Mathematical School

one of the schools in bourgeois political economy. Founded by L. Walras, it arose in the second half of the 19th century. Prominent representatives of the school include V. Pareto, W. Jevons, F. Edgeworth, I. Fisher, G. Cassel, and K. Wicksell. The most prominent forerunners of the mathematical school were A. Cournot and H. Gossen.

The approach of the mathematical school to the fundamental problems of political economy generally differs little from the conceptions prevalent in bourgeois economic thought in the second half of the 19th century and first third of the 20th. One difference in the theoretical framework of the mathematical school is an orientation toward marginalism. The use of marginal categories (marginal utility, marginal efficiency, marginal productivity) and of the principles of diminishing utility and of scarcity link the mathematical school with the Austrian school.

The mathematical school’s place in the history of economic science, however, is due to its attaching decisive importance to mathematics as a method of studying economic phenomena. This is the principle that brought together within the school scientists whose economic views sometimes differed greatly.

For the mathematical school the mathematical models of economic phenomena are of value not so much because they make it possible to describe the phenomena concisely but because they enable economists to derive from stated premises conclusions that cannot be obtained in any other way. Representatives of the mathematical school, particularly Walras, saw in mathematics a method for investigating both particular and global economic phenomena. Walras’ model of national economic equilibrium is typical. Unlike the national economic model of the post-Keynesian period, this model is not based on macroeconomic indexes such as national income, number of employed persons, and gross investment; it is based on indexes that describe the behavior of individual producers and consumers (the microeconomic approach). Each producer is described by a supply function and each consumer by a demand function. The demand and supply for each commodity are made equal in the model by means of equilibrium prices. Only outside forces can knock the system out of balance. The analysis made by Walras, Jevons, and Pareto of equilibrium conditions in the market economy had a major influence on those bourgeois economists of the mid-20th century who were studying the construction of mathematical models of the capitalist economy.

The models of Walras and other representatives of the mathematical school are far from adequately describing even the economy of capitalism in the period of free competition. They simplify and frequently also distort the real conditions of the functioning of the capitalist economic system. It is sufficient to point out that the models are static and ignore the cyclical nature of capitalist economic development, the class struggle, and other such features. At the same time, the models developed by the mathematical school have also played a positive part by stimulating the research that led in the 1950’s to the creation of an input-output intersectorial national economic model and to interesting results in the field of price formation under conditions of economic equilibrium (the models of D. Gail, K. J. Arrow, and G. Debreu).

The growth in the mathematical school’s prestige in bourgeois economic science in the second half of the 20th century is also related to a significant degree to the importance that mathematical economic models have acquired in the practical work of the state-monopoly regulation of the capitalist economy.

The mathematical school has always attracted the interest of Marxist economists. Soviet economist I. G. Bliumin made a thorough critical analysis of the representatives of the school as early as the 1920’s. With the sharply increased use of mathematical models in Soviet economic science since the 1960’s, the mathematical school has again become the object of intensive critical analysis.