Coefficients of Total Expenditures

(coefficients of total expenditures of the objects of labor), the sum of direct and indirect expenditures of the output of one sector to produce a unit of output of another sector. For example, the total expenditure of coal to produce machine tools involves more than just the coal expended at machine tool plants. The expenditure also includes the coal used to produce the metal, plastics, and other materials from which the machine tools are made, to generate the electric power involved in the production, to extract and concentrate the ores and to produce the coke and other raw materials from which the metals and other materials used in manufacturing machine tools are made, and to ship the materials to the points of use. In brief, it is necessary to consider the total expenditure of coal along the entire chain of technological links between machine tool manufacture and other sectors of physical production. Coefficients of total expenditures are calculated by computer on the basis of tables (matrices) of coefficients of direct expenditures.

Unlike the coefficients of direct expenditures, which are a part of the costs of producing the particular type of output, the coefficients of total expenditures cover elements of the costs of producing the products indirectly related to production of the given type of output. It follows from this that the coefficients of total expenditures for individual sectors cannot be added up and related to gross output of these sectors, such as is done with the coefficients of direct expenditures. The sum of the coefficients of total expenditures for sectors expresses the enormous internal circulation that occurs during the process of producing products under conditions of the social division of labor.

Coefficients of total expenditures are very closely related to final product, that is, to the part of output used for nonproductive consumption, savings, export, and replacement of worn-out fixed capital. Thus arises one of the most important features of coefficients of total expenditures: multiplying the matrix of coefficients of total expenditures by the vector of final products yields the volume of gross output for each sector. This multiplication is carried out according to the rules of matrix calculus and is expressed as follows:

(E − A)⁻¹ · Y = X

where (E − A)^-l is the matrix of coefficients of total expenditures; Y, a vector, is the final product column; and x, a vector, is the output column. This characteristic of coefficients of total expenditures is very important for planning calculations. With data on the volume and composition of final products and the coefficients of total expenditures, the dimensions of the gross output of each sector can be calculated. Thus, depending on the proportions outlined in the plan between consumption and savings and the sectorial structure of each, it is possible to obtain different variations of the national economic plan and select the optimal one.