Interindustry balance. Model of interbranch balance. The task of interbranch balance

About planning enough is said. Regardless of our attitude to this process, we are constantly confronted with the need to compare our forces with our desires. And if in the life of one or two people it is possible to make mistakes with plans, then on an economy of the state, or even a whole union of powers, incorrectly correlated costs with profit can be catastrophic. Therefore, in the modern economy, the interbranch balance, with its detailed production of goods and services, takes the leading place.

The balance model - what is it?

Economic and mathematical modeling of systems and production processes actively uses so-called balance models, based on the comparison and optimization of available resources. From the point of view of mathematics, the balance method presupposes the construction of a system of equations that describe the conditions for equality between the products produced and the demand for these goods.

The group under study most often consists of several economic objects, some of which are consumed internally, and some are outside its scope and are perceived as "the final product". Balance models that use the concept of "resource", rather than "product", provide an opportunity to manage the optimal use of resources.

What does the model

The method of interbranch balance is one of the most important elements of economic analytics. It is a matrix of coefficients reflecting the expenditure of resources in the specified areas of use. To make the calculations, a table is compiled, the cells of which are filled with the direct costs of manufacturing a unit of production.

Due to the complexity of the system, it is not possible to use the real indicators of any one enterprise. Therefore, the coefficients (norms) are calculated on the so-called "clean industry", ie, one that unites all production enterprises without regard for departmental subordination or form of ownership. This creates significant problems in the preparation of the information component for the model of economic systems.

Nobel Prize for the model

Soviet economists, who studied statistical indicators of the development of the national economy for the years 1923-1924, proposed the necessity of finding a balance of production between different branches. The first proposals contained only information about the quality of the links between the manufacturing industries and the use of manufactured products.

But these ideas have not found any real practical application. A few years later, economist V. V. Leontiev formulated the importance of interbranch relations in the economy. His work was devoted to the creation of a mathematical model that allowed not only to analyze the current state of the state's economy, but also to model possible development scenarios.

Interbranch balance received the name of the "input-output" method in the world. And in 1973, the scientist was awarded the Nobel Prize in Economics for developing an applied model of cross-sectoral analysis.

How the model was used

Leontiev applied the model of inter-branch balance for the analysis of the state of the US economy. By that time, theoretical postulates had taken the form of real linear equations. This calculation showed that the coefficients proposed by scientists as indicators of interrelations between industries are fairly stable and constant.

During the Second World War Leont'ev analyzed the interbranch balance of the economy of Hitler's Germany. According to the results of this study, the US military has identified strategically significant goals. And at the end of the war, the quality and volume of Lend-Lease was again determined on the basis of information obtained through the model of the inter-branch balance of Leontiev.

In the Soviet Union, this model was built 7 times, beginning in 1959. Scientists assumed that for five years, economic ties can be considered stable, so all conditions were considered static. Nevertheless, the methodology was not widely disseminated, since the political conjuncture was more influenced by the interconnection of production industries. Real economic relations were considered as secondary.

The essence of the concept

The model of interbranch balance is the determination of the interrelations between output in one industry and the costs and consumption of goods of all industries involved in the production of these products. For example, coal mining requires steel tools; At the same time coal is needed for steel smelting. So, the task of interbranch balance is to find a correlation of coal and steel, at which the economic result will be maximum.

In a broader sense, we can say that based on the results of the constructed model, it is possible to determine the efficiency of production in general, to find optimal methods of pricing and to identify the most significant factors of economic growth. In addition, this method allows for forecasting.

Main goals

• Structuring the reproduction processes, based on the material and material composition of the sectoral resources.
• Illustration of the processes of output and its distribution.
• A detailed study of the production process, the creation of goods and services, the accumulation of income at the level of branches of the economy.
• Optimization of identified significant production factors.

For the input-output method, analytical and statistical functions are defined. Analytical allows to predict dynamic processes of development of branches and economy as a whole; Simulate situations, changing various data and indicators. The statistical function ensures verification of consistency of information coming from various sources - from enterprises, regional budgets, tax services, etc.

Mathematical view of the model

From the point of view of mathematics, the balance model is a system of differentiated equations (and not always linear ones) that reflect the equilibrium conditions between the total output produced in the industry and the need for it.

Models of economic systems are often presented in the form of a table (see the figure). In it, the aggregate product is divided into 2 parts: internal (intermediate) and final. The national economy is seen as a system of n pure industries, each of which acts as a producer and consuming.

Quadrants

Leontief's interbranch balance is divided into four parts (quadrant). Each quadrant (in the figure they are denoted by the figures 1-4) has its own economic content. In the first one, inter-branch material relations are displayed - it is a kind of chess game. Coefficients located at the intersection of rows and columns are denoted by XY and contain information on the flow of products between industries. X and Y are the numbers of industries that produce and consume products. The designation x23, for example, should be interpreted as follows: the cost of the means of production produced in the industry 2 and consumed in the industry 3 (material costs). The sum of all elements of the first quadrant is an annual fund for the reimbursement of material costs.

The second quadrant is the totality of the final output of all production branches. The end product is a product that goes beyond the production sphere to the area of final consumption and accumulation. The detailed balance sheet illustrates the use of such goods: public and personal consumption, accumulation, reimbursement and export.

The third quadrant describes the national income. It is the sum of net output (wages and net income of industries) and a reimbursement fund. And in the fourth, information about the final distribution is displayed. It is located at the intersection of the columns of the second and the lines of the third quadrant. This information is necessary for understanding the formation of the system of incomes and expenditures of the country's population, sources of financing, expenditures of the non-productive sphere, and so on.

Note that the total of the second, third and fourth quadrants (each separately) should be equal to the product created for the year.

The system of equations

Despite the fact that the gross social product is not formally part of any of the above parts, it is still present in the balance sheet. The column that is to the right of the second quadrant, and the row below the third, represent the gross public product. The information obtained from these elements allows you to verify the correctness of filling the entire balance. In addition, it can be used to compile an economic-mathematical model.

Denoting the gross product of the industry through X with an index corresponding to the number of this industry, we can formulate two basic relationships. The economic meaning of the first equation amounts to the following: the sum of the material costs of any branch of the economy and its net production is equal to the gross product of the industry described (columns).

The second equation of the interbranch balance shows that the amount of material inputs consuming a certain product and the final product of a particular sphere represent the gross output of the industry (the balance line).

The finite form of the system of equations

Taking into account all the above formulas, the following concepts are introduced into the model:

• Matrix of coefficients of direct costs A = {ay};
• Vector of gross output X (column);
• Vector of final product Y (column).

The model in the matrix form will be described by the relation:

X = AX + Y.

It remains only to recall that the balance is made in both natural values and in the monetary dimension.