Enough has been said about planning. Regardless of our attitude to this process, we are constantly faced with the need to balance our strengths with our desires. And if in the life of one or two people it is possible to make mistakes with plans, then the economy of the state, or even the whole union of powers, incorrectly correlated costs with profit can have a catastrophic effect. Therefore, in the modern economy, the intersectoral balance with its detailed production of goods and services takes a leading place.
The balance model - what is it?
Economic and mathematical modeling of systems and production processes actively uses the so-called balance models based on the comparison and optimization of available resources. From the point of view of mathematics, the balance method involves the construction of a system of equations that describe the conditions of equality between the manufactured products and the need for these products.
The studied group most often consists of several economic objects, part of the products of which are consumed internally, and part is taken out of its framework and is perceived as the “final product”. Balance models that use the concept of “resource” rather than “product” make it possible to manage the optimal expenditure of resources.
What gives the model
The intersectoral balance method is one of the most important elements of economic analytics. It is a matrix of coefficients reflecting the expenditure of resources in a given direction of use. For calculations, a table is compiled, the cells of which are filled with direct costs for the production of a unit of output.
Due to the complexity of the system, it is not possible to use the real indicators of any one enterprise. Therefore, the coefficients (standards) are calculated on the so-called "clean industry", that is, one that unites all production enterprises without regard to 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 Model
For the first time, the Soviet economists who studied the statistical indicators of the development of the national economy for 1923-1924 proposed the need to find a balance of production between different industries. The first proposals contained only information about the quality of relations between manufacturing industries and the use of manufactured products.
But these ideas did not find real practical application. A few years later, the economist V.V. Leontyev formulated the importance of intersectoral 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 economy, but also to model possible development scenarios.
Intersectoral 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 the development of an applied model of intersectoral analysis.
How was the model used?
For the first time, Leontyev applied the model of interindustry balance to analyze 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 the relationships between industries are quite stable and constant.
During the Second World War, Leontyev analyzed the intersectoral balance of the economy of Nazi Germany. According to the results of this study, the US military 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 Leontyev model of interindustry balance.
In the Soviet Union, such a model was built 7 times, starting in 1959. Scientists have suggested that for five years, economic relations can be considered stable, therefore, all conditions were considered static. Nevertheless, the methodology was not widely used, since the political conjuncture was more influenced by the interconnection of production sectors. Real economic ties were seen as secondary.
The essence of the concept
The intersectoral balance model is the definition of the relationship between the output of products 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 steelmaking. So, the task of the interindustry balance is to find a ratio of coal and steel at which the economic result will be maximum.
In a broader sense, we can say that according to the results of the constructed model, it is possible to determine production efficiency in general, find optimal pricing methods and identify the most significant factors of economic growth. In addition, this method allows you to do forecasting.
Main tasks
- Structuring reproduction processes, based on the material composition of industry resources.
- Illustration of the processes of production and its distribution.
- A detailed study of the production process, the creation of goods and services, the accumulation of income at the level of economic sectors.
- Optimization of identified significant factors of production.
For the input-output method, analytical and statistical functions are defined. Analytical allows you to predict the dynamic processes of development of industries and the economy as a whole; simulate situations by changing various data and indicators. The statistical function provides verification of the consistency of information coming from various sources - from enterprises, regional budgets, tax services, etc.
The 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) that reflect the equilibrium conditions between the total output produced in the industry and the need for it.
Models of economic systems are most often presented in the form of a table (see. Fig.). In it, the total product is divided into 2 parts: internal (intermediate) and final. The national economy is considered as a system of n pure sectors, each of which acts as a producing and consuming.
Quadrants
Leontief's interindustry balance is divided into four parts (quadrant). Each quadrant (in Fig. They are indicated by the numbers 1-4) has its own economic content. The first displays interbranch material ties - this is a kind of chess. Coefficients located at the intersection of rows and columns are denoted by XY and contain information on the flow of products between sectors. 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 released in industry 2 and consumed in 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 aggregate of the final products of all manufacturing sectors. The final product is called, which goes beyond the scope of production in the field of final consumption and accumulation. A detailed balance sheet illustrates the directions of use of such a product: public and private consumption, accumulation, compensation and export.
The third quadrant describes national income. It represents the sum of net production (labor remuneration and net income of industries) and the reimbursement fund. And the fourth displays information about the final distribution. It is at the intersection of the columns of the second and the rows of the third quadrants. This information is necessary for understanding the formation of the system of incomes and expenditures of the country's population, sources of financing, costs of the non-productive sphere, etc.
Note that the total result of the second, third and fourth quadrants (each separately) should be equal to the product created for the year.
System of equations
Despite the fact that the gross social product is formally not part of any of the above parts, it is still present in the balance sheet. The column to the right of the second quadrant and the row below the third display the gross social product. The information obtained from these elements allows you to check the correctness of filling the entire balance. In addition, it can be used to create an economic-mathematical model.
Having designated the gross product of the industry through X with an index corresponding to the number of this industry, two main relations can be formulated. The economic meaning of the first equation is as follows: 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 interindustry balance shows that the sum of the material costs of consuming some product and the final product of a particular sphere is the gross output of the industry (balance sheet).
