About planning Enough said.Whatever our attitude to this process, we are constantly faced with the need to match their strength with their wishes.And if the life of one or two people can make mistakes with the plans on the economy of the state, and even the whole Union powers incorrectly correlated costs with a profit can dramatically affect.Therefore, in today's economy intersectoral balance with its detail of goods and services is a leader.

## Balance model - what is it?

Economic-mathematical modeling of systems and processes to actively uses the so-called balance models based on the comparison and optimization of available resources.In mathematical terms, the balance method involves the construction of a system of equations that describe the condition of equality between the products and the need for these products.

study group often consists of several economic projects, which are part of the production is consumed domestically, and is excreted beyond it and is perceived as the "final product".

## What gives

model of interbranch balance method - one of the most important elements of economic analysts.It is a matrix of coefficients reflecting the expenditure of resources for given areas of use.For the calculations, a table whose cells are filled with the regulations of direct manufacturing costs per unit of output.

Because of the complexity of the system using real indicators of a single enterprise is not possible.Therefore, the coefficients (ratios) are calculated on the so-called "clean industry", ie. E. One that integrates all manufacturing facilities without regard to departmental subordination or form of ownership.This creates a significant problem in the preparation of the information component of the model of economic systems.

## Nobel Prize for model

the first time about the need to find a balance between the various branches of production offered Soviet economists who have studied the statistics of economic development for 1923-1924.The first proposals contained only information about the quality of links between the industrial sectors and the use of these products.

but the real practical application of these ideas are not found.Several years later, the economist W. Leontief formulated the importance of inter-sectoral linkages in the economy.His work has been devoted to creating a mathematical model that allows us not only to analyze the current state of the economy of the state, but also to simulate possible scenarios.

interbranch balance was in the world the name of a "cost-output".And in 1973 the scientist was awarded the Nobel Prize in economics for developing application model input-output analysis.

## how to use the model

first model of interbranch balance Leontiev applied to analyze the state of the US economy.By the time the theoretical postulates acquired real form of linear equations.This calculation showed that the rates proposed by scientists as indicators of linkages between sectors, are quite stable and constant.

During the Second World War has been analyzed Leontief input-output balance of the economy of Nazi Germany.According to the results of this study US military identified the strategically important objectives.And after the war, the quality and volume of Lend-Lease back still determined on the basis of information obtained through the Leontief input-output model.

The Soviet Union built a model 7 times since 1959.Scientists suggest that the past five years economic relations can be considered stable, so the conditions were considered static.However, the technique has not received the widest distribution, t. To. On the relationship productive sectors largely influenced the political situation.The real economic relations were seen as secondary.

essence of the concept model of interbranch balance - the definition of the relationship between the production in the same industry, and the costs and consumption of goods of all sectors involved in the production of these products.For example, coal mining, steel tools are needed;while for steel needs coal.So, the problem of interbranch balance is to find such a ratio of coal and steel, in which the economic result will be maximum.

In a broader sense we can say that the results of the constructed model can determine the efficiency of production in general, find the optimal pricing policy and to identify the most important factors of economic growth.In addition, this method allows you to engage in forecasting.

## main tasks

- structuring the process of reproduction, on the basis of the material and the material composition of industry resources.
- Illustration of production and distribution.
- detailed study of the production process, the creation of goods and services, income generation at the level of industries.
- optimization revealed the essential factors of production.

to the method of "input-output" are defined analytical and statistical functions.Analytical predicts the dynamic processes of development of industries and the economy as a whole;to simulate the situation by changing various data and indicators.Statistical function ensures consistency check information from different sources - from enterprises, regional budgets, tax services, and so on. D.

## Mathematical model view

In mathematical terms, the balance model - a system of differential equations (andnot always linear), which reflect the conditions of equilibrium between the industry generated total production and the need for it.

models of economic systems often presented in tabular form (see. Fig.).It combined the product is divided into 2 parts: the inner (intermediate) and final.The national economy is considered as a system of n net branches, each of which plays the role of producing and consuming.

## Quadrants

Interbranch balance Leontief divided into four parts (quadrants).Each quadrant (Fig. They are numbered 1-4) has its economic content.In the first display intersectoral communication material - a kind of checkerboard.The coefficients located at the intersection of rows and columns, designated XY and contain information about the flow of goods between branches.X and Y - number of industries that produce and consume products.Designation X23, for example, should be interpreted as follows: the cost of capital goods produced in sector 2 and 3 consumed in the industry (material costs).The sum of all elements of the first quadrant is the annual fund compensation for material costs.

second quadrant is a collection of the final product of all industrial sectors.The end product is called, which is beyond the scope of production to final consumption and savings.The detailed diagram illustrates the balance of uses of such goods: public and private consumption, capital formation, compensation and export.

third quadrant describes the national income.It is the sum of net production (wages and net income of branches) and the compensation fund.And in the fourth display information about the final distribution.It is at the intersection of rows and columns of the second third quadrants.This information is essential for understanding the formation of revenues and expenditures of the population, sources of financing, the costs of non-productive sphere, and so on. D.

Note that the overall outcome of the second, third and fourth quadrants (individually) shall be established for the year product.

## system of equations

Despite the fact that the gross social product is not formally a part of any of these parts, it is still present in the balance sheet.The column to the right of the second quadrant, and the string located under the third, reflect 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 help to create economic and mathematical models.

Designating industry gross product by X with the index corresponding to the number of the industry, we can formulate two basic relations.The economic meaning of the first equation is the following: the amount of material costs of any branch of the economy and its net production is described by industry gross product (columns).

second equation interbranch balance shows that the amount of material costs consume some goods and the final product of a sphere are the gross output of the industry (line balance).

## end view of the system of equations

With all these formulas in the model introduced such concepts:

- matrix of coefficients of direct costs A = {ay};
- gross output vector X (column);
- vector of the final product Y (column).

model in matrix form will be described by the relation:

X = AX + Y.

remains only to recall that the balance is in a life-size, and in terms of money.