Intersectoral balance is used for analysis and planning. Fundamentals of the national economy Intersectoral balance

Intersectoral balance reflects the production and distribution of the gross national product in the sectoral context, intersectoral production relations, the use of material and labor resources, the creation and distribution of national income.

The intersectoral balance is represented by natural and cost interdependencies of the sectors of the economic system, shown in tables (matrices) and analytically (systems of equations and inequalities).

Consider a simple example of a cost balance for an economic system with three sectors: agriculture, industry, and households. In each sector, for the production of goods and services, resources are spent (raw materials, labor, equipment) created in it and in other sectors of the economic system.

Each sector in the system of interbranch relations is both a producer and a consumer.

The purpose of the balance sheet analysis is to determine how much output each sector must produce to meet the needs of the economic system for its products.

The unit of measure for the volume of goods and services is their cost.

1. Agriculture - 200 thousand rubles, including:

• for their needs - 50 thousand rubles,
• in industry - 40 thousand rubles,
• in households - 110 thousand rubles.

2. Industry - 250 thousand rubles, including:

• within your sector - 30 thousand rubles,
• in agriculture - 70 thousand rubles,
• in households - 150 thousand rubles.

3. Households - 300 thousand rubles, including:

• within this sector itself - 40 thousand rubles,
• in industry - 180 thousand rubles,
• in agriculture - 80 thousand rubles.

These data are summarized in the input-output balance table: numbers in the lines tables reflect product distribution produced in each sector.

The last cells of the rows (in the rightmost column) reflect the volume of production in the sectors of the economy (total output).

Data in columns show products, consumed in the process of production by sectors of the economic system.

The bottom line shows the total costs of the sectors.

Production	Agriculture	Industry	Housekeeping	General release
Agriculture	50	40	110	200
Industry	70	30	150	250
Housekeeping	80	180	40	300
Expenses	200	250	300	750

Here, all sectors are producing products and they also consume all products.

it closed model of intersectoral relations - in it, the costs of sectors (sums of columns) are equal to the volumes of manufactured products (sums of rows).

The intersectoral balance table describes the flows of goods and services between sectors of the economy during a specific period of time (year, quarter).

Matrix representation of input-output balance

Strings tables (matrices) with generating sectors have numbers: i=1- n, where n is the number producing sectors.

columns tables (matrices) with consuming sectors are numbered j=1-n, where n is the number consuming sectors.

The matrix appears to be square. The address of each cell of the table (matrix) of the input-output balance consists of a row number and a column. The value of goods and services produced in sector i and consumed in sector j is denoted by (b ij ) .

So the cost of agricultural products consumed in agriculture itself is b 11 =50; the cost of industrial products consumed in agriculture – b 21 =70.

The balance between total output and inputs in each sector satisfies the system of equations:

This type of input-output matrix is ​​called the matrix closed the input-output model of Leontiev, who first described it in 1936.

An example of an open input-output system

The linear input-output model reflects the relationship of output with demand and determines the total output in each sector to meet changing needs (demand).

Let the country's economy have n industries material production. Each industry produces a certain product, part of which is consumed by other industries (intermediate product), and the other part goes to final consumption and accumulation (final product).

In other words: in an open system, all manufactured products (total product) are divided into two parts:

• one (intermediate product) is consumed in the producing sectors;
• the other (final product or final demand) is consumed outside the sphere of material production, i.e. in the final demand sector.

Denote by:

• X i (i=1..n) - gross product i th industry;
• b ij - the value of the product produced i th industry and consumed in j-th industry for the manufacture of products costing X j ;
• Y i - final product i th industry.

Part of the production is used for intra-production consumption by this industry and other industries, while the other part is intended for the purposes of final (outside the sphere of material production) personal and public consumption.

Since the gross output of any i-th industry is equal to the total volume of products consumed n industries and final product, then:x i = (x i1 + x i2 + … + x in) + y i (i = 1,2,…,n).

These equations are called balance relations. We will consider the cost intersectoral balance, when all the quantities included in these equations have a cost expression.

Let's introduce odds direct costs: aij = b ij / x j (i, j = 1,2,…, n) ,

showing how many products i-th industry is necessary (only direct costs) to produce a unit of output j-th industries.

If you enter:

• matrix of coefficients of direct costs A = (a ij ),
• column vector of gross output X = (X i)
• final product column vector Y = (Y i),

then the mathematical model of the input-output balance will take the form X=AX+Y

Its essence is that all costs must be offset by income. The creation of balance models is based on the balance method - a mutual comparison of available resources and needs for them.

Total cost factor (b ij ) shows how many products i-th industry needs to be produced in order to take into account direct and indirect costs of this product, get a unit of final product j-th industries.

Full expenses reflect the use of the resource at all stages of manufacture and are equal to the sum direct and indirect costs at all previous stages of production.

In the model describing the country's economy, the sum of payments from production sectors to the sector of final demand forms national income.

Matrix A Performance Criteria

1. The matrix (A) is productive if the maximum sum of the elements of its columns does not exceed one, and at least for one of the columns the sum of the elements is strictly less than one.

2. In order to ensure a positive final output in all industries, it is necessary and sufficient that one of the following conditions be met:

• The determinant of the matrix (E - A) is not equal to zero, i.e. matrix (E - A) has inverse matrix (E - A) -1 .
• The greatest modulo eigenvalue matrices (A), i.e. solution of the equation |λE - A| = 0 is strictly less than one.
• All principal minors of the matrix (E - A) of order from 1 to n are positive.

Matrix (A) has non-negative elements (see the solution in the downloaded file) and satisfies productivity criterion(at any j sum of elements of 2 columns ∑a ij ≤ 1 (point 1 of the condition).

An example of a cost input-output balance for an open economic system with four sectors of the economy:

Production	Agriculture	Industry	Transport	final demand	General release
Agriculture	50	16	120	60	246
Industry	30	10	180	100	320
Transport	15	14	140	80	249

Required to define new product release vector X with a new demand vector At (You will find the solution in the downloaded file).

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Tutorial

Novosibirsk

UDC 33

PhD in Economics, Associate Professor

Intersectoral Balance Model: Textbook / Sib. state University of Telecommunications and Informatics. - Novosibirsk, 2010. - 40s.

Let's consider the intersectoral balance scheme (hereinafter referred to as IBI) in the context of its major components (table 1.1.).

In the input-output balance, four parts with different economic content are distinguished, they are called balance quadrants and are indicated in the diagram by Roman numerals.

I IRD quadrant - this is a chess table of intersectoral relationships for the use of products for current production consumption. It is a square matrix consisting of ( n+1 ) strings and ( n+1 ) column. This section is the most important part of the balance sheet, since it is here that information on inter-industry relations is contained. The indicators placed at the intersections of rows and columns represent the values ​​of intersectoral product flows and are generally denoted хij , where i and j are the numbers of producing and consuming industries, respectively. Quantities хij characterize the intersectoral supply of raw materials, materials, fuel and energy, due to production activities. So magnitude x23 is understood as the value of products produced in industry number 2 and consumed as material costs in industry number 3.

Table 1.1.

Scheme of input-output balance

Distribution Costs for production	Current production consumption in industries	end products (according to elements)	Gross product
Material costs of industries
	QuadrantI		QuadrantII

AT economic theory for the first time, the idea of ​​research and analysis of intersectoral relations was proposed by Soviet statistician economists when compiling a balance National economy for the 1923-1924 business year. The ϶ᴛᴏm pioneering balance contained information on the links between the main sectors of the economy and the direction of the production use of products.

The scientific relevance and prospects of the analysis of intersectoral relations was one of the very first to be realized by a graduate of St. Petersburg University V.V. Leontiev. It is worth noting that he was able to formulate clear theoretical foundations of the input-output method and its applied value. As a result of many years of research, linear differentiated equations were compiled, mathematical methods were developed that allow analyze the state of the economy and simulate various scenarios for its development.

Based on the intersectoral balances developed for the USA and some other countries, V.V. Leontiev analyzed the state and structure of the economy, assessed the possible consequences of structural adjustment, developed a program for the restructuring of industries, rationalization of transport communications, etc. Leontiev was awarded Nobel Prize for achievements in the field of economics.

The practical significance of intersectoral balances has found its second embodiment in the economy of the USSR, Russia and many countries of the world, they made once every five years(1959, 1966, 1972, 1977, 1982, 1987, 1997) On the basis of the system of tables of current statistics and other economic information in Rosstat, balances began to be built annually.

Intersectoral balance (the "Input-output" method) in the international interpretation is a kind of balance constructions that characterize intersectoral relations, proportions and structure social production. It is worth noting that it is integrated into the system of national accounts, specifies the main accounts of the SNA and allows you to reflect the efficiency of social production, pricing, the impact of economic growth factors and ensure the forecasting of processes in the economy.

The main tasks of the input-output balance ᴏᴛʜᴏϲᴙ are:

• characteristics of reproduction processes in the economy in terms of material and material composition in a detailed sectoral context;
• reflection of the process of production and distribution of products created in the field of material production and services;
• detailing the accounts of goods and services, production, generation of income and capital transactions at the level of industry groups of products and services;
• identification of the role of production factors and their effective use for economic development.

The input-output table system implements two functions: statistical and analytical.

statistical function essentially consists in the fact that the system provides a check of the consistency of economic information (enterprises, households, budgets, customs payments) characterizing the flows of goods and services.

Analytic function of the system is expressed in the possibilities of its use for the analysis of the state, dynamics, forecasting of processes and modeling of scenarios for the development of the economy as a result of changes in various factors. It was through the symmetrical model of the "Input-output" system that V. Leontiev developed methods for analyzing the relationships between primary costs and output in individual industries and the final demand for them. This analysis is based on the assumption that the cost of producing a product over a certain period of time will be a constant.

Sectoral and intersectoral structure of the national economy

Industry structure national economy consists in grouping economic entities into groups that are homogeneous in terms of their composition, connected by homogeneous functional characteristics - branches of the national economy.

The sectoral structure of the national economy goes through the following stages of its development:

• the first is associated with the active development and predominance of the primary sectors of the economy, such as agriculture, mining;
• the second is associated with the development and dominance of secondary industries - production, construction;
• the third is connected with the development and predominance of tertiary industries - the service sector.

These stages of development of the sectoral structure of the national economy succeeded each other, but for each individual country they had ϲʙᴏ and specific features.

Dynamic changes in the sectoral structure occur cyclically over a period of 10 to 20 years. It is worth saying that they are characterized by the following features:

• increasing the value and volume of the service industry - the intellectual, information sphere;
• a decrease in the volume of the extractive industry compared to others;
• growth of industrial production against the backdrop of the agricultural sector of the economy.

Intersectoral Leontief balance

The history and practice of the balance of the national economy in our country has served as an important basis for compiling intersectoral balances. It is important to know that a great contribution to the study of the organization of interbranch relations was made by the outstanding Russian scientist V.V. Leontiev, kᴏᴛᴏᴩy developed intersectoral balance, or the input-output method. It is worth noting that he gave a mathematical description of the organization of the main correlations of the input-output balance, which made it possible to measure the actual coordinated relationships for the purpose of planning and forecasting processes. V.V. Leontiev "for the development of the input-output method and its application to solving important economic problems" was awarded the Nobel Prize in Economics in 1973. The development of intersectoral later became an organic part of the SNA.

Note that the theory of "intersectoral balance" was developed in the USA by V. V. Leontiev as an effective tool in the analysis and forecasting of structural relationships in the economy. It is worth noting that it proceeds from the possibility of achieving a general macroeconomic equilibrium, for which a model of the ϶ᴛᴏth state has been developed, which includes the structural relationship of all stages production process— production, distribution or exchange and final consumption.

In the Leontief inter-industry balance model, an inter-industry balance scheme is used for analysis, consisting of four main quadrants, reflecting certain stages of the production process:

• volumes of consumption for the needs of production - the first quadrant;
• grouping the product depending on how it is used - the second quadrant;
• inclusion of the added value of the goods, for example, wages of employees, taxes and other - the third quadrant;
• the structure of national income distribution is the fourth quadrant.

Note that the theory of input-output balance allows:

1. to analyze and forecast the development of the main sectors of the national economy at various levels - regional, intra-industry, inter-product;
2. to make an objective and relevant forecasting of the pace and nature of the development of the national economy;
3. define the characteristics of the main macroeconomic indicators, at which the state of equilibrium of the national economy will come. As a result of the impact on them, approach the equilibrium state;
4. calculate the full and direct costs of producing a certain unit of the good;
5. determine the resource intensity of the entire national economy and its individual sectors;
6. determine the directions for increasing the efficiency and rationalization of the international and regional division of labor.

The intersectoral balance method was first used in 1936 in the USA, when V. V. Leontiev calculated it for 42 industries. At the same time, its effectiveness was recognized when used to develop the state economic policy and forecasting of the national economy. Today it is widely used in many countries around the world.

In practice, the International Standard Classification of all fields is widely used. economic activity, in which a classification of all sectors of the national economy is given. It is worth noting that it allows you to form a system of national accounts (SNA). Classification and grouping by sectors of the national economy allow you to determine the volume and contribution of a particular industry to total GDP and GNP, to characterize the links between industries and the formed proportions. The formed functional group makes it possible to conduct an objective analysis of the role of economic entities in the production of national wealth.

The number of industries included in the inter-sectoral balance is determined by its specific goals. Transport, communication, agriculture, production will be basic. If necessary, a branch of the national economy can be divided into smaller branches that are part of it.
It should be noted that the grounds for attributing units of the national economy to a particular industry can be different - the similarity of the technological and production process, the homogeneity of the required raw materials, the nature of the products.

The modern sectoral structure of the national economy of Russia characterized by the predominance of the fuel and energy complex (FEC). It is worth noting that it will be one of the most capital-intensive industries, in connection with which there is an outflow of capital from other industries. The orientation of the fuel and energy complex to the international market makes Russia dependent on global price fluctuations. As a result, more than half of the country's GDP is formed from the sale of resources. The predominance of the extractive industries of the economy has a negative impact on the overall pace of development of the national economy. The dominance of the fuel and energy complex hinders the development of knowledge-intensive sectors of the economy.

Calculation of intersectoral balance

The general scheme of the input-output tables is presented in the table.

When compiling the "Input-output" tables, classifiers of types of economic activity, industries and products (OKVED) and (OKPUD) can be used

There are three blocks of so-called quadrants in the tables. Quadrants I and II reflect intermediate (production) and final demand for resources, while quadrant III shows value added by industry.

The main attention in these tables is given to the relationship of industries in the production and use of their products. In the predicate of the table, industries-consumers of products are given, in the subject - industries-suppliers.

Based on all of the above, we come to the conclusion that for columns I and III of quadrants, the sum of intermediate consumption and DC represents production costs, and for rows of I and II quadrants, the sum of intermediate and final demand characterizes the use of resources.

The system of tables "Input-output", proposed for development by the 1993 UN Guide to National Accounts, contains a sequence of tables characterizing the formation of a country's resources, the direction of their use, the formation of value added, the transformation of the cost of goods and services in basic prices into value in buyers' prices.

The table dataset consists of:

• supply and use tables;
• symmetrical input-output tables;
• tables of trade and transport margins;
• tables of taxes and subsidies on products;
• tables for the use of imported products.

Table "Resources of goods and services", presented in Table. 5.4, ​​describes in detail the process of formation of resources of goods and services in the country's economy through its own production and imports.

The Resources table consists of two parts. The first part of the table demonstrates the formation of resources of goods and services through domestic production and imports. The second part gives a quantitative description of the main components of the market price of buyers: taxes (N); subsidies (С), trade and transport margin (TTN)

The Usage table will be a logical extension of the Resources table. It gives a detailed description of the distribution of disposable resources by directions of use. There is an intermediate (production) and final use.

The "Usage" table is built according to the general scheme of the "Input-output" tables, i.e. consists of three quadrants and is a type of "industry x product)

In the first quadrant of the table (Table 6.5), intermediate consumption is shown by columns - industries, by rows - groups of goods and services.

In the II quadrant of the table - the end use, which is divided into the following elements:

• HH final consumption expenditures;
• final consumption expenditures of non-profit organizations serving households;
• government final consumption expenditures;
• gross fixed capital formation;
• change in inventories; net acquisition of values;
• export of goods and services.

Table 5.5. "Use of goods and services"

Quadrant III of the table "Use" shows the formation of value added by sectors of the economy.
It should be noted that the main components of the VA, allocated in the ϶ᴛᴏth quadrant, ϲᴏᴏᴛʙᴇᴛϲᴛʙ correspond to the components of the income generation account. These are: wages of employees; gross mixed income; other net taxes on production; consumption of fixed capital; gross profit; indirectly measured financial intermediation services.

Within the framework of the SNA, supply and use tables serve as a tool for reconciling statistical data, obtaining value added by industry, final demand by product, both in current and comparable prices. This is achieved by the fact that the method of comparing table data involves reconciling data on available resources (production + imports) with data on resource use for each group of goods and services at a fairly high level of detail. Such a method in statistics is called the commodity flow method.

Symmetric input-output tables are product x product tables.

The ϶ᴛᴏth table assumes that the industry is a collection of homogeneous products. In the subject and predicate of the I quadrant, the same nomenclature of branches is distinguished.

Symmetrical input-output tables can be compiled in two ways: by direct tabulation on the basis of specially conducted surveys of enterprises on the structure of production inputs, or by mathematical transformation of supply and use tables.

Let's show ϶ᴛᴏ on an abstract example:

Stage I (initial data)

Table 5.6. "Resources"

These methods are based on the assumption of the stability of the industry technology or the assumption of the stability of the technology for the production of homogeneous products. In the conditions of limitations, the format of the manual, we will consider the algorithm for converting the table of resources and use into a symmetrical matrix based on the assumption of the stability of the industry production technology.

Table 5.7. "Industrial use"

Table 5.8. "Structures of production* (S)"

* With the conversion of the table of the subject and the predicate of the table of resources.

According to the accepted hypothesis, product i is produced by different industries J. With ϶ᴛᴏm, each industry J spends a certain amount of product q on the production of all ϲʙᴏ products.

Table 5.9. Direct cost ratio (according to the table of industrial use) (K)

To determine the specific consumption of products for the production of products, the weighted average value of the costs of products for the production of products is found. As weights for ϶ᴛᴏm, the shares of production by industries in the total volume of production are taken.

The mathematical record of the algorithm for carrying out this calculation is as follows:

• A is the matrix of coefficients of direct costs of products i for the production of products J for the symmetrical table "Costs-output";
• K is the matrix of coefficients of direct costs of products I for the production of products J;
• S - table of the structure of production.

In the inverse matrix, the coefficients of direct costs, calculated by the formula a = Aij / Xj and presented in the form of a matrix, characterize the volume of various direct costs for the production of a unit of output and do not take into account the indirect costs associated with the production of ϶ᴛᴏ products.

For example, the production of automobiles requires metal, energy, tires, etc. At the same time, for the production of metal, it is required to extract ore raw materials, spend some money to pay for services for its transportation to the place of metal production.

Almost every cost element is a product, the production of which took a whole list of resources. It is important to note that one cycle of product use is preceded by another, followed by a third cycle, and so on.

Based on all of the above, we come to the conclusion that a long chain of interaction between production processes is being created. If we try to consider the production process of any product along the entire production chain, then it is easy to see that it is practically endless.

It is possible to determine the amount of total costs (direct and indirect) for the production of a product based on the inverse matrix. In the economic literature, it is often called the Leontief matrix. The formula for calculating the ϶ᴛᴏth matrix is ​​derived quite simply. As mentioned above, the output vector is determined by the formula:

(I - A) X = Y;

X = (I - A) -1 Y

I is an identity matrix, the diagonal values ​​of which are equal to one (1), and the rest are equal to zero (0)

(I - A) 1 - ϶ᴛᴏ is the inverse matrix. The mathematical solution of the ϶ᴛᴏth problem can be written as follows:

(I- A) -1 = I+A + A 2 + A 3 + ... + A n

When analyzing intersectoral interactions using the input-output method, it is assumed that the incentive for increasing demand for products will be an increase in final demand. For example, increasing demand foreign countries for mineral resources. This assumption is conditional, since an increase in demand for products can arise as a result of various circumstances. At the same time, the simplification of the situation makes it possible to assess the impact of an increase in demand on the output of all products, taking into account all intersectoral interactions.

It should not be forgotten that an important feature of the SNA will be the inclusion of the input-output formula in the overall structure of the system of national accounts. This applies mainly to the accounts of goods and services. Complementing the complete sequence of accounts for institutional sectors, covering all types of accounts in the SNA, supply and use tables and symmetrical tables allow for a more detailed analysis of industries and products by breaking down the accounts of production and generation of income, as well as the accounts of goods and services, which leads to compiling a symmetrical input-output table. "Symmetric" means that, in both rows and columns, the same classifications or units (i.e. the same product groups) can be used.

in the SNA and economic analysis tables (or matrices) "Input-output" of the following types can be used:

• supply and use tables;
• symmetrical tables (Leontief tables)

Square symmetrical tables are built on the principle of "product - product", or "industry - industry" ("manufacturer - manufacturer")

Institutional units may be involved in several different types production activities at the same time. Therefore, for a detailed analysis of the SNA, it is recommended to break them down into separate establishments, each of which is engaged in only one type of activity in one place. Therefore, industries are defined as groups of establishments engaged in the same type of production activity.
With all this, it is extremely important to take into account the fundamental difference between the main and secondary activities, on the one hand, and auxiliary activities, on the other:

• the main activity of the establishment - ϶ᴛᴏ activity, the GVA of which exceeds the GVA of any other activity carried out within the ϶ᴛᴏth same unit;
• secondary activity - ϶ᴛᴏ activity carried out within the framework of a single institution in addition to the main activity;
• ancillary activities - ϶ᴛᴏ ancillary activities undertaken to create conditions in which other types of enterprise activities can be carried out.

Ancillary activities usually produce services that can be used as factors of production in almost all types of production activities. Material published on http: // site
The cost of such services is traditionally small compared to the cost of the results of the main and secondary activities of the enterprise. Therefore, ancillary activities are considered as an integral part of the main or secondary activity with which it is associated.

In the process of constructing an input-output balance, disaggregation of the goods and services account is required.

The goods and services account shows the ratio between the total amount of products available (supply) and the total amount of its use.
It is worth noting that the main elements of the original equality (balance sheet) are expressed as follows: output + imports (= all resources) = intermediate consumption + exports + final consumption + gross capital formation (= total use)

All stages of the movement of goods and services in the economy can be traced from their original producers to users.

A detailed consideration of such flows is usually called the commodity flow method. ϶ᴛᴏm uses the original statistical information about goods and services, as well as additional information necessary for proper valuation. The maximum efficiency of the commodity flow method is achieved in cases where independent estimates can be made for each of the articles of use, i.e., when specific information is taken as a basis on the distribution of the supply of products between various types use. With ϶ᴛᴏm, it is essential to ensure that the parties agree on resources and use.

The tables present product groups based on the classification of main products, and cover more than 1800 goods and services (five-digit level) and about 300 products (three-digit level)

The valuation and the procedure for accounting for taxes and markups are carried out according to certain rules.

The SNA recognizes the following components of the price paid by the buyer of a product:

• the basic price of the product as a result of production;
• product taxes;
• minus product subsidies;
• trade and transport margins for the delivery of the product to the buyer.

Some of the four components are amenable to further disaggregation, for example, trade and transport margins can be treated in a more disaggregated way, in particular by separating these margins into separate trade and retail components, and value added tax (VAT) can be separated into a separate component.

Buyer's price - ϶ᴛᴏ the amount paid by the buyer (excluding VAT) for the supply of a unit of goods or services at the time and place specified by the buyer. The buyer's price for the goods includes any shipping costs paid separately by the buyer for the delivery.

Producer price - ϶ᴛᴏ the amount to be received by the producer from the buyer for a unit of output produced as a good or service, minus any VAT charged to the buyer. By the way, this price does not include any transport costs charged separately by the manufacturer.

Base price is the amount receivable by the producer from the buyer for a unit produced as a good or service, minus any tax deductible, and plus any receivable subsidies on that unit in connection with its production or sale. By the way, this price does not include any transport costs charged separately by the manufacturer.

Between these three price concepts, which are central to the analysis of the input-output table, by definition, there are the following relationships:

• purchase price (which includes non-deductible VAT) - trade and transport margins (including taxes other than VAT, less product subsidies payable/received by wholesalers and retailers), non-deductible taxes such as VAT taxes = producer price ( which excludes non-deductible VAT);
• producer price - taxes (other than VAT) less subsidies on products payable/receivable by producers = base price.

For exports and imports, the SNA adopts similar price concepts: free on board (FOB) for exports and total imports, and value, insurance, freight (CIF) for individual imports. The difference between the FOB price and the CIF price, the cost of transportation and insurance from the border of the exporting country to the border of the importing country, and for paying insurance on the ϶ᴛᴏth route.

CIF price - ϶ᴛᴏ the price of a good delivered to the border of the importing country, or the price of a service provided to a resident, up to
payment of any import duties and other taxes on imports or domestic trade and transport margins.

Supply and use tables are compiled with product groupings (supply of goods and services). Product data is shown in rows, industries in columns. Tables cannot be compiled independently, as they are interconnected with the balance sheet.

The SNA uses table provides information on the uses of goods and services, as well as the cost structure of industries.

The input-output balance of production and distribution of products and services is a statistical table that demonstrates the relationship between gross value added, intermediate consumption and final use in sectors of the economy.

The following articles stand out from the GVA in the IRB:

The main source of information for determining the volume and structure of household expenditures for the purchase of goods will be trade statistics on trade turnover, as well as HH survey data.

The IRB details the accounts of goods and services, providing information management bodies to build cross-industry
models, forecasts, analysis of the functioning of industries, as well as identifying the role of individual factors of production (for example, the dependence of the economy on energy supply or on changes in energy prices)

The results of the GVA by the sectors of the IOB are calculated by two methods:

• as the difference between gross output and intermediate consumption;
• as the sum of value added elements.

The input-output balance is widely used for statistical purposes, determining the commodity structure of flows, and also to check the balance of the entire system of statistical data covering various aspects of the economic process.

Enough said about planning. Regardless of our attitude to this process, we are constantly faced with the need to compare our strengths with our desires. And if in the life of one or two people it is possible to make a mistake with plans, then on the economy of the state, and even of the whole union of powers, incorrectly correlated costs with profits can have a catastrophic effect. Therefore, in the modern economy, the intersectoral balance with its detailing of the production of goods and services occupies a leading place.

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, it involves the construction of a system of equations that describe the conditions for equality between manufactured products and the need for these goods.

The group under study most often consists of several economic entities, part of the production of which is consumed internally, and part is taken out of its framework and is perceived as a “final product”. Balance models that use the concept of "resource" rather than "product" make it possible to manage the optimal use 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 for given areas of use. For calculations, a table is compiled, the cells of which are filled with standards for the manufacture of 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 for the so-called "pure 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 systems.

Nobel Prize for Model

For the first time, the need to find a balance of production between different sectors was proposed by Soviet economists who studied the development of the national economy in 1923-1924. The first proposals contained only information about the quality of links between production sectors and about the use of manufactured products.

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

The input-output balance has 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 intersectoral analysis.

How the model was used

For the first time, Leontiev applied the intersectoral balance model to analyze the state of the US economy. By that time, theoretical postulates had acquired the form of real linear equations. This calculation showed that the coefficients proposed by scientists as indicators of the relationship between industries are quite stable and constant.

During the Second World War, Leontiev analyzed the intersectoral balance of the economy of Nazi Germany. Based on the results of this study, the US military identified strategically significant targets. And after the end of the war, the quality and volume of Lend-Lease was again determined on the basis of information obtained through the Leontiev interbranch balance model.

In the Soviet Union, such a model was built 7 times, starting in 1959. Scientists assumed that economic ties could be considered stable over the course of five years, and therefore all conditions were considered static. However, the methodology was not widely used, because the relationship between industrial sectors was largely influenced by political conjuncture. Real economic ties were seen as secondary.

The essence of the concept

The inter-industry 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 this product. For example, coal mining requires steel tools; at the same time, coal is needed to make steel. So, the task of the input-output 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 based on the results of the constructed model, it is possible to determine the efficiency of production in general, to find optimal pricing methods and to identify the most significant factors of economic growth. In addition, this method allows you to engage in forecasting.

Main goals

• Structuring based on the material composition of industry resources.
• Illustration of production processes and distribution.
• A detailed study of the production process, the creation of goods and services, the accumulation of income at the level
• Optimization of identified essential 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 checks the 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) that reflect the conditions for equilibrium 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 industries, each of which acts as a producer and consumer.

quadrants

Leontief's input-output balance is divided into four parts (quadrants). Each quadrant (in the figure they are indicated by numbers 1-4) has its own economic content. The first one displays intersectoral material ties - this is a kind of chessboard. Coefficients located at the intersection of rows and columns are denoted XY and contain information about 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 value of the means of production produced in industry 2 and consumed in industry 3 (material costs). The sum of all elements of the first quadrant is the annual fund for the reimbursement of material costs.

The second quadrant is a set of final products of all manufacturing industries. A final product is a product that goes beyond the production sphere into the area of ​​final consumption and accumulation. A detailed balance sheet illustrates the areas of use of such a product: public and private consumption, accumulation, reimbursement and export.

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

System of equations

Despite the fact that the gross social product is not formally included in 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 information obtained from these elements, allows you to check the correctness of filling in the entire balance sheet. In addition, it can be used to create an economic and 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 is as follows: the sum of the material costs of any branch of the economy and its clean production is equal to the gross product of the described industry (columns).

The second equation of the input-output balance shows that the sum of the material costs of those who consume a certain product and the final product of a particular area represent the gross output of the industry (balance lines).

The final 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 А = (ау);
• gross output vector X (column);
• final product vector Y (column).

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

It remains only to recall that the balance is drawn up both in physical terms and in monetary terms.

The intersectoral balance is an economic and mathematical model of the reproduction process, which in an expanded form reflects the relationship in the production, distribution, consumption and accumulation of the social product in the context of the sectors of the national economy and in the unity of the material and cost aspects of reproduction.

Intersectoral balances can be developed for the planned and reporting period in physical, physical value and value terms.

Intersectoral balances in physical terms (in physical terms) cover only the most important types of products. Natural value (balance of mixed type) covers the entire social product. The cost balance characterizes the process of reproduction in terms of money.

When constructing the input-output balance, the concept of a “pure” industry is used, i.e. a conditional branch that unites all the production of a given product, regardless of departmental subordination and forms of ownership of enterprises and firms. The transition from economic sectors to pure ones requires a special transformation of real data of economic objects, for example, aggregation (combination) of sectors, exclusion of intra-industry turnover.

The input-output balance can be presented in the form of a scheme and a model. The scheme of the intersectoral balance of production and distribution of the social product in value terms is given in Table. 2.1.

The entire national economy is represented as an aggregate n industries. All products of industries are divided into intermediate and final.

The following symbols are used on the diagram:

- industry production costs i (
) for the production of industry products j (
);

- end product of the industry i;

–gross output i th industry;

– added value j th industry.

In the IOB scheme (inter-industry balance), three sections or quadrants can be distinguished.

Section I is a matrix of elements at the intersection n first lines and n the first columns of the balance sheet. This section reflects intersectoral relationships on the use of products for current production (intermediate) consumption (see Table 2.1).

Quantities (
) characterize the production consumption of products i th industry, magnitude (
) - the amount of production costs j th industry. Number
equal to the sum of all production costs of all industries. This is the so-called intermediate product of the national economy.

Section II is located to the right of the intermediate consumption column. This section is given in an enlarged way, in the form of a single column of values. . The detailed diagram shows the use for personal and public consumption, gross capital formation. In addition, the final product includes the balance of exports and imports of products. Section II reflects the sectoral and material structure of the final use of the social product.

Section III is located under the first. The section is also given enlarged, in the form of a line of values . The detailed scheme reflects the elements of added value: consumption of fixed capital, profit, wages; indirect taxes, subsidies. Section III reflects the cost structure of the gross domestic product.

Table 2.1

Scheme of the reporting MOB in monetary terms

Manufacturing industries	Consuming industries					Intermediate consumption		End use		Gross output
Intermediate costs
Gross value added
Gross output

In the IOB scheme, two private intersectoral balances are combined - the balance of product distribution (I and II sections) and the balance of costs (I and III sections).

Sections I and II present the distribution of manufactured products for the needs of current production and final consumption. The ratio of indicators is expressed by a system of equations

(2.1)

In sections I and III, in the sectoral context, the costs incurred for the production of products and the added value are presented.

(2.2)

Let us sum up all the equations of system (2.1), as a result we obtain

+=.

Similarly, summing the equations of system (2.2) gives

+=.

Because the =, then

+=
+,

Consequently =.

The volumes of the gross domestic product in terms of material and cost composition are equal.

The MOB model for the planning period is based on the assumption that cost rates do not depend on the volume of output. Under this assumption, the values ​​of intersectoral supplies can be determined by the formula

,
;
. (2.3)

Direct cost ratios
i-th industry is necessary for the production of a unit of gross output j th industry. Together they form the direct cost matrix

Let us write system (2.1) taking into account relation (2.3)

(2.4)

Denote by gross output vector, and through final product vector. We write (2.4) in matrix form

, (2.5)

where
is the identity matrix.

Express from the balance relation (2.5)

, (2.6)

where
– matrix, inverse
. It is called the matrix of coefficients of total costs and denoted

.

Total cost ratios show how many products i-th industry is necessary to obtain a unit of final product j th industry.

The MOB model can be used to predict prices. Forecasting for a period t is carried out on the basis of the data of the IRD of the previous period ( t- one). The structure of costs in comparable prices for the considered period of time
assumed to be unchanged. Let the price change be characterized by the price index (
) in industries. Under these assumptions, sections I and III of the MOB scheme will be written as shown in Table. 2.2.

The balance ratio for price forecasting has the form

. (2.7)

Table 2.2

Scheme I and III sections MOB at current prices

Manufacturing industries	Consuming industries
Wage
Consumption of fixed capital
Indirect taxes
Subsidies
Gross output

Example. For a conditional economy, consisting of three industries, the MEB scheme is known for the reporting period:

Manufacturing industries	Industries-consumers			End use	Gross output
Gross value added (GVA)
Gross output

2) Determine what should be the gross output of industries in the planning period, if the output of products for final use is known
.

3) What is the impact in market conditions of a 2-fold increase in the price of products of the second industry on price changes in other industries. Form the cost structure of the reporting period independently, based on the fact that wages account for 30%, and other elements of gross value added - 70% of gross value added. The actual cost dynamics in the forecast period remains unchanged. Take into account that the growth of wages lags behind the rise in prices, and the coefficient of elasticity of wages from prices is 0.8.

4) What impact does a 50% increase in wages in the first sector have on an increase in product prices under market conditions. Wages in the second and third sectors remain unchanged.

Solution

1) Direct cost factors are determined in accordance with the ratio

.

For the problem being solved

,

,

,

.

Find the input-output matrix:

The final use vector will be determined on the basis of the balance ratio

.

.

Let us determine the volumes of intersectoral supplies according to the formula

,
,
;

etc. Calculations can be arranged in the form of a matrix

Determine the gross value added by the formula

.

For the planning period

MOB scheme for the planned period

Manufacturing industries	Industries-consumers			End use	Gross output
Gross value added
Gross output

2) Define the vector of gross output of industries
by known end-use vector
according to the formula

.

Total cost coefficient matrix
calculated by matrix inversion
.

,

where - algebraic complements of the corresponding elements of the matrix
.

Let's find the matrix determinant

Let's find algebraic additions matrix elements
.

The vector of gross output in the planning period

.

3) Let us determine the impact of a doubling of the price of products of the second industry on the prices of products of the first and third industries.

Let's form the cost structure of the reporting period, based on the fact that wages (WRP) account for 30% of gross value added (GVA).

Gross value added is defined as the difference between gross output and intermediate costs using the formula

.

For the reporting period

;

;

.

.

For the reporting period

Other elements of gross value added are found as the difference between gross value added and wages.

The first and third sections of the reporting MOB will look like:

The balance ratio for price forecasting (2.7) for our problem will look like

,

where – price index j th industry;

–i th element of gross value added j th industry.

Since the growth of wages lags behind the rise in prices, and the coefficient of elasticity of wages from prices is 0.8; then wages must be multiplied by 0.8. By condition
. Then I and III

Manufacturing industries	Industries-consumers
	90	40	50
	70	60	40
	50	60	20
Wage	21	30	18
Other elements of GVA	49	70	42
Gross output	280	260	170

The value of costs for the products of the second industry does not affect the formation of prices in this industry, so the system of balance equations includes equations only for the first and third industries and will look like

Solving the system, we find

Consequently, the price index in the first sector will be 187.44%, and in the third sector - 185.6%.

Thus, with a 2-fold increase in the price in the second sector, the price in the first sector will increase by 87.44%, and in the third - by 85.6%.

4) Calculate what impact, under market conditions, an increase in wages in the first sector by 50% will have on an increase in prices for the products of sectors.

I and III sections of the reporting IOB at current prices will look like:

Manufacturing industries	Industries-consumers
	90	40	50
	70	60	40
	50	60	20
Wage	21
Other elements of GVA	49	70	42
Gross output	280	260	170

The system of balance equations will look like:

After reducing similar ones, we get the system

Solving the system, we find

Consequently, the price index in the first sector will be 116.88%, in the second sector - 110.62%, and in the third sector - 111.75%.

Thus, with an increase in wages in the first industry by 50%, the price of the products of the first industry will increase by 16.88%, the second industry - by 10.62%, the third industry - by 11.75%.