# Divisia, François

# Divisia, François

Frangçis Divisia (1889–1964), was born at TiziOuzou, the principal town in the Great Kabylia region of northern Algeria. His family had been established for three generations on both the French and Algerian shores of the Mediterranean. He was awarded baccalaureates in mathematics and philosophy at the Algiers *lycée.* In 1910 he won admission to both the École Normale Supérieure and the École Polytechnique and chose to attend the latter. After two years at the École Polytechnique, he entered the government department of civil engineering (Fonts et Chaussées). In 1913 he became a graduate student at the École Nationale des Fonts et Chaussées, and at the outbreak of World War I he was mobilized as a lieutenant in the engineering corps. Promoted to the rank of captain in 1916 and wounded in 1917, he was commended in dispatches and named chevalier of the Legion d’Honneur. Having completed his engineering studies in 1919, he pursued his career as a government engineer for about ten years and was then transferred to the Ministry of National Education to devote himself entirely to research and teaching in economics, a subject that had previously absorbed his spare time. It was the influence of Clément Colson that was decisive in turning Divisia toward economics; eventually he was to succeed Colson as professor of applied economics and finance at the ficole Nationale des Fonts et Chaussées. (This was in 1932, after he had also taught for brief periods at the École Libre des Sciences Politiques, the Conservatoire National des Arts et Métiers, and the École Polytechnique.)

Divisia was to remain strongly influenced by the training, both practical and scientific, that he had received as an engineer. It played an important role in his contributions to mathematical economics, where statistical data are constantly used, and it led him quite naturally to take an active part first in the creation and then in the development of econometrics. A founding member and vice-president of the Société d’Économétrie in 1931, he was elected president of the society in 1935. In the meantime he was also elected to the Institut International de Statistique in 1933, and he became president of the Société de Statistique de Paris in 1939.

At the outbreak of World War ii, he was asked to administer the seaports for the Ministry of Public Works. There he was one of the first to appreciate the problem of determining optimum transportation routes. Confronted by the mathematical difficulties that this problem involved, he called upon the mathematician Maurice Fréchet. Frechet turned the problem over to two of his students, one of whom, Nachman Aronszajn, submitted a solution, published only much later. In this way, Divisia contributed to the genesis of linear programming, which was soon to be one of the most productive branches of operations research [*see*Operations research; Programming]. In his work *Technique et Statistique* (1941), he was also one of the first, perhaps the very first, in France to envisage and advocate the application of statistics to technical problems.

Divisia resumed his many teaching activities during the occupation and in the years following France’s liberation. He participated in an increasing number of scientific organizations, particularly on an international level. In 1951 he became a foreign member of the Accademia Nazionale dei Lincei. In 1950 he resigned from his professorship at the École Nationale des Fonts et Chaussees and was then able to give more of his time to work in the laboratories he had set up at the Conservatoire National des Arts et Métiers in 1943 and at the École Polytechnique in 1950. The laboratory at th latter institution concentrated its research on the relationships between the French economy and national defense; that at the Conservatoire focused on the collection and interpretation of statistics relevant to the state of the economy: rates of return, price indexes, and characteristics of industrial, commercial, and banking activity, as they are related to international commerce. Divisia valued this kind of research very highly and devoted considerable time to it.

**Major contributions** . The earliest of Divisia’s important contributions to economics is contained in his book *L’indice monétaire et la théorie de la monnaie* (1926). The monetary index, commonly known as the “Divisia index,” is related to a general equation of exchange, known mainly through the work of Irving Fisher but independently developed by Divisia [*see*Money, *article on*quantity theory]. Using this equation, Divisia, by differentiation, distinguished two indexes whose product is always proportional to the total payments, expressed in money, of the period to which the equation applies. These two indexes are a monetary or price index, expressing the general level of prices for the totality of monetary transactions, and an index of exchange activity (a quantity index), measuring the volume of transactions for the period involved.

The first of these is a weighted price index, with weights that vary from period to period, each period being treated as sufficiently short for the weights to be regarded as constant within the period. Price level comparisons between periods further separated in time are effected by the chain index method, which in contrast to a fixed-base method compounds the price index changes of successive (intermediate) periods, each with its own set of weights. Consequently, it is not possible to compare the price levels of nonadjacent time periods that link together the extremities of the chain of prices. The Divisia monetary index therefore involves more information about prices and quantities than do fixed-base indexes.

Divisia’s *Économique rationnelle* (1928*a*) is without doubt his masterpiece: witness its favorable reception by mathematical economists as well as by economists of the traditional school. Essentially devoted to the classical interrelationships, it is a didactic account, both synthetic and concise, and its conclusions are drawn from concrete and objective observations. The work also advances an original view of the role of money in the theory of value and of economic equilibrium. Divisia’s reputation in the scientific world was enlarged by this book; in France the work was awarded prizes by the Académic des Sciences and by the Academic des Sciences Morales et Politiques.

The questions that Divisia raised in his *L’épargne et la richesse collective* (1928*b*) in many instances anticipated aggregative problem areas that have since become very important in the writings of economists.

Since Divisia addressed himself in his teaching to practitioners in business and in industry and to students of engineering with a scientific background, he was able, while at the École Nationale des Fonts et Chaussées, to maintain close contact with the problems faced by nonacademic economists, especially problems related to technological change. In his courses he discussed, with great care and originality, problems concerning money, credit, the establishment and management of public works, and the operation of transportation facilities.

Divisia’s last important work, *Traitement économétrique de la monnaie, l’intérêt, l’emploi* (1962), is a kind of summing up of his opinions on some of the most important problems in economics. It is necessary to remember that Divisia was moved to write it primarily because of his dissatisfaction with the lack of precision in Keynes’s general theory. To highlight Keynes’s deficiencies, Divisia used mathematics for logical sequence and statistics for handling evidence.

Reacting against Keynes’s methods and faithful, instead, to classical traditions, Divisia stressed the danger of macroeconomic studies. He based his own model on the analysis of individual behavior, i.e., on microeconomics. In his opinion this is the only approach that offers sufficient reliability for the analysis of the permanent motives in decision.

The most original characteristic of his model is its distinction between three kinds of flow: (*a*) the technical flow of the circulation of goods, meaning physical units; (*b*) the monetary flow, expressed in nominal value and fed by payments correlative to the transactions involving the goods of the technical flow; and (*c*) the flow of credits and claims arising from these transactions and expressed in monetary terms. These three circuits do not overlap. They are interrelated, however, in that claims originating on the technical level are established on the contractual level and are liquidated by the circulation of money.

This analysis of economic behavior is highly aggregative, since it introduces only four types of economic agents: the household, the business enterprise, the state, and the bank. Even with this limitation, the model generates a great many equations dealing with the categories that are usually considered in presentations of this kind.

Divisia then attempted to discover the “degree of freedom” possessed by the economy, given a system of relationships that contains seven mathematical unknowns. He subtracted what are now called “policy variables,” that is, the behavioral data reflecting the policies of the economic agents. (After extensive research he had decided that there are five such variables, corresponding to policies with respect to the floating of shares, loans, self-financing, production, and the issuing of currency. ) The number of unknowns is thus reduced to two, and these must be identified with the rates of flow in the technical and monetary circuits, i.e., the total flow of goods and the total flow of money —in other words, the real and nominal manifestations of national income. In terms of equations, the two unknowns are the flow of the labor force employed and the general price level governed by the monetary unit chosen.

This leads to conclusions sharply opposed to the theories of Keynes. Here is how Divisia put it: “Full employment is possible provided that we accept the real wages that follow from it; or, if real wages are fixed, in any way, at a higher level, the necessary outcome is a certain amount of un-employment” (1962, p. 179). The model on which Divisia essentially based his critique of Keynes is a revised version of Walras’ concept of equilibrium. To be sure, it differs considerably from the latter, for it is in no way static or timeless; it can be applied to a trend and also to cyclical fluctuations. It is well suited to economic calculations because of its high degree of aggregation.

Divisia therefore confidently expressed his judgment of Keynesian theories: “… both the concept of a general, long-term equilibrium that establishes endemic underemployment without any reaction from the economic agents, and a theory of interest rates that is based solely on a preference for liquidity and excludes the productivity of capital, seem indefensible” (1962, p. 195). At best, he felt Keynes’s propositions may be used to explain relative changes over short periods of time. Construed in this way, they do not even differ fundamentally from other explanations of the particular relationships that constitute the framework of the general equilibrium. A necessary further step is to account for all the factors involved and for their various interrelationships.

RenÉ Roy

[For *the historical context of Divisia’s work, see the biography of*Keynes, John Maynard. For *discussion of the subsequent development of Divisia’s ideas, see*Econometric models, aggregate; Economic equilibrium; Index numbers; Programming.]

## WORKS BY DIVISIA

1926 *L’indice monétaire et la theorie de la monnaie.* Paris: Sirey.

1928*a Économique rationnelle.* Paris: Doin.

(1928*b*) 1931 *L’épargne et la richesse collective.* Paris: Sirey.

(1941) 1943 *Technique et statistique.* Privately published. → First published in the *Annales des ponts et chaussées.*

1950 Aspects de la technique des sondages statistiques dans le domaine social. International Statistical Institute, *Bulletin* 32, no. 2:240–244.

1951–1965 *Exposés d’économique.* 3 vols. Paris: Dunod. → Volume 1. *Introduction générate: L’apport des ingenieurs français aux sciences économiques.* Volume 2: *Assise pour les études et techniques monetaires.* Volume 3: *Assise pour les études et techniques monétaires d’économique.*

1954 Sur un avantage de la statistique graphique. International Statistical Institute, *Bulletin* 34, no. 2:268–273.

1954–1957 Divisia, Francois; Dupin, Jean; and Roy, RenÉ À *la recherche du franc perdu.* 3 vols. Paris: Société d’Édition de Revues et de Publications.

1957 Corrélation ou régression? Un exemple instructif de statistique inductive: La hausse des prix 1913–1953 en France. International Statistical Institute, *Bulletin* 35, no. 4:231–239. → Contains a summary in English.

1962 *Traitement économétrique de la monnaie, l’intérêt, l’ernploi.* Paris: Dunod.

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**Divisia, François**