- 1 An English translation, with extensive comments and notes, is in Mirowski and Cook (1990).
1Much has been written about the complex relationship between economics and physics. One of the most well-known examples is Philip Mirowski’s provocative book More Heat than Light, in which he went to great lengths to show “the wholesale piracy of some physics by a doughty band of economists” (Mirowski, 1989, 4). One of the villains in his story is Léon Walras, who is presented as having very little mathematical skills and only a shallow knowledge of the theories of physics. Yet Walras repeatedly stressed the strong similarity between economics and physics. Perhaps the most explicit exposition of his views can be found in one of his very last papers, ‘Economics and Mechanics’ (Walras,  1987), written in 1907-8 and first published in 1909.1 Here Walras argued that the psycho-mathematical science of pure economics, as he conceived it, used identical methods as the physical-mathematical sciences of rational and celestial mechanics.
2A similar, but not entirely identical, position was defended by Édouard and Georges Guillaume, who in the 1930s launched an ambitious project of mathematical economics under the title of ‘rational economics’, a term previously coined by economists explicitly as an echo of ‘rational mechanics’. Mirowski did not mention the Guillaume project in his More Heat than Light, but in his more recent book Machine Dreams he included an anecdote which involves a publication of the Guillaume brothers (Mirowski, 2002, 104). The story comes, in fact, from Robert Leonard (1995, 736-738), who quoted extensively from a letter which John von Neumann in May 1935 wrote to Abraham Flexner, director of the Institute for Advanced Study at Princeton, who the month before had sent him a copy of their 1932 book Sur les Fondements de l’Économique Rationnelle. Although von Neumann had some sympathy for their methodological principles, he was of the opinion that “the mathematical technique of the authors is not good enough, to carry all the theoretical and statistical structures, which they want to build on it”. More generally, he had “the impression that the subject is not yet ripe (I mean that it is not yet fully understood, which of its features are the essential ones) to be reduced to a small number of fundamental postulates—like geometry or mechanics”.
3The work of Édouard and Georges Guillaume is not very well known among economists and historians of economics. In recent years Marianne Fischman and Emeric Lendjel (2000), Lendjel (2002, 21-33) and Michel Armatte (2005, 99-102) have examined some aspects of their writings. In this paper I explore the specific blend of physics and economics proposed by the Guillaume brothers, and in particular trace the connections between their theoretical work and its more practical manifestations. They rejected what they called the ‘subjective’ rational economics of Cournot, Jevons, Walras and Pareto, and instead aimed for an economic science based upon an ‘operational’ axiomatic system. After a short biographical sketch, I analyse the theoretical contributions of the Guillaume brothers, and present a survey of the activities of their research centre, the Centre d’Analyse Économique, and its collaborators.
- 2 The English connection apparently explains why the (French versions of the) names of the English ki (...)
- 3 The information on the Guillaume family comes from Rosny (1927, 201-23), Petitpierre (1955), Mollie (...)
4Édouard and Georges Guillaume had Swiss roots. The Guillaume family, of which a reduced genealogical tree can be found in Figure 1, came from the village of Fleurier in the Val-de-Travers district of the canton of Neuchâtel. Business interests—some family members were prominent watchmakers—as well as political turmoil had pushed the family to maintain a settlement in London.2 One of these watchmakers, George Guillaume (1817-1896), also owned of a printing shop in Neuchâtel, and served as a Conseiller d’État of the canton of Neuchâtel from 1853 to 1886.3 Around 1870, three of his sons had moved from Neuchâtel to Paris. His oldest son James (1844-1916) was a socialist and would later become a well-known historian of the Socialist International Movement (Vuilleumier, 1964). Édouard (1850-1897), on the other hand, was an aspiring painter, and Charles (1854-1903) a graphical artist. During the 1870s and 1880s Édouard and Charles operated a zinc engraving company in Paris, Guillaume frères et Cie. Around 1885 Édouard launched himself in the printing and publishing business, specializing in colourfully illustrated literary books. Using innovative marketing techniques he managed to sell enormous amounts of books—apparently more than two million volumes marketed under the brand name Collection Guillaume, including books by Alphonse Daudet, Émile Zola and Edmond and Jules de Goncourt, went over the counter in the period 1885-1893. In 1895, however, the Guillaume firm was declared bankrupt, and Édouard died soon thereafter.
Figure 1: Reduced genealogical tree of the Guillaume family
Source: Petitpierre (1955) and own research.
- 4 This information on Édouard and Georges Guillaume comes from their birth certificates in the Archiv (...)
- 5 In 1920 it was widely expected that Einstein would win the prize for his contributions to relativit (...)
5It is from the marriage of this Édouard Guillaume with Nina Nacamulli from Venice that Édouard and Georges Guillaume were born. Édouard Guillaume junior was born in Paris on 25 January 1881; Georges Guillaume was also born in Paris, but more than 15 years later, on 25 August 1896.4 Interestingly, they are also related to another, and more famous, member of the Guillaume family living in Paris in that period: the physicist Charles-Édouard Guillaume (1861-1938). He was director of the Bureau International des Poids et Mesures in Sèvres, and the surprise laureate of the Nobel Prize for Physics in 1920 for his work on nickel-steel alloys which remain almost invariant under different conditions (Genovesi, 2000).5
- 6 As one prominent observer wrote: “Au bout de quelques instants il devint évident que ce ne serait p (...)
- 7 One of the persons involved in this debate—on the side of Poincaré—is Maurice Allais (2005).
6Édouard Guillaume was a physicist, too. In 1908 he obtained a PhD in Philosophy from the University of Zürich with a thesis entitled Les phénomènes de Bose et les lois de l’électrisation de contact. At that time he worked for the Swiss Federal Office for Intellectual Property in Bern, where Albert Einstein was one of his colleagues. Einstein and the theory of relativity seem to have been the focus of Édouard Guillaume’s attention in that period: in 1913 he translated a booklet by Einstein into French, in 1920 he gave a series of lectures on the theory of relativity at the University of Lausanne (Guillaume, 1921), and throughout the 1910s and 1920s he published several articles on the topic in both physical and philosophical journals (e.g. two articles in the Revue de Métaphysique et de Morale; Guillaume, 1918; 1920). He was, however, not an uncritical admirer of Einstein and his work. In 1922, when Einstein visited Paris, Guillaume travelled from Switzerland to give a lecture in which he, according to the announcements in the press, would show that Einstein’s theory contained fatal mathematical flaws. But neither Einstein nor his colleagues were impressed by the value of his arguments, and the episode was widely perceived as a humiliating defeat for Guillaume.6 In his last contribution in this field—the edition of a number of writings of the French physicist Henri Poincaré, with an extensive introduction (Guillaume, 1924)—Guillaume suggested that Poincaré had independently obtained the same results as Einstein, but by following a different and from his point of view more acceptable route. The Poincaré-Einstein issue was the subject of a protracted exchange of letters between Einstein and Guillaume (see Genovesi, 2000), and led to a debate about the priority of the theory of relativity, which continues until today.7
- 8 See Guillaume (1937, 1943).
7Through his work in physics Édouard Guillaume also developed an interest in probability theory (Guillaume, 1946, 53-54). In 1915 he moved from the Federal Office for Intellectual Property to the Federal Office for Insurance, and from 1916 to his retirement in 1946 he worked for the Swiss insurance company La Neuchâteloise, of which he became a director (Moatti, 2007, 143). In the decades that followed he regularly published articles on life insurance and actuarial subjects, but not as much as he did on physics. In the academic year 1936-7 he was appointed as “privat-docent” at the University of Neuchâtel, where he lectured on financial economics.8
8Observing the usefulness of probability theory in the actuarial sciences, Édouard Guillaume began wondering whether it would be possible to bring more mathematical rigour to economics in general. At that point his brother’s researches must have played an important role. In Édouard Guillaume’s words:
- 9 “The 1914/18 war broke out. Mr. Georges Guillaume, who was then an arbitragist at the Banque de Par (...)
Survint la guerre mondiale de 1914/18. M. Georges Guillaume, qui était alors arbitragiste à la Banque de Paris et des Pays-Bas, faisait des observations extrêmement curieuses dans le domaine monétaire, et me les communiquait. Les booms et les dépressions économiques commençaient à se succéder à un rythme assez rapide, et l’on acquérait de plus en plus la conviction que nous étions tous pris dans un mécanisme inexorable, obéissant à des lois aussi précises qu’inéluctables. (Guillaume, 1946, 55)9
- 10 The published book version of the dissertation has the following on the page facing the inner front (...)
- 11 Founded in 1931, X-Crise was originally conceived as a study group where graduates of the École Pol (...)
- 12 On Coutrot and his influence in X-Crise, see Dard (1995; 1999, 55-98).
- 13 “Ces extensions ont fait l’objet de diverses communications au Centre Polytechnicien d’Études Écono (...)
9Exactly at what date they started to collaborate is unknown. In any case, in 1932 Georges Guillaume obtained a PhD in Economics at the University of Neuchâtel, with a thesis entitled Sur les fondements de l’économique rationnelle, avec une technique de la prévision.10 This marked the beginning of a period of intense discussion of their economic work. They found a receptive audience at the École Polytechnique in Paris, where the Centre Polytechnicien d’Études Économiques, also known as X-Crise, gathered engineers, economists and others to discuss economic issues.11 Georges Guillaume was closely associated to Jean Coutrot (1895-1941), a polytechnicien and one of the driving forces of X-Crise.12 The Guillaume brothers presented their work at different occasions, beginning in January 1933. The X-Crise group also supported the publication of their next book, Économique Rationnelle, which appeared in 1937 as Documents 6-7 of the centre’s book series, with a postface by Jean Coutrot.13
- 14 On this association and the role of Georges Guillaume in it, see Henry (2004, 54-64).
10In the 1930s Georges Guillaume also founded the Centre d’Analyse Économique and the Centre de Gestion Guillaume in Paris. The first presented itself as a scientific research institute where ‘usable laws’ were derived based on the theoretical work of Georges and Édouard Guillaume; the aim of the second was to proceed to ‘experimental verifications’ of these laws by means of a capital fund (Le Centre d’Analyse Économique, 1935, 8). The address of these two centres (9, rue Lincoln in the 8th arrondissement of Paris) in 1937 also became the headquarter of the journal Humanisme Économique and of the Centre d’Études des Problèmes Humains, an interdisciplinary association created by Jean Coutrot and supported by influential personalities like Alexis Carrel (1873-1944), winner of the Nobel Prize for Medicine in 1912, Aldous Huxley (1894-1963), the English writer, and Pierre Teilhard de Chardin (1881-1955), the Jesuit palaeontologist and philosopher.14 During World War II Georges Guillaume’s name was rumoured to be on the member list of the ‘Synarchic’ movement, a presumed conspiracy against the Vichy regime (Dard, 1995, 145).
- 15 Some copies of this study seem to carry the title Construction d’une économie française.
- 16 In 1947 they apparently also wrote a report Contribution à l’étude préliminaire sur le projet d’enq (...)
- 17 The outer cover carries a different title: L’Arbitrage du Cosmisme. It was published by the Édition (...)
- 18 The information on Édouard comes from the registry office of the Arrondissement du Val-de-Travers i (...)
11It is not clear how and when the Centre d’Analyse Économique ceased to exist. As we shall see in Section 6, it still operated for a few years after World War II. Immediately after the liberation of France in 1944, it published the Guillaumes ambitious study Construction d’une économie mondiale—Les conditions de l’harmonie—Le plan rationnel.15 This was followed in 1947 by the book L’Arbitre Suprême, in which they developed a ‘general energetics’ as a foundation for conflict resolution, a summary of which can be found in Guillaume and Guillaume (1949). This book signalled a mystical turn in their work, and it seems that they gradually lost contact with the mainstream of economic research and retreated into an esoteric world of their own.16 This is perhaps best illustrated by the publication, in 1960, of Georges Guillaume’s book L’Accord par le Cosmisme, an ambitious attempt to formulate a general theory of nearly everything which exists.17 The book also contained a picture of Édouard Guillaume, who had died on 9 November of the year before in Delémont, Switzerland. Georges Guillaume, attaché aux recherches scientifiques, died on 14 July 1969 in his home, 25bis rue Franklin in the 16th arrondissement of Paris.18
- 19 An abridged edition, containing only the Introduction and the Économique rationnelle part, was reis (...)
12In the above-mentioned paper ‘Economics and mechanics’ Walras systematically designated the science of economics by the term l’économique rather than by the term l’économie politique, which he used in his earlier work. Walras shifted to the new term in the 1890s (see, e.g., Walras,  1992, where he used l’économique pure and l’économique appliquée), following up on Jevons’s suggestion to replace political economy, “the old troublesome double-worded name”, by economics, “perfectly analogous in form to Mathematics, Ethics, Æsthetics, and the names of various other branches of knowledge” (Jevons,  1888, Preface to the 2nd ed., 5). Albert Aupetit, a young economist acting as Walras’s first disciple and protégé in France at the beginning of the 20th century, also contributed to this terminological change. In 1901 Aupetit had written a PhD thesis in which he formulated a general theory of money along the lines sketched by Walras. He distinguished two parts in his work: an abstract and theoretical part which he called Économique rationnelle and an empirical part entitled Économique expérimentale.19 The distinction was motivated by the way things were done in physics, where ‘synthetic or rational’ research existed side by side with ‘analytical or experimental’ research (Aupetit,  1957, 23-24). As much as rational mechanics studied an ideal world based upon a number of abstractions, rational economics studied a non-existent world based upon abstractions such as the homo œconomicus and perfect competition (ibid., 28-29). Gaëtan Pirou (1929, 113-115) stressed that this was not the same as the distinction of pure and applied economics, but simply two different approaches of the same problem. He pointed out that similar distinctions were made by Marcel Lenoir (1913), Jacques Rueff (1922), Charles Bodin (1926) and François Divisia (1928).
13From Walras’s correspondence we know that in 1907 Albert Aupetit had agreed to write a book Économique Rationnelle for the applied mathematics section of the massive Encyclopédie Scientifique series edited by Édouard Toulouse (Jaffé, 1965, III, letters 1660 and 1674). Aupetit’s book was never published, and one had to wait until the year 1928 when François Divisia published his book with the same title in the series. According to Divisia (1951, 12) the term rational economics had been invented by Walras, but Divisia did not provide a specific reference. Whatever the source of the term may be, it is clear that it was chiefly used by those who claimed to be working in the tradition of Walras.
- 20 “tantamount to a body of doctrine, as is rational mechanics”.
14When the Guillaume brothers chose this term to designate their project, they did not imply to be continuing the Walrasian tradition, and they did not refer to Aupetit’s or Divisia’s previous use of the label. They simply wanted to express their ambition to create an economic science “semblable à un corps de doctrine comme l’est la Mécanique rationnelle” (Guillaume and Guillaume, 1937, 3)20. Édouard Guillaume described the specific meaning which they attached to the term ‘rational’ as follows:
- 21 “A body of doctrine appears to us as rational—e.g. Mechanics—when it rests entirely on a small numb (...)
Une doctrine nous apparaît comme rationnelle—telle la Mécanique—lorsqu’elle repose entièrement sur un petit nombre de principes—d’axiomes—fondamentaux, dont elle développe les conséquences à l’aide de l’instrument mathématique. (Guillaume, 1935, v)21
15The number of axioms had to be small so that one could ‘easily dominate them by a geometry’ (Guillaume and Guillaume, 1937, 14). The role of mathematics would be to show that the set of principles was free of internal contradictions, and to derive the logical consequences of the principles adopted. Empirical verifications would reveal whether the chosen principles were true.
- 22 P.W. Bridgman (1882-1961) was a physicist who was awarded the Nobel Prize in Physics in 1946. Fisch (...)
16According to the Guillaumes, economics had not yet reached this status of a scientific, i.e. axiomatic, discipline. In their view, the history of economic research could be seen as exploring four different methods (ibid., 9-17). Political economy, akin to law, was based on the dialectical method: it used mainly verbal logic and common sense to derive economic laws. Business cycle studies used both historical and statistical methods to discover correlations between different factors. The school of Cournot, Jevons, Walras and Pareto relied on mathematics and the hedonistic method to formulate a general economic theory. But this ‘subjective rational economics’, as the Guillaumes called it, had one basic flaw: its axiomatic system was not operational. Here they referred explicitly to the views of Percy Williams Bridgman.22 Their main criticism was that the subjective concept of value did not obey the principle of conservation.
- 23 “Indeed, the use of mathematics supposes that the object of analysis—in this case value—obey a prin (...)
L’usage des mathématiques suppose, en effet, que l’objet de l’analyse—en l’occurrence la valeur—obéisse à un principe de conservation. C’est grâce à l’énoncé d’un tel principe que la Physique et la Chimie ont pu faire, depuis Lavoisier et Mayer, les progrès fabuleux que l’on connaît. Malheureusement la valeur étant, pour les hédonistes, une grandeur essentiellement subjective et qualitative, l’analyse ne pouvait porter que sur des fonctions psychologiques dont la détermination quantitative est inextricable. (Guillaume and Guillaume, 1937, 13-14)23
17Their alternative, rational economics tout court, was based on the axiomatic method and operational concepts. It purged economics of the variable and in their view unfathomable concept of value based on individual utility, and replaced it by an objectively defined and numerically expressed value concept obeying a principle of conservation. They did not deny that at the individual level consumers make choices based on utility considerations and producers try to exploit profit opportunities, but they were convinced that at the level of the economic system values were determined by objective forces, embodied in conservation principles. In most cases individual behaviour could not change the fundamental tendencies of an economic system. Such was the power of accounting identities:
- 24 “If free will does exist for individuals, all the more there exists a sure determinism of the accou (...)
S’il existe un libre arbitre des individus, il n’en existe pas moins un déterminisme certain du compte des recettes et dépenses. Ce qui sort d’une poche entre dans une autre, et l’on est en droit, en se basant sur un principe postulant cette constatation, d’examiner le problème sous un aspect purement objectif. (ibid., 34)24
18The two crucial conservation principles were (i) the conservation of flows of goods (flux de commodités), and (ii) the conservation of flows of values (flux de valeur). In mathematical terms, they can be expressed as follows (ibid., 248-257). Let qH denote a quantity of good H, and dqH the production of good H between time t and time t+dt. Suppose that this production requires the amounts
19of the n different goods A, B, …, N, with the services of capital and labour also treated as goods. Using the shorthand notation
20the basic principle of the conservation of flows of goods can then be expressed as a system of n equations:
21(In the case of lags these equations have to be modified.). Let the prices of the n goods be equal to
22with pO representing the price of gold. The second principle expresses that, in equilibrium, the prices must be such that every producer earns exactly what he needs to cover his costs. For instance, the producer of good A earns a flow of value equal to
23this should be equal to the flows of value which he has to pay for the productive services which he uses. The principle of the conservation of the flows of value therefore defines a second system of n equations:
24Since there is one degree of freedom, the Guillaumes suggested to use gold as the numéraire, i.e. to put the price of gold, pO, equal to 1.
25The two conservation principles were seen as counterparts of the two conservation principles of physics, with the first corresponding to the conservation of matter and the second to the conservation of energy (Guillaume, 1946, 58-61). The two principles provided the foundation for a twofold accounting system, one with regard to goods and the other with regard to values, which constituted the core of their rational economics theory. The models developed by the Guillaumes are therefore built around a nucleus consisting of variants of the two systems of equations expressing the two conservation/accounting principles.
26The Guillaumes claimed that by following their approach they were able to arrive at a truly ‘general theory’ (Guillaume and Guillaume, 1937, 241-242). They certainly did not lack ambition: they started from ‘small models’ (ibid., 39-42), which they gradually made more ‘realistic’ by relaxing some simplifying assumptions and by exploring different types of equilibria. Various adaptations ensured that these models could also be used to analyse non-equilibrium situations such as price adjustments, economic crises, etc. Their aim was to use these models to make predictions about the economic world which could be tested empirically, in the same way as models in physics (e.g., Niels Bohr’s model of the atom) were used to explain phenomena in the physical world. In particular, they claimed that by using probability theory they were capable of forecasting rates and prices of different assets. As we will see in the section 6, it appears that they were effectively using this information.
27It is not difficult to understand why their attempt to formulate a general economic theory based on purely objective grounds failed to convince mathematicians strongly interested in economics like von Neumann. von Neumann and Morgenstern (1944, 1-8), in their opening paragraphs on ‘The mathematical method in economics’, stressed the limitations of the use of mathematics for the analysis of economic problems, “due to a combination of unfavorable circumstances” (ibid., 4). Often the problems were formulated in vague terms only and not clearly understood. Moreover, empirical knowledge was very much incomplete. As a result, modesty was called for when using mathematics in economics: “It is futile to explain—and ‘systematically’ at that—everything economic. The sound procedure is to obtain first utmost precision and mastery in a limited field, and then to proceed to another, somewhat wider one, and so on.” (ibid., 7) Judged by the standard of modesty of von Neumann and Morgenstern, the project of the Guillaumes could only be seen as premature and overly ambitious.
28The approach of the Guillaumes led to a succession of ever more complicated models. It would require a lot of space to present them in a systematic way. What I will do instead is to focus on some of their relatively simple models, since these bear a striking resemblance to linear models which were developed by various authors in the first half of the 20th century. The similarity with the systems of equations presented by Remak, von Neumann, Leontief and Sraffa has been pointed out by Gilibert (2000). In this section I will concentrate on the links with the work of Sraffa and von Neumann, and also with the work of a much less known pioneer of linear economic models, Maurice Potron.
- 25 Please note that the symbols I am using here differ from the ones used by the Guillaumes.
29Let us begin with the first ‘reduced model’ of Georges Guillaume’s PhD dissertation. The model assumes there are three commodities: two goods which are produced and consumed (1 and 2), and one type of labour. In a given unit of time the production processes of the two goods can be represented as follows25:
30where Aij stands for the amount of good j and Li for the amount of labour used for the production of Bii units of good i. (It is assumed that good i is not used for the production of itself.) The total amount of labour is equal to L, and labourers consume Ci units of good i. Under the assumption that everything which is produced is immediately consumed (“Monde homogène sans stock”, Guillaume and Guillaume, 1937, 249-250), system (1) can therefore be written as:
31Likewise, system (2) becomes:
32Using a more compact and obvious matrix notation, systems (4) and (5) can be expressed as:
33where A is the square input matrix, B the square output matrix, C the labour consumption (row) vector, L the labour input (column) vector, p the price (column) vector, and u the summation (row) vector. If prices are expressed in ‘human labour’, i.e. if we take
34(Guillaume, 1932, 86), it is quite easy to see that the prices of the two goods are determined by the first equation of system (7). We have in fact:
35 These values are what the Guillaumes called ‘cost prices’ (prix de revient), which capture and measure the energy present in the economic system:
- 26 “From the cost prices we are able to define numerically what we mean by “value”. And since, eventua (...)
Le prix de revient nous permet ainsi de définir numériquement ce que nous entendons par “valeur”. Et puisque, en définitive, il exprime un travail, c’est-à-dire une énergie, [et] que celle-ci obéit à un principe de conservation, il est naturel d’admettre que la valeur elle-même doit obéir à un principe semblable. (Guillaume, 1932, 68)26
36According to the Guillaumes, the connection ‘energy → labour → cost price → value’ not only provided the foundation for the principle of the conservation of values, but also for the principle of the ‘universal interdependence of cost prices’ (ibid., 69).
37This simple model is virtually identical to the one examined by Piero Sraffa in the first chapter of Production of Commodities by Means of Commodities (Sraffa, 1960, 3-5). The difference is that Sraffa did not specify how much labour is used for the production of each good, but instead added the wage goods to the inputs. As a result, the inputs considered by Sraffa are equal to the goods which “are used, in part as sustenance for those who work, and for the rest as means of production.” (ibid., 3) The model of the Guillaumes can, however, quite easily be transformed into Sraffa’s. It suffices to define the augmented input matrix
38to see that systems (6) and (7) imply:
39 which are Sraffa’s equations. Hence Sraffa’s exchange values in a ‘production for subsistence’ system coincide with the relative cost prices of the first reduced model of the Guillaumes.
- 27 In Guillaume and Guillaume (1937, 279-280) some ‘structural coefficients’ are defined in terms of t (...)
40Although systems (4) and (5) are expressed in terms of actual flows of goods, the Guillaumes pushed the analysis one step further by introducing the notion of production coefficients, based on the assumption that the ratios of the inputs to the outputs they help to produce remain the same (see, e.g., Guillaume, 1932, 95).27 In other words, they implicitly adopted the hypothesis that in normal circumstances the economy operates under constant returns to scale. This means there is some similarity with the model which John von Neumann presented in 1932 in Vienna (see von Neumann, 1945-6). Although it is obvious that von Neumann’s analysis had a different scope, it is remarkable that the Guillaumes derived a number of results which are reminiscent of von Neumann’s. For instance, in the third reduced model of 1932 (which more or less coincides with the first reduced model of 1937) they showed that under certain conditions economic equilibrium required a constant growth rate of production of all commodities (Guillaume, 1932, 108; Guillaume and Guillaume, 1937, 284), something which brings to mind von Neumann’s “coefficient of expansion of the whole economy” (von Neumann, 1945-1946, 2).
41There is also a similarity with some variants of the economic models formulated by Maurice Potron in the periods 1911-1914 and 1935-1942 (see Bidard and Erreygers, 2007 and 2010, and Bidard, Erreygers and Parys, 2009). In the second reduced model of 1932 the Guillaumes explicitly introduced a variable representing the non-active part of the population, such as the unemployed, the invalid, the sick and the old (Guillaume, 1932, 92). This allowed them to say something about the effects of increasing unemployment levels, although their analysis does not go very deep (ibid., 93). In Potron’s models the category of non-actives is represented by two vectors of variables, one for the number of non-working consumers in each social class (the rentiers), and the other for the number of hours or days that the workers of each type of labour are unemployed. But here too, we must be well aware of the fact that the approach of Potron was of a different nature than that of the Guillaumes.
42In spite of these analogies, there is no evidence of any kind of influence between the Guillaumes and the authors just mentioned. For all it seems, the originality of their work cannot be doubted. Some aspects of their models have no counterpart in any of the other linear models developed in the first half of the 20th century. The central place they gave to gold and the intricate schemes they developed to integrate monetary and financial mechanisms into their models serve as illustrations.
43Even if the Guillaumes had no discernible influence on the development of linear production theory, there may have been other channels through which their work got disseminated. We have seen that the interpretation of prices as energetic values, as indices revealing the amount of effort required to produce different goods, constituted a core element of their theory. With some pride they reproduced a letter written by Albert Einstein on 24 August 1946 in which he expressed support for that aspect of their work:
TO WHOM IT MAY CONCERN!
Dr. G. Guillaume, whose family was well known to me in Switzerland, has explained to me a method for mechanized determination of the relative values of the various commodities (in function of time). I believe that the use of this method may be practical and useful in providing an objective way to obtain an incontestable measure of economic values. (Guillaume and Guillaume, 1947, 62)
44In spite of that, it would be exaggerated to say that the work of the Guillaume brothers made much of an impact—neither in the economics profession, nor in other circles. Apart from their direct collaborators, very few authors have tried to develop their ideas, and those who did had limited success. In 1935 Maurice Bouytaud published his Essai d’Économique Rationnelle, with a preface by Édouard Guillaume. Ostensibly inspired by the Guillaume approach, Bouytaud presented a very formal kind of general equilibrium model, but without abandoning all references to utility and preferences as advocated by the Guillaume brothers. The market for these fairly abstract mathematical economic models must have been pretty thin, since both the book and its author have left hardly any traces in the economic literature. The same cannot be said of the Austrian art historian Robert Eisler (1882-1949), who often wrote about value and money. In his writings he repeatedly recommended the ideas of the Guillaume brothers. For example, in a 1946 review essay of Ludwig von Mises’s Omnipotent Government: The Rise of the Total State and Total War, he wrote:
(…) a complete plan for an entirely free, uncontrolled and throughout competitive liberal economy has been drawn up in a newly published French book by two Swiss economists, Dr. Georges and Edouard Guillaume, Le Plan Rationnel (Paris, 1944). It is the indispensable counterpart of Professor von Mises’ Omnipotent Government. (Eisler, 1946, 247)
- 28 The connection between Eisler and Georges Guillaume dates from the 1930s; see Fisher (1935, 102) an (...)
45And in the book Winning the Peace. A Comprehensive Policy, a section was devoted to the views of the Guillaume brothers (Eisler and Hart, 1948, section 79).28
46A remarkable affinity exists between their work and the esoteric economic writings of the mineralogist André Amstutz (1901-1981) and the chemist Arnold Borloz (1899-1960), both from Switzerland. First in a series of short papers published during World War II in the Compte rendu des séances de la Société de Physique et d’Histoire Naturelle de Genève, and then in a longer article in the Revue suisse d’économie politique et de statistique (Amstutz and Borloz, 1945), they expounded a mathematical economic model in which gold played the role of standard of value. Making use of datasets of the League of Nations, the US Department of Labor and Bureau of Census, and data made available by the economist Carl Snyder (1869-1946), they proceeded to elaborate empirical calculations. Both Édouard Guillaume (1943, 103) and Amstutz and Borloz (1945, 591) acknowledged the resemblance between the two approaches, but a promised in-depth comparison of the two was apparently never published.
47As already mentioned, their theories were intensively discussed during the meetings of X-Crise (Gibrat, 1936), but even there the reception was not uniformly positive. Their 1937 book provoked a rather critical reaction by Divisia (1938), to which Georges and Édouard Guillaume (1938) duly replied. Divisia maintained that by purging economics from its hedonistic content, the Guillaumes were performing an amputation which entailed the loss of “tout ce qui fait de l’économique une science morale” (Divisia, 1938, 191).
48Of the main economics journals, only the Economic Journal published a review, by Michal Kalecki (1940). He noted several deficiencies, but nevertheless concluded that “their work represents a serious contribution to this field of thought, and abounds in original and stimulating ideas” (ibid., 278). In their native Switzerland the Bulletin Technique de la Suisse Romande published three reviews of their books: one by the mathematician Gustave Juvet (1932), one by the engineer Charles Jaeger (1937a), and another one by J.C. (1938). Jaeger (1937b) also published a much longer article on mathematical economics in the Schweizerische Bauzeitung. Harold T. Davis (1938) published a joint review of the 1937 book by the Guillaumes and of Jan Tinbergen’s An Econometric Approach to Business Cycle Problems in the Bulletin of the American Mathematical Society. Davis saw both books as indicative of “the trend that modern studies [on mathematical economics and econometrics] are taking” (ibid., 761), but stopped short of making a comparison between the two.
- 29 The first report “Centre d’Analyse Économique (Visite à M. G. Guillaume)” (Note N° 8447) is dated 1 (...)
- 30 See Marjolin (1937), Picard (1937) and Guillaume and Guillaume (1937, 246-247 and passim).
49It is very difficult to find information about the Parisian research centre of the Guillaumes. Our main source is a brochure published in 1935 by the centre itself: Le Centre d’Analyse Économique—Son Organisation—Son Utilité (henceforth: CAE). Apart from that, we have two internal reports by the department of economic and financial studies of the Crédit Lyonnais,29 and a few sporadic remarks in other publications.30
- 31 After the inner title-page, there is a page with two photographs, one of Georges Guillaume and anot (...)
- 32 In 1935 these sections were headed by Stéphane Leven, Antoine Pourquié, Jacques Bourcier-Omètre, Re (...)
50The centre was founded and directed by Georges Guillaume. The main purpose of this non-profit organisation with scientific aim was to transform the principles of rational economics of the Guillaumes into propositions which could be applied to real-world problems.31 The centre was divided into five sections: (I) Business cycles (La Conjoncture Générale); (II) Sectors and markets (Les Branches de l’Activité Économiques); (III) Assets with variable revenues (Les Valeurs Mobilières); (IV) Assets with fixed revenues, and interest rates (Les Valeurs à Revenu Fixe et les Taux); and (V) The Guillaume management technique (La Technique de Gestion Guillaume).32 This last section elaborated and refined a financial technique described as the ‘Guillaume Technique’ of generalized systematic arbitrage. The centre seemingly attached great importance to data collection and graphical illustrations; it boasted of continuously updating a series of ‘atlases’ with data and diagrams (CAE, 26-27).
- 33 E.g., it published a bulletin which was only available to subscribers (Lemaître, 1937, 343); both M (...)
51It is unclear how the centre managed to finance its operation. Presumably it made revenue by selling information and data to interested parties.33 The contacts with the Crédit Lyonnais were clearly meant to explore the possibilities for future cooperation. The bank’s report of the visit stated:
- 34 “Mr Guillaume has contracted with a ‘major’ Swiss insurance company, a contract by which the latter (...)
- 35 My guess is that the ‘major Swiss insurance company’ is La Neuchâteloise, of which Édouard was dire (...)
M. Guillaume a passé, avec une ‘importante’ société suisse d’assurances, un contrat réservant à cette dernière l’exclusivité de ses travaux concernant les travaux à revenu fixe; il fait également certaines recherches pour des banquiers (Rothschild, B.N.C.I., etc.), des industriels (raffinerie de sucre, etc.) et des particuliers. Il estime que des études analogues concernant les prix des principales matières premières seraient susceptible d’intéresser le Crédit Lyonnais, auquel il serait prêt à en réserver l’exclusivité moyennant le droit d’utiliser la documentation des Etudes Financières du Crédit Lyonnais et le versement d’une somme annuelle qu’il évalue ‘au maximum à 300.000 frs par an’ (frais d’entretien du bureau spécialisé). (“Centre d’Analyse Économique (Visite à M. G. Guillaume)”, 1935, 3)3435
52The Crédit Lyonnais seems to have declined Georges’s offer. The report was sceptical about his methods and warned that “l’application systématique des mathématiques supérieures à des raisonnements qui ne reposent en fait que sur des tissus d’hypothèses risque de donner une apparence de rigueur à des conclusions qui peuvent être dangereuses” (ibid., 4).
53Probably the centre also benefited from the profits made by its sister organisation, the Centre de Gestion Guillaume, which had the task of empirically verifying the propositions established by the Centre d’Analyse Économique by means of a capital fund (Groupement de capitaux) brought together for this purpose (CAE, 8). The capital apparently belonged to Georges Guillaume, his collaborators and their families (“Centre d’Analyse Économique (Visite à M. G. Guillaume)”, 1935, 1). It was claimed that the two centres operated in harmony:
- 36 “Far from being in hardship because of the operations following the need to register the works of t (...)
Loin de se mal trouver des opérations dictées par les nécessités d’enregistrement des travaux du Centre d’Analyse Économique, le Groupement de capitaux a montré, au contraire, qu’il en profite grandement. L’ensemble a pu ainsi se développer harmonieusement. Il présente une cohésion qui lui confère la puissance investigatrice et la compétence voulues. (CAE, 8)36
54A number of examples were given which purportedly showed the superiority of the Guillaume arbitrage technique in comparison to other financial techniques (CAE, 21-28).
- 37 The second report by the Crédit Lyonnais staff had in appendix a leaflet on the Atlas and two of it (...)
- 38 Once again the bank seems to have declined Guillaumes services. The report mentioned several inaccu (...)
55By the year 1938 a third centre had been created at the same address, the Centre de Documentation Économique. This appears to have been mainly a financial service centre, collecting, processing and selling information on quoted stock companies. Its main output was the Atlas International de Valeurs, consisting of Les Planches Guillaume with detailed information and graphs on individual firms.37 The theoretical foundations of the Atlas were said to be the ‘Models’ of rational economics and a ‘Manual’ with general explanations. Specific information relative to each firm was grouped into two files, a dossier général and a dossier matrice, and Guillaume invited the bank to come and consult these files.38
- 39 Some confusion may be possible with another Paris-based Centre d’Analyse Économique, the one headed (...)
- 40 They mentioned explicitly the ‘remarkable researches’ of Stéphane Leven on the construction of a le (...)
- 41 Octave Gélinier (1916-2004), a civil mining engineer, later became one of France’s leading manageme (...)
56During the 1930s and 1940s several theoretical and applied studies of the Guillaume brothers were published by the Centre d’Analyse Économique (see, e.g., Guillaume and Guillaume, 1947), but most of them are nowadays very hard to find.39 Although they claimed that its members were also engaged in personal research, some of which they used for their theories (Guillaume and Guillaume, 1937, 246-247)40, little traces of this can be found. One exception is a very broad and non-technical paper on dynamics by Octave Gélinier (1946)41, heavily inspired by the work of the Guillaumes and the centre. At the end of his study Gélinier mentioned that it had been written at the Institut d’Analyse, de Synthèse et d’Orientation des Activités (I.A.S.O.A., 9, rue Lincoln, Paris)—probably a spin-off of the other Guillaume centres at the same location, about which I have been unable to find further information. Interestingly, he pointed out that the centre had used four different techniques:
- 42 “To build in practice economic models which comply with the previous characteristics, different tec (...)
Pour construire pratiquement des modèles économiques conformes aux caractéristiques précédentes, diverses techniques ont déjà été utilisées: modèles mathématiques, qui se prêtent à l’étude des propriétés formelles; modèles graphiques commodes pour illustrer un exposé de principe; modèles numériques, reproduisant quantitativement les flux de matière et de valeurs réels mesurés à un instant donné, mettant en évidence les tensions-valeur et permettant la prévision pratique; enfin modèles électriques qui, substituant aux flux de valeur des courants électriques (qui obéissent au même principe de conservation), et figurant les contraintes matérielles par des liaisons électriques appropriés, constituent une image souple et mouvante douée d’une évolution spontanée parallèle à l’évolution du milieu réel. (Gélinier, 1946, 264)42
57This is the first mention of the use of electrical models by the centre; I will explore this branch of activity in the next section.
58When applied at the level of the nation-state, the conservation and accounting laws which the Guillaumes considered to be the core of their rational economics models eventually led to the construction of tables of national accounts, representing flows of goods and value between different sectors. For instance, in one of their publications they included a number of folding pages with a detailed table of this kind representing the economy of Switzerland in 1939 (Guillaume and Guillaume, 1947, 61). They also claimed to have invented a device which enabled them to trace the dynamics of the economic system:
- 43 “We have built an electric calculator that enables to follow, almost in continuous time, the interv (...)
Nous avons construit une calculatrice électrique qui permet de suivre, d’une façon quasi-continue, les intervalles entre les tableaux dressés à des instants aussi rapprochés qu’on le désire. Cette machine reproduit ainsi une synthèse dynamique de l’évolution en fonction du temps. (ibid., 34)43
59This raises two interesting questions: were the tables of the Guillaume similar to the input-output tables constructed by Wassily Leontief since the early 1930s, and what exactly was the electrical calculator to which they referred?
- 44 Patent number FR992866, applied for on 18 September 1944, delivered on 11 July 1951, and published (...)
- 45 Patent numbers UK600795, US2509718 and CH253045.
60A partial answer to these questions can now be given. Just a couple of weeks after the Liberation of Paris in August 1944, Raymond Alphonse Marie Barbey submitted a patent application to the French authorities for a Dispositif électrique pour l’étude des variations corrélatives de grandeurs liées entre elles par un système de relations mathématiques formant tableau à double entrée.44 In 1945 he submitted the same application for an electric calculator also in the UK, the USA and Switzerland.45 The application file started with a simplified representation of economic transactions in a national economy by means of a double-entry table arranged according to the method of Georges and Édouard Guillaume of the Centre d’Analyse Économique (see Figure 2).
Source: Patent number US2509718, columns 1-2.
61Barbey then noted that the entries of this table are such that for each sector i (i = 1, 2, 3, 4), the following equation holds:
62His invention was based on the idea that it should be possible to translate this information on economic exchanges between sectors into flows of electric energy:
The invention has for its object to device an electrical apparatus permitting to instantaneously and continuously compute correlative variations of the quantities
when one or several of them are adjusted or undergo a variation. The invention has further for its object to devise an electric integrator adapted to integrate variations of these quantities in function of the time, so as to totalize the exchanges between the groups as well as the profits or losses of any one of these groups. (Patent US2509718, column 3)
63He went on to describe the technical details of the system of instantaneous and totalizing meters which he had in mind.
- 46 Barbey to Leontief, 6 March 1946, Appendix, p. 2. The Barbey-Leontief correspondence comes from the (...)
64On 6 March 1946 Barbey informed Leontief that he had developed an “Overall Surveying Machine”, called the “Grid” (see Figure 3), which would allow “easy handling of statistical data and economic information”.46 Without going into technical details, he explained that the Grid was an electric device that functioned “much like a telephone exchange”. He was convinced that it would make economic calculations much easier:
This electrical coordination, flexible, instantaneous, and complete, is a revolutionary change for statistical work. Its consequences are bound to be far reaching, and will prove to be [an] asset to the organizations who will be first to use it. A development equipment is built on a semi-industrial scale for a private investment trust in France. (Barbey to Leontief, 6 March 1946, Appendix, 2)
Source: Barbey to Leontief, 6 March 1946, Appendix: 5 (Papers of Wassily Leontief).
65The investment trust to which Barbey referred in his letter was the Centre d’Analyse Économique of the Guillaume brothers. In another letter to Leontief, Barbey inserted a note on the history and development of the Grid, and there he explained:
At the beginning of 1944 the author saw the double-entry tables of the Center [sic] d’Analyse Économique, Paris, on the national product.
He was struck by the difficulty of mutual adjustment within the frame of double-entry accounting, of large numbers of statistical or tentative figures. He wondered whether electric currents would not spontaneously give the answer to such large systems of linear equations and he built a first very small electric “Grid” of four accounting units exchanging through sixteen points.
The Centre d’Analyse Économique bought it, and asked the inventor to design and build a more important “Grid”. With the collaboration of the Centre, the inventor developed a thoroughly changed structure of the double-entry table, in order to make it more comprehensive, explicit, practical. All the economic functions should appear on a well-designed table. At the expense of the Centre, he built the Grid which has been finished just now. (Barbey to Leontief, 14 June 1946, Appendix, 5)
- 47 Leontief to Barbey, 14 March and 19 June 1946. Interestingly, in the first letter he mentioned that (...)
66Barbey was obviously trying to make money from his invention. Leontief was not interested, however. In two letters he maintained that the computational work for his input-output tables could be accomplished without any serious difficulty by the existing techniques.47
- 48 Patent number CA484584; the application date is unknown, but it was issued on 1 July 1952.
- 49 Patent numbers FR1002557 and US2503932; the quote is from the US application (columns 8-9).
- 50 Patent numbers CH297068 and DE910906 for the first and CH297465 for the second.
67The exact relation between Barbey and the Guillaumes remains a bit of mystery. When the previously mentioned patent application was submitted in Canada, the inventor was listed as Raymond Barbey but the owner as Georges Guillaume.48 In 1946-7, Barbey submitted patent applications in France and the USA for an “electric calculating machine for studying the variations of linear functions of several variables and for solving systems of equations with several unknowns”.49 He reproduced the same table as in his previous application (Figure 2), but he dropped the reference to the Guillaumes and instead claimed that it had been prepared in accordance with the methods of Leontief’s input-output analysis. To make things even more complicated, a few years later Georges Guillaume also submitted patent applications for electric calculating machines, entitled Appareil électrique de mesure, permettant notamment de faire des prévisions économiques and Appareil électrique de mesure, permettant notamment de déterminer l’équilibre dans un système d’échange.50 In the first he referred explicitly to the Économique Rationnelle book which he and his brother had published in 1937. He claimed that he had found a way to construct an electric device which established an exact correspondence between economic variables and electric variables. The main terms of correspondence are given in Figure 4. In the second, clearly a variant of the first, he suggested that the patent which Barbey had applied for in 1945 was, in fact, his. It is uncertain whether any of the devices invented by Guillaume has ever been built.
Source: Patent number CH297068, p. 7.
68In this paper I have tried to show that the Guillaume brothers have gone quite far in their attempt to reconcile economics and physics. Taking their distance from the general equilibrium tradition of Walras and Pareto, of which they disliked the subjective elements, they elaborated their own version of rational economics in which values were derived objectively, based upon two conservation principles. They applied their theoretical knowledge to the real world and offered information and advice to parties willing to pay for it. Apparently capable of making a profit by investing their own funds according to what they identified as lucrative investment opportunities, they stimulated the development of electric devices which would facilitate the calculations needed to construct and use tables of national accounts. This remarkable blend of original theoretical work and practical applications constitutes a fascinating but hitherto largely unknown episode in the history of economics-as-if-it-were-physics.
69That said, it must be acknowledged that their rational economics project can only be described as a failure. Mathematically inclined economists such as Divisia were offended by their obsession to purge economics from all subjective elements. Mathematicians with a strong interest in economics such as von Neumann were critical of the ambition to create a general economic theory simply by mimicking the conservation principles of physics. And economists who worked with linear models of production, such as Leontief, failed to perceive the usefulness of the electric devices of which the design was purportedly based on their theories. In addition, there may have been other reasons why their theories did not gain much ground. They worked mostly outside of academia, at a time when a full-blown mathematical approach such as theirs was still considered to be arcane by most economists. Even though they found a receptive audience at X-Crise, the association with this technocratic group apparently did not open many doors, at least not in terms of academic recognition. And the claims that their theoretical constructions provided the basis for superior investment strategies are impossible to verify, given the lack of evidence. It is, therefore, far from surprising that the grandiose ‘rational economics’ project of the Guillaumes quickly fell into oblivion.
I thank Martine Balsalobre, Christian Bidard, Jocelyne Dufour, Claude Jeanrenaud, Alexander Müller, Roger Nougaret, Jean-Pierre Potier and Libb Thims for valuable advice and assistance. The comments and suggestions by the two anonymous reviewers and by the editor have been very helpful. I have also benefited from comments by participants of the 35th Annual HES Conference (York University, Toronto, Canada, June 2008), the International Summer School of History of Economic Thought (Lucca, Italy, September 2008) and the Conference “The Pioneers of Linear Models of Production” (EconomiX, Université Paris Ouest Nanterre La Défense, January 2013), where I presented earlier versions of the paper. Originally this started as a joint project with Albert Jolink, who drew my attention to correspondence he had found in the Papers of Wassily Leontief. I assume full responsibility for all errors and inaccuracies.