General economic equilibrium, Social efficiency and the Economy of markets

By Bertrand Munier

For Maurice Allais the three greatest economists were Vilfredo Pareto, Irving Fisher and Léon Walras (in that order). So it will come as no surprise that, in his efforts to rebuild economic analysis on new foundations, between 1941 and 1947, Allais should have concentrated on the general equilibrium introduced by Walras and revised by his successor at Lausanne Vilfredo Pareto. What is less well known is that, in the light of experience, Maurice Allais went on to qualify and modify this remarkable initial contribution by offering a second conception of economic analysis in the form of a general theory of surpluses and of the economy of markets (note the plural)..

I. The reconstruction of economic analysis (1943-1947)

Three works were to punctuate this fundamental formative period in the thought of Maurice Allais:

• The monumental Traité d’Economie Pure [Treatise on pure economics], published[1] in 1943 by the Ateliers Industria under the title À la Recherche d’une discipline économique [In search of an economic discipline], and later (1952) as Treatise on pure economics by the Imprimerie Nationale (with the addition of a long 63-page General Introduction) – a difficult and technical work in which Maurice Allais describes the basic behaviour of consumption and production as well as the states of the economic system to which they lead. He then tackles the properties of these states in detail and demonstrates for the first time with rigour that:
1. an equilibrium state necessarily displays maximum social efficiency (i.e., in more everyday language, is Pareto-optimal) under certain fairly general assumptions, but for a given distribution of incomes (the theorem called direct in the New Welfare Economics);
2. that a Pareto-optimal state can be achieved, under more restrictive conditions, as equilibrium state, if the economy is managed in a decentralized way by a system of prices. This “second theorem of Welfare Economics” was to provide the basis of the economic and political programme of the Prague Spring, never in fact implemented for obvious reasons. The proof used by Maurice Allais to demonstrate it was entirely original in formulation and is worth comparison with Lyapunov’s second method.
• A work of more modest dimensions, which reprises the bulk of the findings just mentioned in a more condensed form – Economie Pure et rendement social [Pure economics and social efficiency], published in 1945. This work was to be complemented a few years later (1953) by an article published in Econometrica under the title “The extension of the theories of general equilibrium and of social efficiency to the case of risk”, an article which makes use of the progress in risk theory discussed elsewhere in this site.
• Finally a work of decisive importance, Economy and Interest, published in 1947 by the Imprimerie Nationale in two volumes (some 800 pages in all), which introduces a major idea in economic analysis, that of overlapping generations, an idea often, but wrongly, attributed to Samuelson (1958) in an article written eleven years later. This concept notes the apparently simple fact that in the same economy there coexist different generations, whose characteristics in terms of wealth, income, etc., are not the same today and will not be the same tomorrow. Maurice Allais reprises therein the main themes of the preceding work, while focussing attention on economic dynamics and the role played by the determination of the rate of interest in this social dynamic. Specifically he points out that the coexistence of different generations calls for regulation by the State – the limits of the market economy having been reached – to help determine a suitable level for the rate of interest. In particular he demonstrates that in a stationary economy the rate of interest must be zero. This was the first statement of what later came to be called the “golden rule”, attributed – once again mistakenly – to Phelps (1960), according to which the “pure” rate of interest, if the optimum is to be ensured, must be equal to the economy’s sustained rate of growth. Moreover, in a footnote to the same work, Allais formulates the model of money balances later christened the “transaction money” model, the paternity of which, by yet another error, is attributed to William Baumol (1952) [2].

The three works mentioned comprise a remarkable ensemble. Indeed they comprise the very ensemble which the Nobel Prize Committee made a point of saluting in 1988. At the prize-giving ceremony, Ingemar Stahl presented it in the following words: “In 1943, during the dark years of German occupation, a remarkable work in economic theory was published in France. The title was À la Recherche d’une Discipline Économique [In Search of an Economic Discipline] (…) Along with a new extensive study published in 1947 entitled Economy and Interest, his work from 1943 constituted a more complete, more rigorous and more generalized mathematical description of a market economy than anything published earlier by economic scientists or at about the same time, though independently, by previous laureates, the British economist Sir John Hicks and the American economist Paul Samuelson.”

II. The general theory of surpluses and the economy of markets (1967–)

Right from his ground-breaking work of the preceding period, which I shall henceforth refer to as the Treatise on Pure Economics, Maurice Allais had introduced a notion of economic “surplus” or “loss”, which generalized the earlier notions of “consumer surplus” (due to Marshall – in partial equilibrium – and to Hicks). These notions have an immediate relevance in terms of characterizing Pareto-optimal states. But their significance for the notion of economic equilibrium enabled Maurice Allais to contribute an original generalization of the modelling of economic behaviour which leads into the theories of markets and their microstructures, which were to be developed later.

The difficulties involved in calculating the marginal costs in various studies connected with transport (1947, 1964) were the starting point which led Maurice Allais to question the construction of the neoclassical economy of the Walrasian tradition. In the fable of the “Traveller from Calais”, he enquires how much it costs to convey a traveller by train from Calais to Paris. The ticket-inspector replies: almost nothing, for the presence or absence of an unoccupied seat in a carriage makes practically no change to the costs incurred by the railway company. The conductor replies that it is a fraction $\frac{1}{n}$ of the overall costs of the $n$ seats available in a carriage, for if the number of travellers continues to increase after the carriage is full, a new carriage will be needed… Indeed the conductor goes further, for he notes that the number of carriages to be pulled by a locomotive cannot be increased indefinitely: so above a certain number $w$ of carriages, another locomotive will be called for. Hence in total each seat costs $\frac{1}{n}\times\frac{1}{w}$. But the network manager remains unsatisfied, for it is not possible for an indefinite number of trains to travel on the same track and above a number $t$ of trains, the track will have to be doubled. Hence in his view the seat costs $\frac{1}{n}\times\frac{1}{w}\times\frac{1}{t}$… Always assuming, of course, that a single price applies to each carriage, each locomotive and indeed to each track…

As the fable illustrates, there are grounds for doubting the assumption of the general convexity of the total and marginal cost functions – an assumption without which the Walrasian economic equilibrium is not defined, at least in the short term. Doubts may also be entertained as to whether the price system is in fact unique at every point in time… This led to a paper read by Allais at Milan (1967), followed up by an article in the Revue d’Économie Politique (1971), and ultimately to the book on the General Theory of Surpluses (1981) which has since been republished.

Allais observes that the academic literature over-concentrates on equilibrium – its existence and its implications for the management of the economy – whereas these implications are subject to very restrictive assumptions, particularly that of the uniqueness of the price of each article and that of the convexity of the cost functions – at least above a certain activity level threshold. In reality, noted Allais, the analysis of the processes by which an economic equilibrium is – or is not – reached is of far greater interest. The economic dynamic is at first a series of disequilibria before a state of equilibrium is – perhaps – reached.

Use is then made of the notion of loss or of surplus: Maurice Allais holds that the pursuit, exploitation and distribution of realizable surpluses is the prime mover of economic activity. He further remarks that the definition of the distributable surplus does not depend on any condition of convexity or of uniqueness of prices. This enables the Walrasian vision of the market economy (market in the singular and subject to general convexity and a unique price system) to be replaced by “the model of an economy of markets [plural] in which all the transactions take place [between two agents] at specific prices,” which are not necessarily identical from one transaction to the next or from one sub-set of agents to another. Yet Allais is able to demonstrate that:

(1) every Pareto-optimal state is a state of zero-loss, when no constraint is involved other than is “natural” (i.e. total demand for any good is at most equal to the availability of this good in the economy);

(2) any economic decision not liable to release a surplus is to be avoided;

(3) if further constraints are imposed in addition to those that are “natural” (a point of common ground between the theory of the second best and a good many sociological and even cognitive theories), the choice of the lowest loss starting from the situation one is then in must always be a justified criterion of action;

(4) economic processes are precisely comprised of sets of effective specific exchanges of the kind just outlined (Maurice Allais here distances himself from Walrasian trial-and-error and draws closer to “effective” Keynesian concepts as opposed to “notional” Walrasian ones);

(5) all these processes generally take place in a universe of multiple prices – albeit at the same time and place – for the same good or service;

(6) economic equilibrium is reached when no further surplus can be released among the realizable states of the economic system, and only then can the price system be considered unique;

(7) finally, any equilibrium so defined corresponds to a situation of maximum economic efficiency.

This last finding may be seen as a new demonstration of the first theorem of welfare economics, first demonstrated – though under conditions that are much too restrictive – by Pareto in 1914. But it may also be seen, if non-natural (and possible non-economic) constraints are imposed, as a new demonstration of Lancaster’s (1956) second best theorem, for nothing in such a case implies that the realization of a condition supplementary to those of the Pareto optimum corresponds to the lowest realizable loss starting from the present state of the economy, i.e. draws the state of the economy nearer to a realizable optimum. It will be agreed that the economy of markets, in the plural, represents a considerable generalization of the neo-classical economic analysis.

Here too we find a goldmine for potential research: How, starting from an initial situation of ownership of goods and services, are the possible states of equilibrium to be characterized? How should we characterize the sequences of passing from one realizable state to another in order to attain – at the cost of successive disequilibria in general – a state of economic equilibrium and hence of maximum efficiency (of maximum social efficiency or of Pareto-optimality, or, more often of second-best optimum)? And so on. The basic ideas are here in place and the construction of an alternative intellectual edifice to the Walrasian theory has made remarkable progress thanks to Allais… But this version of the dynamic of a decentralized capitalist economy remains to be completed.

Thus Maurice Allais’s contribution to economic analysis is both multifaceted and coherent, and contains the seeds of a potential renewal awaited by many. It is worth recalling the words of the Governor of the European Central Bank in the speech by which he opened the ECB’s Central Banking Conference (Frankfurt, 18th November 2010): “When the Crisis came, the serious limitations of existing economic and financial models immediately became apparent. Macro Models failed to predict the crisis and seemed incapable of explaining what was happening to the economy in a convincing manner. As a policy-maker during the crisis, I found the available models of limited help. In fact, I would go further: in the face of the crisis, we felt abandoned by conventional tools. In the absence of any clear guidance from existing analytical frameworks, policy-makers had to place particular reliance on experience. These words are eloquent indeed.

Recent work in economics and finance concerning the microstructure of the markets no doubt constitute one of the research paths which continue Allais’s efforts just mentioned, by taking, as it were, the same approach to the problem – that of the technology of individual market exchanges, in order to return, if possible, to the realizable states of the economy, etc. And this is undoubtedly one possible way of shedding light on the Allaisian vision of the current capitalist world. But there are others… so to your screens and keyboards, young researchers!

[1] The word ought to be put in quotation marks: a humble spirit duplicator was the main machine used for this “publication”. These were days of war and hence of penury.

[2] The misattribution of the contributions mentioned have now been admitted, following the publication of the work of Boiteux, Montbrial and Munier (eds., 1986), by all of those previously credited with having originated them; they have shown great kindness in recognizing Allais’s precedence.