Introduction

Input-output model (IOM) distributes gross output on intermediate and final demand. Algebraic input-output method allows simultaneously taking into account production costs of goods with consideration of technological interconnection. The matrix of technological coefficients demonstrates direct costs of industries on production, and matrix of multiplicators shows complete costs of industries on production of their goods (with consideration technologically linked costs of the others industries). A difference between complete and direct costs forms indirect costs.

In article [3] the fraction of indirect costs of industry is calculated by means the language Octave [4] with the using of technological coefficients matrix and eigenvector of matrix.

For the input-output matrix is solved both direct problem (for the calculation of GDP), and indirect problem (for estimation of the gross value added) after the types of economical activities [5] with using existent restrictions (material, labor etc).

Problem Statement

Industry priority is determined by the state on the size of budget revenue in the state budget, by the increasing of employment, by the raising of gross output, that is after explicit (direct) indexes, not taking into account the indirect influencing (external effect), which industry is diffuses on the other industries of country.

Purpose of this article is to define direct and indirect influence (external effect) of every industry of Ukrainian economy on the gross output of country for application of state support for priority development industries.

Results

At construction of interindustry balance take into consideration interdependence between separate economical industries and their links with final demand, that is represented into table 1 (хij -production output of i-th industry, that is used for manufacture of the products of j-th industry; Xj -gross output of j-th industry; Yjfinal demand on the products of j-th industry) [6]:

Industries-consumers

Industriesproducers

1 2 3 … n Final demand Gross output 1 х 11 х 12 х 13 … х 1n Y 1 X 1 2 х 21 х 22 х 23 … х 2n Y 2 X 2 3 х 31 х 32 х 33 … х 3n Y 3 X 3 ………. n x n1 x n2 x n3 … x nn Y n X n Labor cost L 1 L 2 L 3 … L n - L

Let us to denote cost of labor for production of j-th industry good through L j , where j=1,2,…,n -number of industry, and output production of this product (gross output) through X j , then direct labor cost on unit of j-th type of product (coefficient of direct labor-intensiveness) are determined by a formula:

, 1, ..., .

j j j L t j n X  (2)

A general needs in labor resources for n industries is determined after a formula:

1 1 2 2 1 1 ... n n i i i n n i i L L t X t X t X t X              (2)

From a formula X B Y   ( B -matrix of multipliers or complete costs) we will get the following values of industries production output:

1 1 1 1 1 2 2 1 2 2 1 1 2 2 2 2 1 12n n n n n n n n n n X b Y b Y b Y X b Y b Y b Y X b Y b Y b Y                     (3)

Then labor cost can be presented as follow:

      1 1 1 1 1 2 2 1 2 2 1 1 2 2 2 2 1 1 2 2 ... ... ... n n n n n n n n n n L t b Y b Y b Y t b Y b Y b Y t b Y b Y b Y                        

We will rearrange the elements regarding to final demand on the industries products, we will obtain:

      1 11 1 21 2 1 2 12 1 22 2 2 1 1 2 2 ... ... ... n n n n n n n n n n L Y b t b t b t Y b t b t b t Y b t b t b t                        

From the last equation we will calculate the complete labor costs:

1 1 1 1 2 1 2 1 2 1 2 1 2 2 2T b t b t b t T b t b t b t T b t b t b t                     

We will rewrite indirect labor costs as a matrix by the following formula: Difference between direct i t and complete i T labor costs consists in that direct labor costs show an additional (marginal) needs in labor resources for i-th industry after unit increasing of final demand on the products of i-th industry, and the complete labor costs show an additional (marginal) needs in labor resources for all n industries after the unit increase of final demand on the products of i-th industry.

1 11 1 11 11 11 T t B      , 1 11 11 11 11 ( ) B E A     (4) where

On the basis of direct and complete labor coefficients are developed interindustry labor costs balances for available labor resources. These balances are built as matrix models, and all indexes in them (interindustry links, final product etc) are expressed in labor measurer (amount of persons).

V. Kobets

For reduction of matrix model dimension without the loss of generality of its conclusions we reduced the number of Ukrainian industries from 15 to 11 by regrouping, after that we yield:

List of industries: 1. Agriculture, hunting, forestry, fishing, fish-farming. 2. Mining industry, processing industry, production and distributing of electric power, gas and water. Values of table 2 columns for the gross output and final demand are got on the basis of Statistics state committee data [1], employment after industries is received from statistical collection [2], and the gross value added is calculated by the means of MS Excel on the basis of IOM [6]. We got from the indexes of profitability (fig. 2), there are three unprofitable industries in 2010, which give such public benefits as state administration, education and health protection. These industry require considerably greater financing on own activities, than they earn. However finally to make decision about their influence on an economy as a whole it is possible only taking into account externality, i.e. their influence on the other industries of Ukrainian economy. After calculation of industries multipliers from matrix B we will get that a most increase of GDP is induced exactly by those industries which are financed from the state budget. Every hryvnya invested in state administration; education and health protection is enhanced gross output in Ukraine on 7 hrn.; by 61 UAH and 11 UAH accordingly, that with surplus covers direct costs of state on these industries activities. Educational industry has most significant influencing and there is reserve for the increasing of country gross output. Education stimulates a positive GDP dynamics. So after a direct effect this industry on every invested hryvnya gets a loss in size of 10 to UAH, and after indirect get profit in 26 UAH (multiplication of average profitability on multiplier), that together gives the positive influencing in 16 UAH on the gross value added of Ukrainian industries.

Thus the crisis phenomena in the economy of country are not to stipulate the cost decreasing after all directions in same proportion. The state adjusting of industry has to base on that return which is had by every industry and proportionally to its influence on an economy not to decrease, and in the some cases, taking into account their external effects, to increase state costs for them for stimulation of gross output of all linked industry.

After finding relation of final demand to the gross output X (from table 1) we will get what measure of each industry is oriented into final, and which is on intermediate demand (fig. 3). We have, that build industry (3) is most oriented on final demand (94,3% whole product), and  trade industry, activity of hotels and restaurants (4);  financial activity (6) We will consider application of interindustry balance method for direct and indirect influence on Ukrainian industries' production on a labor market. The important analytical possibility of this method is determination of direct and complete labor cost on product unit and development the recommendations in relation to state support of priority development industries for the stimulation of employment growth of country.

After the calculations after formulas (1) and (4) we will present results as table 4: