Economic thought during World War II and the “Trente Glorieuses”

World War II marked a break in both the structure of the French economy and the evolution of economic thought. During the Trente Glorieuses,^[274] the French economy developed many traits of a command economy: a large fraction of the banking system and industrial enterprises were nationalised; indicative planning was introduced.

This section focuses on the two main issues addressed by French economists during the period known as the “Trente glorieuses” years. On the one hand, the debates about choices - collective choices, choices under uncertainty - originated in a dialogue initiated between French and American economists during two collo- quia organised, in 1952, respectively, by the ISEA and the CNRS (Centre national de la recherche scientifique). On the other hand, Allais, in his Traite d’economie pure, raised, without completely resolving them, a series of questions about the existence of equilibrium, its optimality and the pricing of public services. Allais himself and many other economists provided answers to these questions. On both issues, French economists who worked on these problems sometimes taught in foreign universities and collaborated with foreign economists.

A breakthrough

Setting the stage

The human toll of World War II was lower in France than that of World War I - 567 000 dead, including 350 000 civilians -, but material losses were substantial; the overall cost of the damage was estimated at more than a quarter of national wealth. However, reconstruction was achieved quickly: in 1948, production returned to its 1938 level.

At the time of the Liberation, the organisation of the French economy was deeply affected. Nationalisation was central to the programme of the Conseil National de la Resistance. From December 1945 to May 1946, the four biggest banks, insurance companies, gas and electricity, and all coal mines were national­ised by the Constituent Assembly. In 1948, air and sea transport were organised as semi-public companies. French economists were therefore prompted to address the management of public enterprises and, in particular, the pricing of their products and services.^[275] In the meantime (1946), the Commissariat General au Plan (General Planning Commission) was created under the direction of Jean Monnet. The first “plan de modernisation et d’equipement” was adopted in 1947, whose aim was to coordinate the activity of the public sector and to direct reconstruction efforts by defining the objectives for long-term growth. The Commissariat General au Plan played an important role in promoting research in the economic field until 2006. The role of the French state, via its agencies, was to become progressively more important in the development of economic expertise, as Fourcade showed (2009); she identified a “statist pattern of organization which limited the development of economic knowledge (particularly quantitative knowledge) in the non-state sector” (2009, 187).

In 1946, the national statistics service merged with the research departments of the Ministry of the Economy to become the Institut national de la statistique et des etudes economiques (INSEE), in charge of national accounting and forecasting, particularly for the Commissariat General au Plan.

At the same time, the teaching of economics at universities gradually evolved. In 1960, a degree in economics was created within the Law Faculties, whose cur­riculum included mathematics, statistics and econometrics. The end of the Facul­ties in 1969 marked the separation of law and economics in many universities. In the meantime, economics had become a major discipline in French universities.

Several research institutes were thus created. In January 1944, Franςois Perroux founded the ISEA (renamed ISMEA in 1974) with the support of the Banque de France, the Caisse des Depots et Consignations and the Ecole Libre des Sciences Politiques. The ISEA brought together a large number of French economists - Pierre Uri (1911-1992), Gaetan Pirou, Maurice Bye (1905-1968), Emile James (1899-1992), Jean Marczewski (1908-1990) and, later Georges-Theodule Guilbaud (1912-2008) and Henri Aujac (1919-2009) - and developed close links with foreign economists, such as Thomas Balogh, Michael Kalecki, Jan Tinbergen, Joan Robinson and Edward Chamberlin. The Centre National de la Recherche Scien- tifique (CNRS) initiated two econometrics seminars, headed respectively by Allais and Roy, and a research unit which was to be led by Divisia but which Darmois finally took over. Allais’ seminar was a natural continuation of the “Groupe de recherches economiques et sociales” he had created in 1944. This seminar followed the French engineering tradition and focused particularly on the utility and effi­ciency of public spending. Gerard Debreu and Marcel Boiteux (b. 1922), who had been appointed by the CNRS after graduating from the Ecole Normale Superieure, were assigned by Darmois to Allais’ seminar.

The ageing Journal des economistes did not survive World War II, while its rival, the Revue d’economiepolitique, continued its long run under the direction of Rist and Pirou. Three new reviews were launched: Economie appliquee, the Revue economique and Les Cahiers du Seminaire d’econometrie. The first appeared as the journal of the ISEA and was directed by Franςois Perroux. The second was oriented more towards the social sciences, as shown by the presence in the editorial board of historians such as Fernand Braudel (1902-1985) and Ernest Labrousse (1895-1988). The third was directed by Roy and was the expression of the econo­metrics seminar of the CNRS; in 1986, it merged with the Annales de l’INSEE and took the title Annales d’economie et statistique. The AFSE (Association franςaise de science economique) was founded in 1950 and became the most influential pro­fessional association of economists in France.

French economists during World War II

that the demand for a good q_i can be deduced from variations in the indirect util­ity function induced by a marginal variation in its price on the one hand and by a marginal variation in income on the other. This relation, called the Roy identity, is written:

Rueff, for his part, published a book in 1945 which renewed his vision of market adjustment. Prior to this book, he explained that in a liberal system, equilibrium is ensured by price adjustment and that economic intervention, as long as it allows this mechanism to maintain equilibrium, is not in conflict with liberalism.

In a liberal regime, it is... the amount of tax which, added to the income of the public domain, fixes at each moment the maximal possible interven­tion of the State. Within this maximum, the government’s will is almighty; beyond that, it is powerless.

(Rueff 1945, 641)

In the end, liberal intervention is only limited by the amount of tax levied. Second, he opposed two ways of organising society: liberalism and authoritarianism. What differentiates them is not the governmental programmes but the methods of gov­ernment. The liberal method is that of taxation: the government deprives the owner of part of his rights and allocates them to itself. The authoritarian method consists of compelling the owner to choose the purposes that government plans to impose on him.

Perroux’s name is also inevitably associated with this period.^[276] From an ana­lytical viewpoint, the main books that he published during the war - his Cours d’economiepolitique (1939-45) and Le neo-marginalisme (1941) - were seen as expressing a profoundly innovative modern knowledge, their success being evi­denced by the number of reprints. The ambition of his Cours was to achieve a synthesis between abstract analyses - theories of equilibrium and marginal utility - and concrete historical, sociological and statistical studies. Perroux, referring to the work of von Mises, Hayek, Strigl and Morgenstern, argued that neo-marginalism^[277] is superior to equilibrium theory, that it is “the only complete synthetic scientific theory of economic phenomena in our time” (Perroux 1941, 45).

Lastly, the most important of the works published during World War II from an analytical point of view is certainly the Traite d’economiepure written by Maurice Allais between January 1941 and July 1943.

With such an approach, Allais defined what would become the general frame­work for numerous general equilibrium models. The issue he addressed was the stability of equilibrium (not its existence or unicity).^[278] Assuming an exchange economy in which the agents’ utility functions are separable, the adjustment pro­cess works under four restrictive assumptions, characteristic of a Walrasian model: (i) the price system is unique regardless of whether or not there is an equilib­rium; (ii) if supply exceeds demand on a market, the price falls and vice versa; (iii) price adjustments do not occur in all markets simultaneously, but successively when switching from one market to another; (iv) no exchange occurs outside of equilibrium.

Using the notion of surplus proposed by Pareto in his Manuel (1906, 655-6), Allais laid down in 1943 the two propositions of his “theoreme du rendement social” (theorem of social efficiency): any situation of maximum efficiency is a market equilibrium, and any market equilibrium is a situation of maximum effi­ciency. What can be learned from these statements? Allais rejected both laissez-faire and planning. Maximising social efficiency cannot be achieved in a laissez-faire regime; indeed, in industries with increasing returns, monopoly prevails, a higher price than the marginal cost is charged, thus impeding the achievement of the opti­mum. In other activities, imperfect competition, including the absence of a market for future goods, leads to a sub-optimal allocation of resources. Planism has the opposite flaws: prices cannot be determined in the absence of markets. Without this mechanism, no rigorous economic calculations can be made. But the question of the ownership of the means of production remained open.

Economic organisation must be based on autonomous economic agents, each having the free disposal, for his own part, of economic goods. But... one can imagine a society... in which the different managements of enterprises could have... the free disposal of economic goods, without the ownership of these goods ceasing to be collective.

(1943, 663)

The reception of Keynes 's ideas in France

As soon as it was published, the General Theory of employment, interest and money was presented and discussed in France (Sampaio 2016); but research on it especially increased after the Liberation. Three types of contributions can be roughly distinguished: some economists, such as Perroux, contributed to the dif­fusion of Keynes’ ideas without really sharing them, some other economists - Etienne Mantoux (1913-1945), Maurice Halbwachs (1877-1945), Robert Marjolin (1911-1986), Jean Domarchi (1916-1981), Alain Barrere (1910-1995), for instance - wanted to comment, interpret and report on it, while others - Maurice Allais, Claude Gruson (1910-2000) - aimed to develop a different economic theory from Keynes in order to answer the same questions he asked.

The second category of reactions to the General Theory focused on three main issues. How to interpret the savings-investment relationship? Should money wages or even prices be taken as given? Is the interest rate an essentially mon­etary process? While in the Treatise on Money a misalignment between savings and investment was possible and played an essential role in bringing about the appearance of pure profit, in the General Theory savings and investment are always equal. In Mantoux’s view (1937, 1565), this difference could only arise from the treatment of windfall profits, which were excluded from income in the Treatise, but included in the General Theory. Instead, Marjolin (1941, 111) argued that while investment and savings are always equal, they are not identical, as savings is not an independent value (agents are not free to determine its level, as it is set by investment).

Keynes (1937, 245) described interest as a monetary phenomenon. Marjolin justified this assertion by explaining that every individual receiving income first determines its use, and then chooses the composition of his assets by arbitrating between the liquidity and return of the various securities. If an increased invest­ment raises the interest rate, it is not because savings are insufficient but because investors need financing for their projects. For his part, Domarchi (1943) inter­preted Keynes’ view on the basis of Hicks’s formalisation of the liquidity trap (1937, 152), acknowledging that the demand for money only depends on the inter­est rate. The model is recursive: the quantity of money, as an exogenous variable, determines the interest rate which, in turn, determines income via the equality of savings and investment, without the reader knowing whether it concerns real or nominal income. Mantoux argued that Keynes assumed that workers were not looking at their real wages but at their money wages. Such an idea had already been put forward by French-speaking economists (Simiand 1932, vol. I) but took on a new relevance in the General Theory because of its role in the analysis of unem­ployment. Mantoux (1937, 570) disagreed, considering that workers are interested in their real wages. Domarchi shifted the reasoning by replacing monetary illusion with the hypothesis of monetary wage rigidity. Finally, Barrere (1952, 642) sought to refine this analysis by showing that Keynes successively adopted three different assumptions regarding the flexibility of wages and prices. In the first four parts of the General Theory, wages and prices are, for the most part, assumed to be con­stant; but in these same parts, he also proposed an interpretation in which money wage is fixed and prices are flexible. In the fifth part, Keynes studied the effects of a reduction in money wages and argued that it does not increase employment. This appeared to Barrere (1952, 175) as one of Keynes’ most critical conclusions in the General Theory.

Allais and Gruson went further in their own interpretation of the Keynesian theory. To Allais (1947, 319), Keynes’ virtue was to have shown the need to revisit the relationship between the classical theory of interest rate and monetary theory. In Economie et interet, he elaborated his own analysis of this problem without engaging in a systematic discussion of Keynes’s approach. Allais identified two markets: the financial market where bonds and shares are bought and sold, and the money market where the use of circulating money is traded. To these two markets correspond two interest rates: the financial market rate is the user price of capital, while the money market rate is the user price of money. In a stationary economy, quantities, including the quantity of money, and prices are constant over time. In equilibrium, the different interest rates are equal. Relative prices and the real inter­est rate are independent of the quantity of money. If money is growing at a steady rate, the endogenous variables are determined in the following order: first, the equilibrium in the financial market determines the real interest rate; the nominal interest rate is equal to the real rate plus the growth rate of the quantity of money. The nominal interest rate then determines real cash holdings and the ratio of the quantity of money to real cash holdings determines the general price level.

As long as money is an exogenous variable, the adjustment process is simple: if the financial interest rate exceeds the money rate, the agents reduce their money holdings and buy securities. The financial interest rate decreases, the value of indi­rect goods increases, which leads to an increase in income and consumption. Thus, the adjustment leads to a rise in prices which increases the demand for nominal cash holdings and leads to a rise in the monetary interest rate, while the increase in investment leads to a fall in the financial interest rate. However, the existence of this adjustment process does not mean that the system is stable (Allais 1947, 329). If the quantity of money in circulation is endogenous, the equilibrium may be unstable. In the process just described, the increase in money demand will not necessarily lead to a rise in the interest rate because banks will only be encouraged to discount more bills at an unchanged rate, which will lead to an expansion of the quantity of money. Of course, this cannot continue indefinitely: when the cover­age rate of banks is reduced, they will undoubtedly reduce the amount of credit granted. This does not imply stability of the equilibrium, but rather that the expan­sion phase will be followed by a recession. On this basis, Allais later developed non-linear models of cycles^[279] in which the variation in aggregate expenditure is proportional to the difference between the supply and demand of money.

Unlike Allais, Gruson, who was at the head of the Treasury Department in 1948, and the founder of the “Service des etudes economiques et financieres” (SEEF) of the French Finance Minister,^[280] presented himself as a Keynesian with some reluc­tance: he therefore set himself the goal of “introducing more rigour into the intui­tions of the General Theory” (Gruson 1949, 8). He departed from Keynes in two main respects; instead of deducing the demand for money from agents’ portfolio choices, Gruson believed that the main concern of agents was to manage their cash flow so that their cash holdings were never negative; and money, instead of being exogenous, is viewed as endogenous. While Rueff (1945, 227-71) claimed that price changes restore equilibrium, Gruson (1949, 227-31) argued that this is not necessarily the case. Suppose that an excess supply of goods causes a fall in prices. If entrepreneurs consider this fall to be temporary, they will keep a higher- than-normal stock of products and will finance them with short-term advances. The interest rate will likely rise but the central bank can intervene to stabilise it, by issu­ing money, which will tend to clear the initial surplus of goods. But this reaction may not be sufficient if the agents believe that the price decline will persist. Con­sumers will then reduce their purchases, and companies will remove their stocks of finished products and work only to satisfy confirmed orders. The fall in prices may

worsen the initial negative trend. Gruson concluded that “There is no spontaneous equilibrium in a liberal regime.... A direct intervention of public authorities in investments... is therefore necessary” (1949, 250).

Perroux and the domination effect

The end of the 1940s marked a moment of evolution in Perroux’s thinking: the new post-war world economy and the dominant role of the United States led him to revise his earlier theses. He distanced himself from neo-marginalism and general equilibrium, which he criticised for being built on the assumption of reciprocal and universal interdependence while ignoring inequalities. He complained that eco­nomics was only concerned with abstract analyses instead of looking at the actual conditions of life. “Force, power and constraint are objects congenitally unfamiliar to the modern science of economics and which these refinements have failed to integrate” Perroux wrote (1948a, 242).

To address these issues, Perroux referred to the concept of domination, a notion that had been absent from economists’ analysis of exchange until then. In some cases, domination refers to the deliberate intention of an agent to enforce unfavour­able conditions on other agents. He broke with the principle of voluntary exchange, according to which the marginal benefit obtained is equal to the marginal benefit given up. A intentionally dominates B if the marginal utility of the good transferred by B exceeds the marginal utility of the good he receives. However, domination may also be unintentional. Perroux (1948a, 248) therefore wrote that “A has an effect of domination on B if, leaving aside any particular intention of A, A has a definite influence on B without the reciprocal being true or being true to the same degree”.^[281] As he argued, domination power arises from three main sources: bar­gaining power, the nature of activities and size. He therefore believed that more precise distinctions should be introduced, referring to influence, dominance and partial domination.

Perroux first applied his analysis of domination to studying international trade. According to him, imports and exports should be considered not from individuals but from the nation, considered as an economic agent in its own right:^[282] “Eco­nomically, the nation is a group of enterprises and households, coordinated and arbitrated by a centre which holds the monopoly of public power, that is to say, by a State” (1948b, 34). If one can consider a nation’s exports and imports, this is because the units that make up the nation are subject to the same superior decision­making authority, that of the State, and because these units have a specific degree of interdependence resulting above all from the existence of a national currency and the presence of external economies at national level.

Perroux did not rely on his analysis of domination to criticise the function­ing of economic systems and particularly the functioning of capitalism. He recog­nised that domination is the means by which man’s exploitation of man occurs, but pointed out that

the main architects of the development of national economies or of the world economy are the dominant firms, the dominant national economies.... Through them... economic progress is achieved.... Through them, techni­cal and economic innovations, after breaking routines, arouse imitators and spread their benefits to large sections of the public and consumers.

(Perroux 1948b, 43)

Aggregation and choice issues

Two key colloquia were held in 1952 near Paris. In May, Darmois, Allais, Roy and Frechet (1878-1973) organised a symposium on the foundations and appli­cations of risk theory in econometrics under the aegis of the Centre National de la Recherche Scientifique; then, in June, Perroux invited Kenneth Arrow to pre­sent his book, Social choice and individual value, at a symposium on the “avan- tage collectif ’ (collective advantage) held at the Institut de Science Economique Appliquee. These two colloquia shared the common feature of giving French economists the opportunity to discuss the significant proposals put forward by Arrow on the principle of rationality in collective decisions and von Neumann and Morgenstern’s analysis of choices under uncertainty. The debates at these two meetings were different in tone: Allais’ criticism of the postulates and axi­oms of the American school was much more severe than Guilbaud’s comments to Arrow. The impact of these debates was different, undoubtedly because Allais could publish his article on “the behaviour of rational man in the face of risk” in Econometrica, whereas Guilbaud’s contribution was published in Economie Appliquee, whose circulation was more limited. Nevertheless, the debate on these two problems persisted, as shown, for example, by two articles by Mongin (2012, 2019).

From preference aggregation to judgement aggregation

During the symposium organised at the ISEA, Guilbaud, a mathematician who had been a researcher at the ISEA since 1947, gave a brilliant presentation, draw­ing attention in particular to Condorcet’s Essai sur l'application de l'analyse a la probabilite des decisions rendues a la pluralite des voix (1785).^[283] Guilbaud, while acknowledging the value of Arrow’s contribution, did not limit himself to presenting and discussing it. By referring to Condorcet and, to a lesser extent, to Cournot, he shifted the debate and dealt with issues that were close to but different from those analysed by Arrow and Bergson. Arrow’s concern was the existence of a collective welfare function, which he defined as follows:

By a social welfare function will be meant a process or rule which, for each set of individual orderings... for alternative social states (one ordering for each individual), states a corresponding social ordering of alternative social states.

(Arrow 1951, 23)

In Arrow’s analysis, social orderings, which are the arguments of the welfare func­tion, refer to fundamental values or preferences of individuals. In Condorcet’s texts, it was not a question of preference, in the sense that Arrow gave to this word;^[284] Condorcet, and Guilbaud after him, referred to judgement, to opinion. If a voter prefers this or that candidate, it is because he considers him more capable.^[285] By combining rational judgements, an irrational judgement may be obtained, and a defendant whom the majority of jurors do not consider guilty may be convicted. It can thus be argued, as Mongin (2012) did, that by generalising the analysis of aggregation of individual preferences, Guilbaud advanced the theory ofjudgement aggregation or logical aggregation.

To examine the existence of social welfare functions, Arrow assumed that agents’ preferences are complete and transitive. The social order must satisfy these two axioms and meet five conditions: (i) The social welfare function is defined for any set of admissible individual orders; (ii) Individual and collective values vary in the same direction; (iii) The social order is independent of irrelevant alterna­tives; (iv) The social welfare function is not imposed and social order depends on individual preferences; and (v) The social welfare function is not dictatorial. His general possibility theorem of the social welfare function states:

If there are at least three alternatives which the members of the society are free to order in any way, then every social welfare function satisfying condi­tions 1, 2 and 3 and yielding a social ordering satisfying axioms I and II must be either imposed or dictatorial.

(Arrow 1951, 59)

Guilbaud emphasised the significance of this theorem but regretted that Arrow presented his demonstration in a negative form, referring in an indeterminate way to a rule which he proved did not exist; he then proposed another demonstration by seeking to construct a rule that would allow a coherent global judgement to be reached in all cases where individual judgements are known. The “Condorcet effect” - that is, the existence of non-transitive social preferences - is impos­sible if one individual belongs to all majorities because the preferences of indi­viduals are assumed to be transitive. Reciprocally, “the Condorcet effect becomes apparent as soon as majorities are formed on the various questions posed which have no common elements; for then the ‘majority’ opinion is nobody’s opinion” (Guilbaud 1952, 565). In the end, if collective opinion is not to be incoherent - more precisely, if the collective order is to be transitive - one must recognise that the collective opinion is that of one of its members, the same one whatever the question asked.

Arrow (1951, 74) noted that if a majority of individuals have the same ranking of social states, the decision rule could be made by majority, supporting the idea that similar attitudes about social states are necessary for the formation of col­lective judgements. Guilbaud’s position was more radical: he argued that general interest cannot be reduced to particular interests. He demonstrated the impossibil­ity to conceive general interest as a utility function of individuals if one admits that this utility is ordinal; general interest cannot be conceived as a combina­tion of particular interests. When unanimity is not achieved, struggle prevails and, according to him, game theory should provide the basis for analysing the outcome.

Choice under uncertainty

In Theory of Games and Economic Behavior, von Neumann and Morgenstern returned to Bernoulli’s analysis of choices under uncertainty. Their contribution was widely discussed both in the United States and in France. In May 1952, the CNRS organised a conference on the foundations and applications of risk theory where American (notably Samuelson, Savage, Friedman and Morgenstern) and French (Guilbaud, Malinvaud, Pierre Masse (1898-1987), Georges Morlat (1924­2022) and Allais) economists had the opportunity to discuss their ideas. It was only after this colloquium that Allais received the results of the investigation he had car­ried out in June and September 1952, on the basis of which he rejected the theses of the “American school”.

Von Neumann and Morgenstern (1944, 26) considered a system U made up of entities u, v, w.... They postulated the existence of a complete and transitive order relation in U and an operation:

They interpreted u, v and w as cardinal utilities and p as a probability. w is a math­ematical expectation and the relation (1) states the principle of the expected util­ity theory according to which, among various risky alternatives, the one with the highest mathematical expectation of utility will be chosen. They introduce into their algebra the axiom of compound probabilities:

It makes no difference whether a combination of two random perspectives, u and v, is obtained in two successive steps - the first with probabilities p and (1 - p), the second with probabilities q and (1 - q) - or in a single step with probabilities pq and (1 -pq).

In his speech at the CNRS colloquium, Samuelson introduced the axiom of strong independence, which he considered crucial for establishing expected utility theory (1952, 672). Combining, with the same probabilities, two random perspec­tives with a third has no effect on the order of preference:

He noted that none of the axioms stated by von Neumann and Morgenstern cor­responded to his hypothesis of strong independence. Malinvaud (1953, 163) inter­vened in the discussion, arguing it was implicitly introduced in the work of von Neumann and Morgenstern, following from relation (1).

In order to analyse the independence axiom, Masse and Morlat thought that the meaning of the word preference should be clarified (1953). Let us consider two random perspectives, P₁ and P₂. We state that P₂ is absolutely superior to P₁, if, for any x, the probability of winning at least x is greater when P₂ is chosen. If this is true only for certain values of x, the two perspectives are comparable only in a subjective sense. If one perspective is absolutely preferable to the other, the inde­pendence axiom is a theorem. If not, the validity of the axiom cannot be established a priori, it is a matter of fact, and experience must be used to establish it.

Breaking with a long-standing tradition that held experimentation to be impossi­ble in economics, Allais undertook to conduct a survey that would determine whether people (considered to be rational) followed the principles of utility expectation the­ory. He focused in particular on extreme cases of very small or very high gains.

For small payoffs, it can be assumed that their utility is proportional to their amount so that the value of a random perspective is equal to its mathematical expectation. However, individuals do not always prefer the prospects with the highest mathematical expectation: cautious people prefer small but certain gains to risky bets, even if the latter are more profitable on average.

To show this, Allais (1953, 59) asked respondents to choose between the follow­ing two perspectives:

Then he asked them to choose between situations C and D defined as follows:

Cautious people may prefer to receive certainly 100 million than to run the risk, however small, of gaining nothing: they prefer A to B. For them, one can write:

but if this were so, these people would have to prefer C to D because

But this is not always the case: cautious people who prefer A to B, prefer D to C because in this second choice, the attraction of certainty has disappeared. Expected utility theory cannot explain the behaviour of agents because, according to Allais (2008), it ignores factors significantly affecting their choices: it neglects the distri­bution of utilities around their mean, whereas the shape of the density function is a crucial element for the analysis of choices under uncertainty in particular; it dis­regards the strong dependence between the various contingencies when large sums of money relative to the agents’ wealth are at stake, and it neglects the preference for safety in the neighbourhood of certainty.

For a long time, the Allais paradox appeared to be a curiosity. The expected util­ity hypothesis appeared to be a convenient way of making decisions in a risky uni­verse, even if it sometimes went wrong. However, numerous experiments revived the issue at the end of the 1970s and the axiom of independence was clearly chal­lenged. The choice of a risky project cannot be separated from events affecting the agent’s situation.^[286]

Equilibrium and optimum

In his Traite d’economiepure and in Economie et interet, Allais had raised, but not fully solved, a series of questions that French-speaking economists had already tried to answer. They concerned, in particular, the existence of equilibrium, the optimality of resource allocation and the management of public enterprises. Allais had simply noticed that his system of equations was determined. Debreu and Arrow demonstrated the existence of equilibrium, using different mathematical concepts from those employed by Allais. Allais, relying on the notion of distributable sur­plus, proposed a measure of the loss incurred by an economy deviating from the

optimum. Debreu proposed substituting a coefficient of resource utilisation. To the question of whether an increase in the amount of capital available to an economy could increase welfare, Allais answered by reasoning on a stationary economy. The optimum was then reached when the interest rate was zero in the productive sector. Malinvaud, Allais and Jacques Desrousseaux (1912-1993) generalised this reasoning to the case of a growing economy where the optimum is reached when the interest rate is equal to the growth rate. Allais had argued that, to maximise social returns, products should be sold at their marginal cost in the undifferen­tiated sector. How could this proposition be implemented? How to define mar­ginal cost? Can we accept the deficit implied by this pricing when the marginal cost is lower than the average cost? Marcel Boiteux proposed answers to these questions.

Existence of equilibrium

In August 1952, Gerard Debreu presented a paper at the National Academy of Sciences of the United States of America titled “A Social Equilibrium Existence Theorem”; in December of the same year, he presented another paper to the Econometric Society, “Existence of an Equilibrium for a Competitive Econ­omy”, written with Kenneth Arrow. Their purposes were different. In the first, he generalised the concept of game to n people and the notion of Nash equi­librium. In Debreu’s view, the action an agent chooses to take affects not only the payoffs of other agents, but the domain in which they can act. Equilibrium is reached when no player has an advantage in changing his action. What is at stake in the second paper is the existence of a solution to a system of simultane­ous equations, a la Walras, providing the equilibrium of supply and demand in each market. The structure of this model is similar to that adopted by Allais in his Traitef³

In his Theory of value, Debreu took up an idea Arrow had already suggested (1953): when studying the allocation of resources under uncertainty, one must dis­tinguish goods according to the conditions in which they are available: “A contract for the delivery of a commodity now specifies, in addition to its physical proper­ties, its place and date of availability, an event whose realisation conditions the delivery” (Debreu 1959, 106). He presented this theory as an axiomatic analysis of

23 There is no money and the mechanism of exchange is not made explicit. The goods, which are finite in number, are characterised by their physical nature but also by the place and date at which they are delivered. There are three types of agents: firms, consumers and a fictitious agent, the market partic­ipant. Each production unit can access a closed and convex set of production techniques. Production is irreversible in the sense that it is not possible for two vectors of production to compensate each other exactly. Firms maximise their profits. Competition is perfect. Consumers can be individuals or households but also institutions. The set of consumption vectors is closed and convex. A continuous function represented the preferences; there is no saturation point and indifference areas are convex. Arrow and Debreu introduced a more specific hypothesis: they believed that, for an equilibrium to exist, each individual must have enough to live on, possess goods or be able to offer his labour, and that, in equilibrium, the latter has a positive price.

economic equilibrium, probably influenced by Bourbaki’s Elements de mathema- tique (1939). To Debreu,

the theory, in a strict sense, is logically completely disjointed from its inter­pretations. To fully emphasise this split, all definitions, assumptions and main results of the theory, in the strict sense, are written in italics Such

a dichotomy reveals all the assumptions and the logical structure of the anal­ysis. It also makes possible immediate extensions of this analysis without modification of the theory by a mere reinterpretation of the concepts.

(1959, VIII)

In sum, the mathematical expression of an axiomatised theory is entirely separated from its economic content.

In Walrasian general equilibrium models, prices are given. To relax this assump­tion, it is natural to turn to Edgeworth’s analysis of an exchange economy, since he focused on the sole exchanges that are Pareto-optimal and thus defined the con­tract curve. To plot competitive equilibria on this curve, he considered an economy where consumers are divided into two groups, each comprising n agents. Within each group, consumers are identical in their resources and preferences. Edgeworth showed that with an increasing number of agents, a single competitive equilibrium tends to emerge. This outcome was generalised by Debreu and Herbert Scarf in 1963, taking up the notion of core that the philosopher of science Donald Gillies (1928-1975) had put forward: an allocation is in the core if there is no coalition of agents that can improve the situation of some consumers without worsening that of others. After having shown that the competitive equilibrium belongs to the core, Debreu and Scarf followed the procedure used by Edgeworth to prove what hap­pens to the core when the number of consumers tends to infinity: they assumed an economy including m consumer types, with r consumers of each type. They then demonstrated that if an allocation of resources between the m types of agents is in the core for any r, then it is a competitive allocation.²⁴

Resource allocation and optimum

Allais had proposed a measure of deadweight loss in terms of a specific good selected arbitrarily. Boiteux (1951a) transposed this reasoning by using Roy’s indi­rect utility function (1942) so that the loss is measured, like in Hicks, by a compen­satory variation in income. Let us consider an economy at the optimum where the utility of individual h is a function u_h (p, R_h) of prices p and income R_h. If, as a result of government policy, prices become p + δ p and income becomes R_h + δR_h, then the loss of the agent h will be δρ_h so that:

24 On general equilibrium analysis, see the books by Weintraub (1993) and Duppe and Weintraub (2014).

The total loss for the economy is the sum of the compensating movements.

To address this same problem, Debreu (1951) deviated more from Allais’ approach.^[287] He redefined optimum as a situation where, if we want to keep eve­ryone’s utility unchanged, one cannot decrease the quantity used of one resource without increasing the quantity of another. To demonstrate the two fundamental theorems of welfare economics, Allais (1943) used differential calculus; for his part, Debreu relied on the theory of convex sets. Debreu measured the deadweight loss by a coefficient of resource utilisation, defined as the ratio between the value of resources needed to enable each individual to achieve at least a given level of utility, and the value of available resources. In this calculation, resources are valued at their equilibrium price.

Allais (1947, 162-4) showed that, to apply the notion of optimum to an inter­temporal economy, one must redefine it as a situation where any increase in the satisfaction of some individuals during certain periods necessarily has as a counter­part a decrease in the satisfaction of other individuals, or of the same individuals in other periods. One may ask whether, starting from an optimal situation, an increase in initial capital can increase welfare. To address this question, one must take into account the fact that maintaining capital at a higher level requires more resources to be devoted to replacing worn-out capital. Based on this idea, Allais (1947, 180­81) demonstrated that to reach maximum productivity in a stationary economy, the interest rate in the productive sector must be zero. The question is thus what happens in a growing economy. Should one save more today to consume more tomorrow? Is there an optimal amount of capital? To answer these questions, Malinvaud (1953, 1959) and Jacques Desrousseaux (1961) used different models: Malinvaud relied on von Neumann’s model (1935-36) in which he introduced final consumption and the scarcity of natural resources, while Desrousseaux, like Allais (1962), took up the analyses of capital by Stanley Jevons (1871) and Eugen von Bohm-Bawerk (1889).

In a 1953 paper, Malinvaud distinguished between optimality, which he defined as Pareto did, and efficiency. He considered that a “chronicle” - defined as a series of time periods - is efficient if there is no other chronicle that increases the con­sumption of a good in a period while maintaining, at least, the consumption of each good in each period. Malinvaud showed that a vector of prices can be associated with an efficient or optimal chronicle. Von Neumann (1935-36) had developed a model in which all the productions increased at the same rate; the whole outcome was invested, and the final consumption was zero. To discuss optimality in this framework, Malinvaud (1959) introduced final demand into this model, defined as the difference between final consumption and the services that natural resources provide. He defined the “harmonised” growth as a process in which inputs, outputs and final demand evolve at a constant rate. He finally demonstrated that in a com­petitive economy, the rate of interest is higher than the growth rate when the value of final demand is positive (1959, 226), that is, when the value of final consump­tion is higher than that of the primary factors used. The rate of interest is lower than the growth rate in the opposite case, and the two rates are equal only if the value of final demand is zero.^[288]

Allais, on his side, described production as a temporal process (1947). He opposed primary factors - natural resources and labour - and produced means of production. A commodity which is available at time t requires primary produc­tion factors to have been used θ time periods before. The amount of expenditure incurred then depends on the relative price of factors and therefore on the interest rate. He showed that at the optimum, the interest rate must be zero in a station­ary economy. Desrousseaux (1961) extended this analysis to the case of a growth economy by introducing the concept of regularity - more specifically, the regular­ity of employment of workers involved in a given phase of the production process. Under the condition that the proportion of workers whose output will lead to final consumption in θ periods remains constant, the interest rate is equal to the optimum growth rate.

Pricing of public utilities

The nationalisation of a large number of companies after the Liberation led their directors to raise the question of the pricing of public services. In 1949, Gabriel Dessus, who was director of the commercial department of the national com­pany Electricite de France (EDF), submitted a report on the general principles of public service pricing in which he highlighted the difficulties of interpreting the notion of marginal cost. This report had a significant impact; Dessus hired Marcel Boiteux who, after having defended a thesis on the optimum under Allais’s direc­tion, was working at the SNCF (the National society of French railroads) on the possibility of implementing the marginalist principles that Allais had set out in his early works. Boiteux’s work resulted in the introduction of a “green price” (“tarif vert”):^[289] a different charge was applied depending on whether the consumption was for off-peak periods, peak periods or rush hours.

Many economists in the late 1940s took up the idea that public services should be provided at their marginal cost. Boiteux argued that “The purpose of marginal cost pricing is to charge the consumer a price such that any marginal decision concerning his consumption costs him as much as it costs the producer” (1951b, 62). But defining the meaning of the term “marginal cost” is not straightforward. To illustrate the difficulties encountered, Dessus uses the apologue of the Calais traveller. Suppose a passenger arrives at Paris-Nord station just in time to catch the train to Calais. If some seats are vacant, the cost of carrying an extra passenger is close to zero; but if an extra car has to be added (or if another train has to be run, of even a new line has to be built), the cost of carrying an extra passenger increases dramatically and one wonders how, in these circumstances, marginal cost can be measured. But even if this first problem could be solved, another would immedi­ately arise: if the marginal cost is lower than the average cost, should a price be adopted that implies a negative profit for the company? To the questions posed by Dessus, Boiteux provided an answer based on the example of electricity (1949): as consumption is irregular between off-peak and peak hours, electricity tariffs will have to be set in such a way as to flatten the peak while keeping the budget in balance.

A first issue considered is that where demand is random or fluctuates between peaks and troughs. When the firm sets its prices, it enables its customers to know the price at which, during a given period, a product will be supplied to them. Based on this demand, the company will arrange its production, building new facilities or closing down existing ones. Thus, the aim is not to solve the problem of the Calais traveller; the question is how, and at what price, the company will satisfy its customers. However, productive capacity may be inadequate when demand or production techniques change abruptly. Demand for electricity is cyclical and vari­ations in generating capacity cannot be adjusted to variations in demand. There would therefore be permanent unused capacity. Boiteux mentions the example of a power plant that has to cope with alternating days of higher demand and nights of lower demand; it has been built to produce a quantity q₀ when the load is normal. Marginal cost γ is a function of the quantity produced q and the standard load q₀. Assume that q₀ is a continuous variable: when building a power plant one can decide freely on its production capacity. The total expenditure D ( q, q₀ ) involved in producing a quantity q is minimum when the quantity produced is equal to the plant’s regular production level, q₀. The marginal cost of development, δ, is the derivative of the minimum total expenditure, D ( q₀, q₀ ), with respect to q₀. When the load is constant, the size of the installation is optimal if the product can be obtained at minimum cost: the short-run marginal cost is equal to the mar­ginal development cost γ =δ. But when the load is intermittent, that is, q₁ in the daytime and q₂ at night, the plant size will be optimal when γ₁ + γ₂ = 2d. In each period the price should be set at the short-run marginal cost. The size of the facil­ity should be such that arithmetic average prices are equal to the marginal cost of development.

Another issue arises under increasing returns: marginal cost is lower than average cost and the marginal cost pricing rule must be changed when the com­pany is subject to a budgetary condition, such as no deficit, that is incompat­ible with it. To take this issue into account, Boiteux (1956) proposed to add this requirement to the maximisation problem. His model included three sec­tors: consumers, private companies and State-owned companies. The behaviour of consumers and private companies follows the usual pattern. State-owned enterprises are subject to two types of requirements: technical requirements and the institutional rule that prescribes a given amount of profit (e.g. zero); the behaviour of nationalised companies is not a given but is precisely one of the unknowns of the system. The optimum is then searched for, which would later be called the second best, by maximising the utility of one consumer, taking the utility of other consumers as a given.

3.