Scientific journal

European Journal of Natural History

ISSN 2073-4972

ИФ РИНЦ = 0,301

Essentially, all the models are wrong, but some of them are useful.

George Box

In the industry of the Republic of Kazakhstan to share-but-West Kazakhstan region is accounted for about 9 percent of the total volume of industrial production. Let us consider some types of models of production functions, the dynamics of shares of mining and manufacturing industries, the structure of the gross regional product, the coefficient of variation in output growth of the economy in relation to the industrial production of the Wes-Kazakhstan region. And the construction schedule of production functions is considered, where the actual and estimated values of the industrial production volume clearly have been shown.

The industrial production share (e.g. for 2005−2011) is made up about 50 per cent for in the gross regional product (GRP) structure of the Western-Kazakhstan Region. The share of the other major sectors (e.g. the agriculture, building, services’ production) is accounted for the rest part of GRP (Fig. 1).

Fig. 1. The gross regional product (GRP) structure of the Western-Kazakhstan Region, (2005–2011)

About 9 per cent of the total industrial production volume is accounted on the share of the Western-Kazakhstan Region in the industry of Republic of Kazakhstan.

So, the industrial production volume in the Western-Kazakhstan Region for 1994−2011 years has been developed unevenly, which can be seen in the Fig. 2.

Thus, the sustainable industry development has been planned around since 2002.

As a part of the industrial production, the main share is accounted on the mining industry (e.g. about 90 per cent) and the manufacturing one. The manufacturing industry is approximately taken 8,5 per cent of the total industrial production volume.

Fig. 2. The Industrial Production Volume in the Western-Kazakhstan Region (1994 – 2011), mln. tenge

The shares dynamics of the mining and the manufacturing industries in the structure of the industrial production (e.g. in per cent) have been given in the following Table 1.

Table 1

The Region is rich in the fuel and energy resources types (e.g. the crude oil and the petroleum gas, the natural gas), and, in short term, the mining and the manufacturing industries will be remained the main branches of the Region’s industrial production.

The variation coefficient of the volume industrial production for 2005–2011 years has been amounted 6,3 per cent. During the period of 2000–2011 years, the volume variation of the industrial production has been made up 38,9 per cent, while for the period of 1994–2011 years, the variation coefficient is amounted 50 per cent.

Fig. 3. The Structure of the Mining and Manufacturing Industries in the Industrial Production (e.g. 2006 – 2010 years), %

For the period of 1994–2011 years, the average annual growth rate of the volume industrial production has been made up 0,58 per cent.

The economic growth issues are the fundamental question of any economic system. The economic growth is defined and measured in two interrelated ways: it is the real GRP increase over some period of time, or it can be possible to be regarded, as the increase in some time period of the real GRP per capita.

There are two basic types of the economic growth: the extensive and the intensive ones.

The extensive economic growth is meant, that the production volume quantitative increase of the goods and the services is practically taken its place at the qualitative constancy of the production factors.

The intensive economic growth is connected to the fact that the goods and the services production increase is provided by the efficiency improving of the production factors. This production type is led to be overcome the productive resources limitations, it is involved the technological process improvement, and its further introduction into the production process.

So, the extensive factors of the further economic growth are the following: the volume increase in the raw materials, materials, and fuel consumption; the employed workers increase; the investments volume increase with the technologies existing level.

The intensive factors of the further economic growth are the following: the use improving of the fixed and the circulating capitals; the workers skills development; the GDP acceleration (e.g. first of all, the new techniques and the technologies introduction, through the fixed assets renewal); the production organization further improvement.

In reality, the two opposite type of the economic growth can be interacted, and to be coexisted.

The economic theory has long been sufficiently to be investigated the economic growth challenges.

So, the production functions are being widely used for the mathematical description of the manufacturing process in the economic theory.

So, the production function – this is the mathematical – economically correlation, that is specified the link between the economic characteristics of the issue and the used economic resources (e.g. factors), or their shared volumes in the analytical form. The various economic units are described through the production function: the enterprises, the industries, national economy, as a whole. Thus, the production functions are used the most commonly of the type Y = AKαLβ, here Y – issue, K – the production assets, L – the labor, А, α, β – the coefficients, having determined by the statistical data processing.

The most common type of the production function – is the Cobb–Douglas function, having named after its creators. The American economist Paul Douglas has still noticed in 1927, that the national income distribution between the labor and the capital is practically being changed little over time, i.g. the production growth and the workers, and the capital owners are equally enjoyed by the benefits of the thriving economy. Before Douglas the task has been faced to be determined the causes of such constancy shares of the production factors. He had turned to the mathematician Charles Cobb that he found the function with the properties of the permanent shares of the production factors, having provided that the production factors are always received their marginal products. Such function has been derived the following expression:

Y = АKαLβ,

where А – is the proportionality factor; α, β – is the coefficient of elasticity of the goods output by the capital and the labor costs.

The given function is based on the assumption of the complete interchangeability of the labor and the capital, on the constant return of each unit of any factor.

The following application variants of the Cobb – Douglas function are quite possible:

а) α + β = 1 – the constant efficiency of the production factors;

b) α + β > 1 – the increasing efficiency of the production factors;

с) α + β < 1 – the falling efficiency of the production factors.

The further modification of the Cobb – Douglas production function is connected with it, having taken into account the impact of the technological and scientifically progress. The production function after Ya. Tinbergen – is one of the possible forms of these functions. He has removed the restriction on the exponents of the production functions, which are equal to one. So, in this case, the production function is acquired the following form:

Y = АKαLβ,

where a and b – the coefficients of elasticity of the production volume by the capital and the labor, respectively.

When (a + b) = 1, this function is became the Cobb – Douglas production function with its advantages and disadvantages.

The coefficient of elasticity is shown the product’s relative change, having expressed in the percentage, with the relative increase in the factor of one per cent. If the output elasticity by the capital a is more the output elasticity by the labor, then the economy has the labor – saving (e.g. intensive) growth. If the inequality is performed b > a, then we have the asset – saving (e.g. extensive) growth of the econo-world. In this case, the labor force increase by one per cent is practically led to a greater increase in the production volume, than the same increase in the capital.

Another modification of the Cobb–Douglas production function is associated with the name of Robert Solow, who has proposed to be considered the technological – scientifically progress upon the economic growth, as the independent variable. So, in this case, the production function is acquired the following form:

Y = АKαL1–αеλ,

where l – is the growth rate of the production total gross output, at the expense of the technological – scientifically progress.

So, the coefficient value l is indicated the impact degree of the technological – scientifically progress upon the economic growth.

So, let us consider some models types of the production functions, with respect to the industrial production of the Western-Kazakhstan Region.

As the models, let us consider the following five types of the Cobb – Douglas, Ya. Tinbergen, R. Solow production functions; the function, when the information resource is considered, as the GDP par; and the information resource, as the separate factor of the production):

● Y = АKaL1–α;

● Y = АKαLβ;

● Y = АKαL1–βеγt;

● Y = АKαL1–βеγI;

● Y = АKαL1–βIγ.

The model parameters have been calculated by the program PF lite v. 2.2 beta release (e.g. after the author N. Rykov), according to the Annex 2 data.

Y = 0,4986∙K0,3482∙L0,6518;

Y = 0,7021∙K0,1866∙L1,5766;

Y = 0,0889∙K0,0035∙L0,9965∙е0,1679t;

Y = 0,2142∙K0,4118∙L0,5882∙е0,8683I;

Y = 0,6987∙K0,1771∙L1,6025∙I–0,0116.

The average relative error of the approximation (e.g. it has been given in %).

The models 2 and 5 have been given the smallest relative error, i.e. the production function model after Ya. Tinbergen and PF, when the information resource is considered, as the separate factor.

Let us construct the graphs of the production functions for the actual and estimated values of the industrial production volume in the Western-Kazakhstan Region for the 1994–2011 years. These graphs have already been shown in Figs. 4 and 5.

Table 2

Fig. 4. The actual and estimated values of the industrial production volume in the Western-Kazakhstan Region (e.g.1994–2011)

Fig. 5. The actual and estimated values of the industrial production volume in the Western-Kazakhstan Region (e.g.1994–2011)

So, the calculations have been shown, that the industrial production is being developed through the extensive way (e.g. b = 1,5766 > a = 0,1866) in the Western-Kazakhstan Region, i.e. the workforce increase by one per cent is practically led to a greater increase of the industrial production volume, than the same increase by the capital.

And the model is shown the same situation, when the investments are considered, as the production separate factor, and, for this, this factor influence upon the industrial production volume is practically absent (e.g. γ = –0,0116). So, the economic growth in the Region by this model is also pointed to the extensive growth of the industrial production – b = 1,6025 > 0,1771 = a.

Let us make the forecast of the industrial production volume by these models in the Western-Kazakhstan Region for the 2012 year. The ADAPTA program has been used for the forecasting purposes (e.g. after the author N. Rykov).The final results of the calculations by this program have been given in the subsequent Tables 3, 4.

Table 3

Table 4

Thus, the actual value of the industrial production value in the Western-Kazakhstan Region in 2012 has been amounted 1 480 715,8 tenge. The difference in the planned and the actual values of the GRP industry by the considered models are made up 9 and 9,9 per cent, which it can be considered to be the good approximation to the original and the initial data.

The expected calculated volume of the industrial production in the Western-Kazakhstan Region for the 2013 year is made up 1 579 979,4 mln. tenge, with the average relative error of the made prediction is about ± 9,2 per cent.

Table 5

The Origin Data on the Industry of the Western-Kazakhstan Region

Table 6

The Origin Data on the Industry (in the Coefficients – Data Is Divided into the Average Values Indices)