basic of the fundamental insight that supplies of capital goods, relative to unproducible labor, do importantly affect the pricing of the owned factors of production and the market-imputed income of property-less laborers in comparison with propertied people. This is the basic denial of Robinson, Kaldor, Pasinetti, etc. Only if they assume their overly-simple models – fixed capital/output ratio, etc. – do they get the indeterminacies that leave a way for simple power acts by unions to drastically alter distribution and the indeterminacies that can be filled in only by macroeconomic tautologies of the Kalecki-Robinson-Kaldor type.” See Asimakopulos (1975, 1980–1981) for a discussion of how accounting identities—presumably what Samuelson was referring to as “tautologies”—provide a starting point for non-tautological macroeconomic theories of distribution .
- 28.
The date is likely March or April 1972, as Samuelson is responding to a point that Robinson had made (15 March 1972) about labor-value prices in Smith.
- 29.
This is very much like the “provisional” assumption, in static theory, that relative prices are given. First, one works out what the value-maximizing composition of output would be; then, what the utility maximizing composition of demand would be, in light of the factor prices (and therefore the distribution of income, given factor ownership) implied by the given relative prices, assuming there is a unique answer. If they match, the “provisionally” given relative prices are equilibrium prices. If not, one tries again. Where no solution algorithm is known, i.e., in most cases of any degree of complexity, fixed-point theorems can establish existence, but not necessarily uniqueness. There may be multiple, isolated solutions or even a continuum (when a changing distribution of income just happens to leave the composition of final demand unchanged at the point where the value of output is maximized).
- 30.
- 31.
See Bruno (1969: 49), where the common value of such rates of return is the growth rate of the labor force plus the rate at which future consumption is discounted, both in and out of steady-state equilibrium. In a footnote, Bruno states that, “an optimal growth model avoids some of the ‘causal indeterminacy’ problems recently raised by Hahn (1966).” Recent work undermines this optimism: “From the outset, it is admitted that, in all the models considered, the path of prices and quantities is, from the point of view of market adjustment, dynamically highly unstable – namely saddle-path stable” (Burgstaller 1994: 38). See also Gram (1996) and Burgstaller (2001). As for Robinson, Samuelson’s remark to Solow (9 July 1973), doubting that she understood “what a price-quantities warranted dynamic path is,” may not be quite fair. Referring to intertemporal equilibrium theory , she wrote: “[F]or my part, I have never been able to make that theory stand up long enough to knock it down” (Robinson 1980a: 128), an apt quip, in view of the knife-edge property of a convergent saddle path.
- 32.
As noted in the Introduction, Samuelson had asked Robinson if, when Sraffa wrote “constant returns,” he meant “to scale.” It becomes clear (28 February 1972) that Samuelson took it to mean constant opportunity cost, i.e., a linear production possibility frontier, in contrast to “more general models.” Robinson (1 February 1972), for her part, widened the question: “I do not know whether ‘scale’ applies to a plant, a firm, or an industry. I assume you mean the total output of a specified commodity, but then are you discussing a change in the composition of output or an increase in total output?” She reiterates her position that “there are two distinct kinds of prices.”
- 33.
A year earlier, Samuelson wrote to Robinson (23 August 1965): “If the Levhari proof is valid, for such systems it is not possible to find contradictions and flaws in a definition of more-mechanized, more-round-about, more-capital-intensive configurations of the system at lower profit rates.” The reference is to Levhari (1965), later shown to have contained an error (Levhari and Samuelson 1966). With the false proof withdrawn, the “contradictions and flaws” Samuelson had referred to were granted to be entirely possible, as shown by various examples of reswitching, using indecomposable technologies.
- 34.
Robinson dismissed the possibility of finding empirical evidence of reswitching: “Nothing could be more idle than to get up an argument about whether reswitching is ‘likely’ to be found in reality” (Robinson 1975a: 38). She had earlier made the same point: “[E]quilibrium positions with different rates of profit and the same ‘state of technical knowledge’…are not found in nature and cannot be observed”. (Robinson and Naqvi 1967: 591)
- 35.
Under the heading, WHAT THE CAPITAL THEORY CONTROVERSY TAUGHT ME, only this false theorem (Samuelson 1989: 137–139; upper case in original) is mentioned. None of the other issues—and certainly not the central problem of uncertainty in economics raised by Robinson in her published work and in her letters to Samuelson concerning the controversy—were deemed worthy of comment. This is remarkable in an article devoted entirely to his memories of their interactions!
- 36.
In more recent work, Burmeister observes: “There is some irony in the conclusion that a well-behaved aggregate production function exists when (and probably, for all practical purposes, only when) the Marx EOCC [equal organic composition of capital] condition holds. Unfortunately, the conditions required for EOCC are so exceedingly stringent that they are unlikely to be realized in any actual economy” (Burmeister 2008: 344). Nevertheless, the aggregate production function lives on as a seemingly valid theoretical construct in myriad textbooks.
- 37.
When Ragnar Frisch invited her to be a Vice-President of The Econometric Society, “I said that it was no good for my name to appear on the cover of the journal when I could not understand anything inside it” (Robinson 1975b: iii). “The Rate of Interest” (Robinson 1951) was, however, published in Econometrica on the insistence of Frisch who wanted “to get more prose into [the journal, and who] paid me the very valuable compliment of saying that I had Ricardo’s instinct for making realistic simplifications” (Robinson 1975b: iii). In “Thinking About Thinking,” Robinson remarked that, “I had a very literary education and to this day I know only the mathematics that I was able to pick up in the course of trying to formalize economic arguments” (Robinson 1979: 115). She did seem to have had a knack for seeing “the resolution of complex logical and even mathematical problems without any knowledge of mathematics,” as Richard Goodwin experienced first-hand (see Goodwin 1989: 916), but the mathematics that appeared in her writings was generally relegated to Appendices, written by others.
- 38.
Robinson was quoting Heinrich Hertz, who established the existence of electromagnetic waves, theorized by Cambridge mathematician James Clerk Maxwell. Hertz had written: “One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them” (Hertz cited in Sheldrake 2012: 87–88). Hertz celebrated the power of mathematics to generate unexpected results and novel problems. Robinson was wary of the ways in which it can restrict the types of questions that can be asked in a subject like economics.
- 39.
His bold thesis is that all heterodox economics, of which he presents a sweeping survey, can be broadly understood as a rejection of the field concept as the foundation for analytical economics.
- 40.
- 41.
Here, one must mention Brian Loasby, whose work was known to Robinson. She evidently enjoyed learning of his discovery that, “‘Pretending to forecast the future’ shall be classified as disorderly under…the [New York State] Code and liable to a fine of $250 and/or six months in prison” (Robinson 1977: 1322). There is, however, no evidence that Robinson had read the first of his many books (Loasby 1976) published during her lifetime. It offered just the sort of critique of the information structure of mainstream economic theory that would have addressed her Keynesian-inspired concerns about knowledge and expectations. Loasby’s work is cited throughout Potts (2000).
- 42.
This posthumously published paper, originally dated December 1980, was a work-in-progress, “The Theory of Normal Prices, Spring Cleaning.”
- 43.
“Should complete foresight be an indispensable postulate…there results that wider paradox that the science has already posited the object that it is first to investigate; that, without this assumption, the object could not exist at all” (Morgenstern 1935 [1976]: 175). “The intertemporal equilibrium is not an object of analysis , it is not a statement of what is to be determined. It is simply the name attached to the solution of a set of equations. Modify the equations – say by working with expected prices rather than a full set of futures markets – and a new ‘equilibrium’ emerges as the solution of the new equations” (Eatwell 2012: 3–4).
- 44.
The word “integral” sometimes appears in the context of evolutionary analysis so that the question of whether such analysis requires a non-integral space remains open. See Donkers (2016).
- 45.
- 46.
Samuelson makes one concession in a letter (9 July 1973) to Solow: “If from relative factor supply side no distribution of income theory is possible, then a Kaldor-Keynes macro theory might be in order to try to fill the vacuum. That’s the only sense in which ‘generalizing the General Theory’ and ‘post-Keynesian versus pre-Keynesian processes of accumulation’ are relevant.” Solow (3 July 1973) had been more adamant: “Keynes has nothing to do with it one way or the other, since nobody is being Keynesian in the sense of having output limited by effective demand rather than by supply side considerations.”
- 47.
The dates of papers by Robinson are followed by corresponding volume and page numbers from her five volumes of Collected Economic Papers, published by Blackwell, Oxford, in 1951, 1960, 1965, 1973, and 1979; and reprinted with an index by The MIT Press, Cambridge MA, in 1980. New Introductions to volumes 2 and 3 are reprinted as Chapters 9 and 10 in Robinson (1980a). Robinson added occasional postscripts or addenda to her reprinted papers. Among Robinson’s cited papers, two were shortened in their reprinted versions (Robinson 1953–1954; Robinson 1958). For assessments of the work of Robinson and Samuelson, see, respectively, Harcourt and Kerr (2002) and Backhouse (2017), the first volume to be published of a multi-volume work.
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The dates of papers by Robinson are followed by corresponding volume and page numbers from her five volumes of Collected Economic Papers, published by Blackwell, Oxford, in 1951, 1960, 1965, 1973, and 1979; and reprinted with an index by The MIT Press, Cambridge MA, in 1980. New Introductions to volumes 2 and 3 are reprinted as Chapters 9 and 10 in Robinson (1980a). Robinson added occasional postscripts or addenda to her reprinted papers. Among Robinson’s cited papers, two were shortened in their reprinted versions (Robinson 1953–1954; Robinson 1958). For assessments of the work of Robinson and Samuelson, see, respectively, Harcourt and Kerr (2002) and Backhouse (2017), the first volume to be published of a multi-volume work.
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Acknowledgements
We wish to acknowledge Donald J. Harris for insightful comments based in part on first-hand discussions he had with Joan Robinson and Frank Hahn, among others, during the time he spent at Cambridge University. Prue Kerr has also read our drafts and made important points about how mathematics has affected and infected methodological debates.
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Gram, H., with the collaboration of G. C. Harcourt. (2019). Keynesian Uncertainty: The Great Divide Between Joan Robinson and Paul Samuelson in Their Correspondence and Public Exchanges. In: Cord, R., Anderson, R., Barnett, W. (eds) Paul Samuelson. Remaking Economics: Eminent Post-War Economists. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-56812-0_16
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