For what purposes is inter-industry balance used? Linear balance models in economics

As mentioned earlier, the input balance has a huge impact on the economy, and it is calculated not only in Russia, but also in many other countries. But why is this balance so important for the economy? And why is it used in many countries?

This is because Leontief’s inter-industry balance allows for many analyses. The theory of interindustry balance allows:

analyze and forecast the development of the main sectors of the national economy at various levels - regional, intra-industry, inter-product;

make an objective and relevant forecast of the pace and nature of development of the national economy;

determine the characteristics of the main macroeconomic indicators at which the state of equilibrium of the national economy will occur. As a result of the impact on them, they will approach an equilibrium state;

determine the resource intensity of the entire national economy and its individual sectors;

determine directions for increasing efficiency and rationalizing the international and regional division of labor.

Previously, you could see what the “Input-Output” table looks like for an entire country. Namely for Russia. This table is quite lengthy and looks difficult to understand. Now let's look at the compilation of these tables and their calculations. but to do this you need to know how these tables are compiled.

The general layout of the Input-Output tables is presented in Table 2.11

Table 2.11

General scheme of input-output tables

When compiling Input-Output tables, classifiers of types of economic activity, industries and products (OKVED) and (OKPUD) are used.

The tables highlight three blocks of so-called quadrants. Quadrants I and II reflect, respectively, intermediate (production) and final demand for resources, and quadrant III reflects added value by industry.

The main focus of these tables is on the relationship between industries in the production and use of their products. The predicate of the table shows the consuming industries of the products, and the subject - the supplying industries.

Thus, in columns I and III of quadrants, the sum of intermediate consumption and VA represents production costs, and in rows of I and II quadrants, the sum of intermediate and final demand characterizes the use of resources.

The system of “Input-Output” tables, proposed for development by the UN National Accounts Manual in 1993, includes a sequence of tables characterizing the formation of the country’s resources, the direction of their use, the formation of added value, the transformation of the cost of goods and services in basic prices into the cost in buyers' prices.

The set of these tables 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. 2.12, describes in detail the process of formation of resources of goods and services in the country’s economy through its own production and imports.

Table 2.12

Resources of goods and services

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

The “Usage” table is a logical continuation of the “Resources” table. It provides a detailed description of the distribution of available resources according to areas of use. Intermediate (production) and final uses are distinguished.

The “Use” table is built according to the general scheme of the “Input-Output” tables, i.e. consists of three quadrants and represents the “industry x product” view.

Quadrant I of the table shows intermediate consumption by columns - industries, by rows - groups of goods and services.

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

household final consumption expenditures;

final consumption expenditures of non-profit organizations serving households;

government final consumption expenditure;

gross fixed capital formation;

change in inventories; pure acquisition of values;

export of goods and services.

Table 2.13

Use of goods and services

Quadrant III of the “Use” table shows the formation of added value by economic sector. The main components of the VA identified in this quadrant 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 added value by industry, and final demand for products, both in current and comparable prices. This is achieved by the fact that the method of comparing these tables involves reconciling data on available resources (production + imports) with data on the use of resources for each group of goods and services at a sufficiently high level of detail. This method in statistics is called the commodity flow method.

Symmetrical tables "Input - output" are tables of the "product x product" type. This table assumes that an industry is a collection of homogeneous products. In the subject and predicate of the first quadrant, the same nomenclature of industries is distinguished. It was previously shown how the input-output balance table should look in general form. Now let's look at it using the example of some industries presented in table. 2.14.

Table 2.14

Analysis of the general structure of the input-output balance

						Final product	Gross Product
			X 1i	X 1n	U X 1j
			X 2i	X 2n	U X 2j
			I quadrant	II quadrant
P i	X i 1	X i 2	X ii	X in	YX ij	Y i	X i
P n	X n 1	X n 2	X ni	X nn	U X nj
	U X k 1	U X k 2	U X ki	U X kn	UU X kj	U Y k	U X k
Conditionally pure products			V i	V n	U V j	IV quadrant
III quadrant
Gross Product			X i		U X j

Let's now analyze in detail the values of not only each row, but also each column so that in the future we can correctly compile and calculate this table ourselves using the example of our own 5 industries.

First quadrant. In the table, each industry is represented in two ways. As a row element, it acts as a supplier of the products it produces, and as a column element, it acts as a consumer of products from other sectors of the economic system.

If R 1 - electricity production, and P 2 - coal industry, then X 12 - annual electricity costs for coal production, and X 21 - similar costs of coal for electricity production. R 1 acts as a supplier of electricity and as a consumer of coal. Industry R 1 is also a consumer of his own products. Electricity cost X 11 monetary units are used within the industry to ensure the operation of electrical equipment, to illuminate production facilities, etc. It has a similar meaning X 22 and that's it X ii. In general, X i 1 , X i 2 , ..., X ii , ..., X in- volumes of product supplies i th industry to industries included in the economic system. The amount of these supplies

X i 1 +X i 2 +…+ X in = Y X ij

expresses the total production consumption of products R i and is recorded in i th line ( n+ 1)th column of the table.

In our example

X 11 +X 12 +…+ X 1 n = Y X 1 j

is the total production consumption of electricity, and

X 21 +X 22 +…+ X 2 n = Y X 2 j

Total coal costs for the production needs of industries included in the economic system.

Let's now look at P i as per column element. Column number i contains the volumes of current production costs of products of industries included in the economic system for the production of products i-th industry. IN ( n+ The 1st line of the specified column contains the amount of current production costs P i in a year:

= X 1i + X 2 i+ … +X ni

Having summed up the first n elements ( n+ 1)th line, we get the value of current production costs of all industries:

+ +…++…+= (1)

Sum of first n elements ( n+ 1)th column

+ +…++…+= (2)

is the cost of products of all industries that were used for current production consumption.

It is easy to verify that the sums (1) and (2) consist of the same terms (all X kj) and are therefore equal to each other:

Equality (3) means that current production expenses of all industries are equal to their current production consumption. The number is the so-called intermediate product of the economic system.

The elements at the intersection of the first ( n+ 1) lines and first ( n+ 1) columns, form first quadrant(quarter). This is the most important part of the inter-industry balance, since it contains information about inter-industry connections.

Second quadrant located in the table to the right of the first. It consists of two columns. The first of them is the column of final consumption of industry products. Final consumption refers to personal and social consumption that is not used for current production needs. This includes the accumulation and compensation for disposal of fixed assets, the increase in inventories, personal consumption of the population, expenses for the maintenance of the state apparatus and defense, expenses for servicing the population (health care, education, etc.), the balance of exports and imports of products. The second column presents the volumes of gross output of industries. Total (gross) output i-industry is defined as

Equality (4) means that all produced i The th industry consumes its products. Part of it, in the form of total production consumption of products P i goes to the production needs of industries included in the economic system. The other part is consumed in the form of the final product.

Thus, part of the products of the coal industry, as we have already noted, is used within the economic system, and the other - as raw materials, fuel - will be consumed by industries that are not part of the economic system, and will form part of the country’s exports, will be used for heating homes, etc. P.

Quadrants I and II reflect balance between production and consumption .

The second quadrant also includes that part ( n+1)th line in which the total final product is located

and total gross product

Third quadrant located in the table below the first one. It consists of two lines. One of them contains the volume of gross product by industry, and the other contains the conditionally net output of industries V 1 , V 2 ,..., V n. The composition of conditionally net products includes depreciation charges that go to compensate for the disposal of fixed assets, wages, profits, etc.

It is defined as the difference between the gross product of the industry and the sum of its current production costs. Yes, for R i there is equality

The first and third quadrants reflect cost structure products of each industry. Thus, equality (5) shows that the value of the gross product X i i-industry consists of the cost of that part of the output of the system’s industries that was used for production X i, from depreciation charges, labor costs, from the net income of the industry, from the cost of resources not produced within the economic system, etc.

Using equalities (4) and (5), we calculate the total gross product.

From (4) it follows that

and from (5) we get:

The second terms on the right sides of equalities (6) and (7) express the same quantity - the intermediate product. From here and from the equality of the left sides of (6) and (7) we conclude that the first terms are equal:

So, the total final product is equal to the total conditionally net product.

Fourth quadrant It is not directly related to the production sector, so we will not fill it out.

Quadrant IV shows how the primary incomes of the population (wages, personal incomes of members of cooperatives, allowances of military personnel, etc.), the state (taxes, profits from public sector production, etc.), and cooperatives are received in the sphere of material production. and other enterprises are redistributed through various channels (financial and credit system, service sector, socio-political organizations, etc.), resulting in the formation of final incomes of the population, the state, etc.

intersectoral balance Leontief reproduction

Intersectoral balance is an economic-mathematical model formed by the cross-overlay of rows and columns of a table, i.e., balances of distribution of products and costs of their production, linked according to the results (chess balance). The main indicators here are the coefficients of total and direct costs.

The input balance is one of the main sections of the system of national accounts (SNA). In order to study the inter-industry balance in detail, it is necessary to study the SNA.

SNA is a system of interrelated statistical indicators presented in the form of tables and accounts that characterize the results of the country’s economic activity.

To identify problems of insufficient reproduction or identify factors for the success of an economy, a set of methods for measuring the production activity of the economy is used. The combination of these methods forms the system of national accounts.

The system of national accounts plays a special role in the economy:

It allows you to measure the volume of production at a specific point in time and reveal the reasons for this level of production.

By comparing national income indicators over a certain period of time, one can trace the trend that determines the nature of economic development: growth, decline or stagnation.

The SNA allows you to formulate and implement public policy.

The basis of the SNA is the balance sheet method of an interconnected comprehensive study of economic processes and the results of their activities. SNA is used as a method with which it is possible to identify relationships between economic processes and phenomena.

In order to obtain a comprehensive assessment of the state of the country's economy and evaluate the performance of each sector of the economy, the system of national accounts contrasts each stage of reproduction with a corresponding account or group of accounts that characterize the intensity of movement of the value of goods and services through all stages of the reproduction cycle.

For the economy as a whole, provision is made for the compilation of all accounts that form consolidated accounts. Accounts by sector and region are also being developed.

For the successful development of the country, it is necessary to monitor the state of not only the entire economy as a whole, but also each industry. To fully study the economy, macroeconomic indicators were developed, which together make up the SNA.

The need for a system of macroeconomic indicators was recognized by the English economist William Petty, who for the first time in the world assessed the national income of his country. The first macroeconomic model of the national economy was created by the Frenchman Francois Canet, head of the school of physiocrats. Over time, these attempts to develop a system of macroeconomic indicators were not stopped. Attempts to develop a system of macroeconomic indicators to assess the state of the national economy were made in different countries back during the First World War; then this was done with the aim of assessing the military and economic potential of the warring powers.

However, the need for a system of macroeconomic indicators became especially strong in the 20s and 30s. XX century In the USSR, a system of indicators and tables was created, called the balance of the national economy, which was already used in drawing up the first five-year plan for the development of the national economy (1928-1932). In the West, the development of a similar system began after the Great Depression of 1929-1933.

Thus, the system of national accounts was developed in the late 1920s. a group of American scientists, employees of the National Bureau of Economic Research, under the leadership of future Nobel Prize winner Simon Kuznets.

These aspirations were further developed in the mid-1920s. during a period of rapid economic growth in developed countries (the so-called period of prosperity). Their goal was to forecast trends in economic development. Moreover, research was carried out not only in a specially created in the early 1920s. in the USA, a private organization - the National Bureau of Economic Research, where this work was headed by the famous American economist Wesley Claire Mitchell, who studied the problems of the economic cycle (which is impossible in the absence of a system of macroeconomic indicators). In parallel, work in this direction was carried out in Soviet Russia in the All-Russian (and subsequently All-Union) Supreme Council of the National Economy (VSNKh) in connection with the need to develop five-year plans for the development of the country's economy, as well as to assess trends in the development of the world economy and the prospects for the world revolution.

As mentioned earlier, in the West they began to develop a system of macroeconomic indicators in 1929 - 1933. This development was associated with the crisis that gripped America at that time, or the “Great Depression.” As a result, at the beginning of 1930, the US Congress decided on the need to develop a system of indicators (indicators) that would allow assessing the state of the American economy. In fact, such a system has already been created. Thus, at the same time, the US Congress issued a resolution on the development of this system of indicators.

After World War II, international economic organizations became involved in the development of a system of macroeconomic indicators, and in 1953 the UN published a document called “System of National Accounts and Supporting Tables,” which can be considered as the first internationally recognized version of a system of macroeconomic indicators. This system has been revised, and the 1993 version is now in effect. Since the late 80s. Russia also began to switch to it.

In order to take a closer look at the SNA, it is necessary to consider its main components, i.e. indicators:

The central indicator of the System of National Accounts is gross domestic product (GDP). The statistics of a number of foreign countries also use an earlier macroeconomic indicator - gross national product (GNP). Both of these indicators are defined as the value of the entire volume of final production of goods and services in the economy for one year (quarter, month). They are calculated in prices both current (current) and constant (of any base year). The difference between GNP and GDP is as follows:

GDP is calculated according to the so-called territorial basis. This is the total cost of production in the spheres of material production and services, regardless of the nationality of enterprises located on the territory of a given country;

GNP-- this is the total cost of the entire volume of products and services in both spheres of the national economy, regardless of the location of national enterprises (in their own country or abroad).

Thus, GNP differs from GDP by the amount of so-called factor income from the use of the resources of a given country abroad (profits transferred to the country from capital invested abroad, property owned there; wages of citizens working abroad transferred to the country) minus similar exports from the country of income of foreigners. This difference is very small: for leading Western countries it is no more than 1% of GDP.

The SNA uses, but much less frequently, two other general indicators: net domestic product and national income. By reducing the GDP value by the amount of depreciation charges accrued for the year, you can get two macroeconomic indicators - net domestic product (NDP) And national product (ND). The first shows the amount of income of suppliers of economic resources for the land, labor, capital, entrepreneurial abilities and knowledge they provide, with the help of which the PVP is created.

If we add the balance of factor income to PVP, we get net national income. This is the sum of the country's primary income. If we add to them the balance of those incomes that are transferred as transfers during the redistribution process, we obtain a value called national disposable income.

In our country, the transition to new indicators - first GNP, and then GDP - began in 1988. This transition is carried out through recalculation gross social product (GSP) And national income (NI), representing, respectively, the sums of gross output and net output of sectors of material production.

Index GP was the main one in Soviet economic statistics and represented the total value of the total volume of goods and services produced in the sphere of material production, including the costs of raw materials, materials, fuel, etc., i.e. was not free from re-counting. The national income indicator was also calculated only on the basis of material production.

Fundamental differences in the methodology for calculating these indicators and SNA indicators naturally lead to the fact that the recalculated GP and NI of the former USSR and Russia can only approximately characterize their GDP and NI.

In order to make the calculation of these indicators more clear and visual, I would like to present their calculation:

BB -- Gross output = BB products + BB services

PP -- Intermediate consumption

GVA -- Gross value added = ВВ -- PP + VAT + CHNI

GDP -- Gross Domestic Product = ?GVA = ?BB -- ?PP +

VAT + ?PNI = ?GVA of industries = ?GVA of sectors

VAT -- Value Added Tax

CHNI -- Net import tax

NNP -- Net tax on product

NDP -- Net Domestic Product = GDP -- POK

ND -- National income = GDP -- POK

POK -- Consumption of fixed capital

GPE -- Gross profit of the economy = GPE of industries + GPE of sectors

NPE -- Net profit of the economy = VPE -- POK = (BB -- PP) --

- (OT + CHN + POK)

RND -- Disposable national income = NNI + CHTT

GRND -- Gross disposable national income =

VRND sectors = VNS + CP

CNRD -- Net National Disposable Income = GRND -- POK

KP -- Final consumption

GNS -- Gross National Savings = GRND -- KP

Sat -- Savings = Dr. -- Rt

Dt -- Current income

Rt -- Current expenses

CHT -- Net current transfers from abroad

NNS -- Net National Saving = GNS -- POK

P -- Products

U -- Services

OT -- Remuneration

Since we have already become a little familiar with the SNA, in which the interindustry balance plays an important role, we can now take a closer look at the characteristics of the interindustry balance itself.

The rules for compiling the intersectoral balance are coordinated with the rules for compiling key accounts of the System of National Accounts, and the content of the main indicators in the various quadrants of the balance corresponds to the content of these indicators in other parts of the SNA.

There are three main parts (quadrants) in the intersectoral balance scheme according to the SNA methodology:

internal, or first, quadrant (I quadrant);

lateral, or right, wing (II quadrant);

lower wing (III quadrant).

According to the period of analysis of the input-output balance are divided into two types. If the production process in the input balance is considered over several years, and the results of the first year determine the conditions of production in the second year, then such a system is called dynamic. A feature of dynamic input-output balances is that they exclude capital investments from final use. This means that capital investment in the dynamic input-output balance is a function of industry output in subsequent years. Dynamic input balances describe economic development much more accurately than any other economic and mathematical methods. Another type of interindustry balance is static balances, in which capital investment is included in final use. Thus, static input balances are compiled for one year, and dynamic ones - for several years.

In terms of the volume of information used, interindustry balances are divided into:

national (built for the country as a whole);

district (built for individual districts);

inter-district (describing production connections of different regions);

industry-specific (compiled for a particular industry).

By the nature of the meters used, input-output balances There are monetary (cost) and natural.

In monetary (value) inter-industry balances, all indicators are given in monetary terms, and in natural inter-industry balances, some indicators are given in physical terms. The difference between such balances is that the cash balance indicators can be summed up in a column, but the natural balance cannot be summed up.

By the nature of the reflection of intersectoral connections, intersectoral balances are divided into two types: inter-industry balances compiled according to the “Input - Output” scheme, and the tabular form “Resources and use of goods”.

Currently, the system of balance sheet constructions based on the MOB can be classified as follows:

Reporting and planned balance sheets. Reporting balances characterize the relationships between industries according to the reporting period. Planned balances give an idea of changes in inter-industry connections in the future under the influence of shifts in production technology, or under the influence of changes in the sectoral structure of final demand and its functional elements.

By object of observation we can distinguish inter-industry balances of products, inter-industry balances of labor, capital and investment flows.

Types of intersectoral balance sheet constructions by the nature of the model:

static open model;

dynamic model of MOB;

closed MOB model. The closed MOB model is designed to reflect the state of a closed economic system in which there is no autonomously specified final demand at all. In this model, its fourth quadrant reflects the processes of transformation of factor income into elements of final demand.

Interindustry balance with optimization elements. Intersectoral balance with optimization elements is designed to answer the question of finding optimal sectoral proportions in the country's economy. Its practical implementation is associated with solving the issue of the criterion for optimizing the socio-economic development of the country, as well as the problem of the variety of technological methods for producing products of this type.

Thus, we have determined that the intersectoral balance is one of the main components of the system of national accounts. In addition, we considered not only the classification of the input-output balance, but also considered the SNA.

I would like to consider in detail the inter-industry balance “Input - Output”, because this particular balance is called the Leontief inter-industry balance. I would also like to calculate this balance using the example of 5 industries.

Intersectoral balance reflects the production and distribution of the gross national product by industry, 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 sectors of the economic system, shown in tables (matrices) and analytically (systems of equations and inequalities).

Let's consider a simple example of a value balance for an economic system of three sectors: agriculture, industry and households. In each sector, for the production of goods and services, resources (raw materials, labor, equipment) created in it and in other sectors of the economic system are consumed.

Each sector in the system of intersectoral connections is both a producer and a consumer.

The purpose of balance sheet analysis is to determine how much output each sector must produce to satisfy the economic system's demand for its output.

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

1. Agriculture – 200 thousand rubles, including:

for your 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 inter-industry balance table: numbers in 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 economic sectors (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	Household	General release
Agriculture	50	40	110	200
Industry	70	30	150	250
Household	80	180	40	300
Expenses	200	250	300	750

Here, all sectors produce products and they also consume all products.

This closed model of intersectoral connections - 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 the input-output balance

Strings tables (matrices) with producing sectors have numbers: i=1- n, where n is the number manufacturing 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 balance consists of a row and column number. 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 costs in each sector satisfies the system of equations:

An input-output matrix of this type is called a matrix closed Leontiev's input-output model, who first described it in 1936.

An example of an open input-output system

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

Let the country's economy have n industries of 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 produced products (total product) are divided into two parts:

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

Let's denote by:

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

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

Since the gross volume of production is any i-th industry is equal to the total volume of products consumed n industries and the 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 interindustry balance, when all the quantities included in these equations have a cost expression.

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

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

If you enter:

matrix of direct cost coefficients A = (a ij ),
column vector of gross output X = (X i)
column vector of final products Y = (Y i),

then the mathematical model of the interindustry 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 - mutual comparison of available resources and needs for them.

Total cost factor (b ij ) shows how many products i-th the industry needs to produce in order to take into account direct And indirect costs of this product, obtain a unit of final product j-th industry.

Full expenses reflect the use of resources at all stages of production and are equal to the amount direct And indirect costs at all previous stages of production.

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

Productivity criteria of matrix A

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

2. In order to ensure positive final output in all sectors, 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. the matrix (E - A) has the inverse of the matrix (E - A) -1.
The largest absolute eigenvalue of the matrix (A), i.e. solution to the equation |λE - A| = 0 is strictly less than one.
All major minors of the matrix (E - A) of order from 1 to n are positive.

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

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

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

Need to determine new product release vector X with a new vector of demand U (you will find the solution in the downloaded file).

Intersectoral balance

Intersectoral balance(IOB, input-output method) is an economic and mathematical balance model that characterizes intersectoral production relationships in the country’s economy. Characterizes the connections between output in one industry and the costs and consumption of products from all participating industries necessary to ensure this output. The inter-industry balance is compiled in cash and in kind.

The interindustry balance is presented as a system of linear equations. The intersectoral balance (IB) is a table that reflects the process of formation and use of the total social product in a sectoral context. The table shows the cost structure for the production of each product and the structure of its distribution in the economy. The columns reflect the value composition of the gross output of economic sectors by elements of intermediate consumption and added value. The lines reflect the directions of use of resources in each industry.

The MOB Model identifies four quadrants. The first reflects intermediate consumption and the system of production links, the second - the structure of final use of GDP, the third - the cost structure of GDP, and the fourth - the redistribution of national income.

Story

The theoretical foundations of the input-output balance were developed in the USSR in 1923-1924, when V.V. Leontyev made an attempt to present in numbers an analysis of the balance of the national economy of the USSR. The scientist showed that the coefficients expressing connections between economic sectors are quite stable and can be predicted.

In 1959, the USSR Central Statistical Office developed a reporting inter-industry balance in value terms (for 83 industries) and the world's first inter-industry balance in physical terms (for 257 positions). At the same time, applied work began in the central planning bodies (Gosplan and State Economic Council) and their scientific organizations. The first in the USSR and one of the first in the world dynamic intersectoral model of the national economy was developed in Novosibirsk by Doctor of Economic Sciences Nikolai Filippovich Shatilov (source: "Science in Siberia", 2001 http://www-sbras.nsc.ru/HBC/2001/ n03/f12.html). The first planned inter-sectoral balances in value and physical terms were constructed in 1962. Further work was extended to the republics and regions. Based on data for 1966, intersectoral balances were constructed for all union republics and economic regions of the RSFSR. Soviet scientists created the groundwork for the wider use of intersectoral models (including dynamic, optimization, natural-cost, interregional, etc.)

In the 1970-1980s in the USSR, based on data from intersectoral balances, more complex intersectoral models and model complexes were developed, which were used in forecast calculations and were partly included in the technology of national economic planning. In a number of areas, Soviet interdisciplinary research occupied a worthy place in world science.

At the same time, Leontyev clearly understood that the theoretical developments of Soviet scientists did not find practical application in the real economy, where all decisions were made based on the political situation:

Western economists have often tried to uncover the “principle” of the Soviet planning method. They were never successful, since to this day such a method does not exist at all.

Example of calculation of input balance

Let's consider 2 industries: coal and steel production. Coal is needed to make steel, and some steel - in the form of tools - is needed to mine coal. Let's assume that the conditions are as follows: to produce 1 ton of steel you need 3 tons of coal, and to produce 1 ton of coal - 0.1 tons of steel.

We want the net output of the coal industry to be (200,000) tons of coal, and the net output of the iron and steel industry to be (50,000) tons of steel. If each of them produces only tons, then part of the production will be used in another industry.

It takes (150,000) tons of coal to produce tons of steel, and (20,000) tons of steel to produce tons of coal. The net output will be: (50,000) tons of coal and (30,000) tons of steel.

It is necessary to produce additional coal and steel in order to use them in another industry. Let's denote - the amount of coal, - the amount of steel. We find the gross output of each product from the system of equations:

Solution: 500,000 tons of coal and 100,000 tons of steel. To systematically solve the problems of calculating the input balance, they find how much coal and steel is required to produce 1 ton of each product.

AND . To find how much coal and steel is needed for a net output of tons of coal, you need to multiply these numbers by. We get: .

Similarly, we create equations to obtain the amount of coal and steel for the production of 1 ton of steel:

AND . For clean production of tons of steel you need: (214286; 71429).

Gross output for the production of tons of coal and tons of steel: .

Dynamic MOB model

The first in the USSR and one of the first in the world dynamic intersectoral model of the national economy was developed in Novosibirsk by Doctor of Economic Sciences Nikolai Filippovich Shatilov (source: "Science in Siberia", 2001 http://www-sbras.nsc.ru/HBC/2001/ n03/f12.html) This model and the analysis of calculations for it are described in his books: “Modeling of expanded reproduction” (Moscow, Economics, 1967), “Analysis of the dependencies of socialist expanded reproduction and the experience of its modeling” (Novosibirsk, Nauka, Siberian department ., 1974), and in the book “The Use of National Economic Models in Planning” (edited by A.G. Ananbegyan and K.K. Valtukh; Moscow, Economics, 1974).

Subsequently, other dynamic MOB models were developed for various specific tasks.

Based on Leontiev’s model of intersectoral balance and his own experience, the founder of the “Scientific School of Strategic Planning” Nikolai Ivanovich Veduta (1913-1998) developed his dynamic MOB model.

Its scheme systematically coordinates the balances of income and expenses of producers and end consumers - the state (interstate bloc), households, exporters and importers (external economic balance).

The dynamic model of MOB was developed by him using the method of economic cybernetics. It is a system of algorithms that effectively links the tasks of end consumers with the capabilities (material, labor and financial) of producers of all forms of ownership. Based on the model, the effective distribution of public production investments is determined. By introducing a dynamic MOB model, the country's leadership has the opportunity to adjust development goals in real time depending on the updated production capabilities of residents and the dynamics of end-consumer demand. The dynamic model of the MOB is set out in the book “Socially Efficient Economy”, published in 1998.

Notes

Literature

compiled by Gontareva I. I., Nemchinova M. B., Popova A. A. Mathematics and cybernetics in economics: Dictionary-Reference Book / resp. ed. acad. Fedorenko N.F., editor. acad. Kantorovich L.V. et al. - M.: Economics, 1974. - 699 p.

Shatilov N. F. Simulation of expanded reproduction. - M.: Economics, 1967. - 173 p.

Shatilov N. F. Analysis of the dependencies of socialist expanded reproduction and the experience of its modeling / resp. ed. Ozerov V.K.. - Novosibirsk: Science, Sibirsk. department, 1974. - 250 p.

Shatilov N. F., Ozerov V. K., Makovetskaya M. I. et al. The use of national economic models in planning / ed. Ananbegyan A.G. and Valtukha K.K. - M.: Economics, 1974. - 231 p.

Veduta, N. I. Socially effective economics / Ed. Veduta E.N. - M.: REA, 1999. - 254 p.

Veduta, N. I. Economic cybernetics . - Mn: Science and Technology, 1971. - 318 p.

see also

Links

Federal statistical observation "input-output" for 2011

Wikimedia Foundation.

2010.

See what “Inter-industry balance” is in other dictionaries: intersectoral balance - MOB Framework model of the economy, a table that shows the diverse natural and cost relationships in the national economy. Analysis of the MOB provides a comprehensive description of the process of formation and use of the aggregate public... ...

See what “Inter-industry balance” is in other dictionaries: Technical Translator's Guide - Balance of production and distribution of the social product by industry, which serves as a method for analyzing and planning proportions for expanded reproduction in a sectoral context...

Dictionary of Geography Economic dictionary

See Balance of intersectoral... Great Soviet Encyclopedia

Economic-mathematical balance model in the form of a system of linear equations characterizing the relationship between output in one industry (in value terms) and costs, consumption of products of all participating industries, necessary... ... Encyclopedic Dictionary of Economics and Law

Interindustry balance (IB)

Interindustry balance (IB)- a frame model of the economy, a table that shows the diverse natural and cost connections in the national economy. MRD analysis provides a comprehensive description of the process of formation and... Economic and mathematical dictionary

BASICS OF INTER-INDUSTRY BALANCE PLANNING

The most important task of further improving planning is to improve the balance of production, and the production of exactly those products that are needed to develop production and meet the growing demand of the population. For this purpose, a number of economic and mathematical models are used, including inter-industry balances.

The central idea of the inter-industry balance is that each industry is considered both as a producer and as a consumer. The input-output balance model is one of the simplest economic and mathematical models. It represents a unified interconnected system of information on mutual supplies of products between all sectors of production, as well as on the volume and sectoral structure of fixed production assets, the provision of the national economy with labor resources, etc.

We are counting

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and write it down in Table 1 in the corners of the corresponding cells. The found coefficients form a matrix of direct costs

All elements of this matrix are non-negative. This is written as a matrix inequality and such a matrix is called non-negative.

By specifying the matrix, all internal relationships between production and consumption, characterized by the original table 1, are determined.

Now you can write a linear balance model corresponding to the data in Table 1, if you substitute the values in the balance equations

(4)

or in matrix form

, ,,https://pandia.ru/text/78/176/images/image018_44.gif" width="16 height=23" height="23">.gif" width="17" height="23"> and, to study the impact on gross output of any changes in the range of final products, to determine the matrix of total cost coefficients, the elements of which serve as important indicators for planning the development of industries, etc.

General model of inter-industry balance of production

Table 2 considered is nothing more than one of the main economic models (given in abbreviated form), widely known in our country and abroad: the inter-industry balance of production and distribution of products in the national economy (MBB).

In general, the MOB consists of four main parts - quadrants (Table 3).

Table 3

Quadrant I contains indicators of material costs for production. In rows and columns, industries are arranged in the same order. The value represents the cost of means of production produced in the th industry and consumed as material costs in https://pandia.ru/text/78/176/images/image048_17.gif" width="13" height="15"> -th order, standing in the first quadrant, is equal to the annual fund for reimbursement of the costs of means of production in the material sphere.

Quadrant II shows final products used for non-productive consumption, accumulation and export. Then this quadrant can be considered as the distribution of national income into the accumulation fund and the consumption fund by sectors of production and consumption.

In the III quadrant, national income is characterized, but from the side of its cost composition of net products (wages, profits, turnover tax, etc.).

Quadrant IV reflects the redistribution of net production. As a result of the redistribution of the initially created national income, the final income of the population, enterprises, and the state is formed. If all MOB indicators are written in monetary terms, then in the balance sheet columns they represent the formation of the value of gross output, and in the rows - the distribution of the same products in the national economy. Therefore, the indicators of the rows and columns are equal.

The gross output of industries is presented in Table 3 as a column located to the right of the second square and as a line located under the third quadrant. These columns and rows play an important role both for checking the correctness of the balance itself (filling in the quadrants) and for developing an economic and mathematical model of the interindustry balance.

In general, the intersectoral balance within the framework of the general model combines the balances of sectors of material production, the balance of the total social product, the balances of national income, the balance of income and expenditure of the population.

Based on formula (2), we divide the indicators of any MOB column by the total of this column (or the corresponding line), that is, by gross output. Let us obtain the costs per unit of this product, which form a matrix of direct costs:

. (6)

Cost balance along with equations

, (7)

each of which represents the distribution of products of a given industry across all industries, allows the construction of equations in the form of product consumption

, (8)

where is the material costs of the th consuming industry, is its net output ( is the amount of wages, is net income).

Substituting relations (3) into equations (7), after transformations we obtain

(9)

We write the MOB system of equations (9) in matrix form

where is the unit matrix, is the direct cost matrix (6), and are the column matrices.

The system of equations (9), or in matrix form (10) is called the economic-mathematical model of the input-output balance (Leontief model).

The interindustry balance model (10) allows you to solve the following problems:

1) determine the volume of final products of the industries https://pandia.ru/text/78/176/images/image064_11.gif" width="80" height="24">;

2) according to a given matrix of direct cost coefficients https://pandia.ru/text/78/176/images/image065_11.gif" width="91" height="24">, the elements of which serve as important indicators for planning the development of industries;

3) determine the volume of gross output of industries https://pandia.ru/text/78/176/images/image063_12.gif" width="83" height="24">;

4) for given volumes of final or gross output of industries determine the remaining volumes.

Direct costs play an extremely important role in the balance sheet. They serve as an important economic characteristic, without knowledge of which national economic planning would not be possible.

The direct cost matrix essentially determines the structure of the economy. If we know the direct costs and final product of each sector of the economy, then we can calculate the volume of gross output.

To produce a car in Tolyatti, it is necessary to provide electricity not only to the plant itself, but also to the rolling mills of the Magnitogorsk plant, and the tire plant in Yaroslavl, and many others. Therefore, if 1.4 thousand kWh of electricity is spent directly on one car, then at all intermediate stages - another 2 thousand kWh (indirect costs of electricity), and a total of 3.4 thousand kWh. To produce 1 ton of staple fiber from lavsan, about fifty thousand rubles of capital investment are required directly for the chemical fiber plant, and in related industries - about eighty thousand rubles. To produce meat products for 1,000 rubles, capital investments in the meat industry should amount to 900 rubles, and in other related industries. industries - rubles, i.e. 20 times more.

Thus, direct costs do not fully reflect the complex quantitative relationships observed in the national economy. In particular, they do not reflect feedback, which is of no small importance.

How do indirect costs arise? For the manufacture of a tractor, cast iron, steel, etc. are consumed as direct costs. But for the production of steel, cast iron is also needed. Thus, in addition to the direct costs of cast iron, there are also indirect costs of cast iron associated with the production of the tractor. These indirect costs also include the cast iron required to create the amount of cast iron that constitutes the direct costs. These indirect costs can sometimes significantly exceed direct costs.

The gross output of the kth industry is defined as

Optimization of the inter-industry balance

Since the main task of the economy is to improve production and save human labor, the task arose of optimizing the national economic model built on the basis of the MOB.

The possibility of optimizing MOB appears if direct cost coefficients reflect costs not average for the industry, but for each production method and technology. In such MOB models, the production of open-hearth steel, converter steel, and electric steel is presented separately; synthetic and cotton fabrics, etc. As a result, the optimal option with minimal costs for the production of a given volume of products must be found.

What does it mean to create an optimal MOB? If to calculate total costs and price levels it is necessary to solve hundreds of equations and perform millions of computational operations, then calculating the optimal MOB requires millions of equations and many billions of computational operations. At present, there are still no mathematical methods and electronic machines to solve such problems head-on. The data necessary for this is not yet available in full. Now we can only talk about individual important blocks for which such data is available or can be prepared in the near future.

That is why it is necessary to create a system of models for block optimization of MOB. This should be a flexible system, which could include more and more optimal blocks as they become ready.

Since all production is directly or indirectly connected with each other, the optimization of each block each time necessitates a complete recalculation of the MOB on a computer. It’s a lot of work, but the result is incomparably greater - after all, behind every percentage increase in the efficiency of social production, billions of saved rubles are hidden.

We will demonstrate the optimization of the interindustry balance using the example of reducing balance problems to linear programming problems.

reaches a minimum.

Reporting inter-industry balances are a means of analyzing the structure of the economy and the initial basis for compiling inter-industry balances. Reporting interindustry balances are developed on the basis of data on the structure of production costs received from enterprises as a result of a special one-time survey.

The development of planned intersectoral balances is aimed primarily at improving the balance planning method, accurately quantifying the complex interrelations of the process of social reproduction, and calculating balanced options for the structure of the national economy based on the widespread use of electronic computers.