# Economic Model, Mathematical

## Economic Model, Mathematical

a model of an economic entity or process the description of which involves the use of mathematics.

Mathematical economic models may be constructed to analyze various premises and principles of an economic theory, to provide logical substantiation of observed economic patterns, or to process and systematize empirical data. Their applications include the practical forecasting, planning, and management of the national economy and the improvement of planning and management of the economic mechanism as a whole and of other aspects of society’s economic activity.

According to their purpose, models may be classified as descriptive and constructive. Descriptive models are used to help explain various existing economic phenomena and processes. Classic examples are models of economic growth and models of competitive economic equilibrium. The latter may be regarded as the first mathematical economic models in history. Their origins can be traced back to the famous *Economic Table* of the Physiocrat F. Quesnay. In this work Quesnay attempted to explain the creation and redistribution of income.

Modern equilibrium models involve aggregates of producers and consumers, the producers being described by means of a set of production capabilities and the consumers being described by means of certain functions or procedures that specify a preference or a choice of consumer goods. Producers try to select a mode of production that will produce maximum profit, and consumers seek to obtain the market basket of goods that will bring them the maximum degree of satisfaction for the money they have to spend. The consumers’ funds (budget) are formed from producers’ profits through some specified profit redistribution mechanism. A state of equilibrium is attained when no producer or consumer is interested in altering his activity. Equilibrium models are used for the description of both capitalist and socialist economies. In essence, the coordination of various, including opposing, interests is investigated in such models.

Descriptive models include economic growth models designed to forecast the basic aggregate indicators of development of the national economy and forecasting models for various parts of the economy. The latter models, which are based on mathematical statistics, particularly on correlation analysis, are used to study and forecast the behavior of multifactor economic processes, such as the dynamics of prices on the world market or of stock exchange indexes. Also classed as descriptive models are models that merely simulate the behavior of various parts of the economy, for example, models that simulate the development of an enterprise or firm.

The development of constructive models represents a new stage in the modeling of economic phenomena. The principal distinctive feature of such models is that they model the economy that society creates; in particular, they model desirable changes in the existing economy. Constructive models have had a considerable influence on the development of economic theory as a whole. The first models of this type were the reproduction schemata of K. Marx, the analysis of which led Marx and subsequently V. I. Lenin to conclude that the production of means of production—especially the production of means of production for the production of means of production—necessarily develops more rapidly than does the production of consumer goods (*see*REPRODUCTION).

The constructive approach to the modeling of economic phenomena is inherent in the socialist economy, in which economic construction can be carried out on a scientific foundation. The discovery of linear programming, a mathematical discipline for analyzing and solving extremum problems with constraints, in the late 1930’s stimulated the rapid development of constructive models. The optimal planning model of a socialist economy was developed on the basis of linear programming. Within the framework of this model precise definitions were obtained of such concepts as optimum, optimal plan (*see*OPTIMUM, NATIONAL ECONOMIC), social utility, and socially necessary expenditures of labor. This model, like the model of an ideal gas in physics, was an ideal model; it generated an entire spectrum of optimal planning models that take into more complete account various aspects of the actual planning process. To be sure, the model incorporated such assumptions as the linear dependence of output on expenditures, the infinite divisibility of products, the existence of an exact mathematical formulation of the global objective of society, the absolute admissibility and validity of the information used, and the presence of infinite computational capacity. Nevertheless, it provided the foundation for the theory underlying the System for the Optimal Functioning of a Socialist Economy (SOFE), which is being developed in the USSR.

In terms of their basic premises, optimal economic growth models may be classed as optimal planning models. They are used to investigate the potential development of an economic system over time and to define the optimum of economic growth and the factors that influence the maximum growth rate.

The further development of planning models necessitates the creation of systems of planning models where each model in a system is developed and used by an appropriate planning or administrative agency. Mathematical means are being developed for the purpose of resolving problems relating to the coordination of the solutions of individual models. As economic factors are incorporated into models with increasing precision, the models become more complicated, and their subsequent analysis and, in some measure, use become more difficult. For this reason, computers have been increasingly used in the construction, analysis, and practical application of models.

The division of mathematical economic models into descriptive and constructive types is somewhat arbitrary. For example, the report intersector balance is a purely descriptive model, but the planning intersector balance has both descriptive and constructive properties. The construction of integrated models of the functioning of economic systems is one of the basic trends in the development of mathematical economic models. The models of functioning reflect not some isolated economic process, such as the planning process, but the aggregate of all basic processes, including planning, production activity proper, material and technical supply, management of plan fulfillment, coordination of the interests of different agencies, and pricing. For this reason, the model of the functioning of an economic entity consists of building blocks that use diverse mathematical apparatus. The analysis of such an integrated model involves primarily numerical experiments using computers and appropriate statistical processing.

The variables that are to be defined as a result of the “solution of the model” may be not only numerical characteristics, such as output volume or the use or nonuse of various technological methods, but also the algorithm of activity or the structure of the interaction of parts. For example, algorithms pertaining to the compilation of the plan vary, as do algorithms relating to the interaction of enterprises and of material and technical supply agencies; in addition, the production structure of enterprises varies.

### REFERENCES

Nemchinov, V. S.*Ekonomiko-matematicheskie metody i modeli*[2nd ed.]. Moscow, 1965.

*Matematiko-ekonomicheskie metody i modeli: Bibliograficheskii ukazatel’*. Leningrad, 1968.

Kantorovich, L. V., and A. B. Gorstko.

*Optimal’nye resheniia v ekonomike*. Moscow, 1972.

V. L. MAKAROV