Analysis of the problem

Lets identify the problems in the education segment in economy of Ukraine by Cobb-Douglas production function. So first of all lets identify what is Cobb-Douglas production function:

So it is standard production function which is applied to describe much output two inputs into a production process make. This family of functions takes on the form , where ℓ is one factor of production (often labor) and is the second factor of production (often capital). The sum of the exponents determines the returns to scale on factor inputs. This Demonstration visualizes Cobb-Douglas functions by letting the user select the input exponents and as well as a scaling factor . You can also select whether the resulting production function is to be displayed as a contour plot or as a three-dimensional plot.

In its most standard form for production of a single good with two factors, the function is where a,b,c some parameters.

So in our case Cobb-Douglas gives an estimation of Y for GVA Y (Gross value added) for every region. Having annually 27 regional supervisions lnY, lnK, lnL by MS Excel lets estimate values of parameters lnc, a, b of linear dependence (where L = labor input, K = capital input).

.

Table #1

A gross value added Y (million Uah is in actual prices) and fixed assets K (million Uah) in education segment of regions of Ukraine:

	Y	LnY	K	lnK
Region
Vinnitsa		7,2		7,24
Volynsk		6,75		7,06
Dnipropetrovsk		7,98		8,31
Donetsk		8,22		8,63
Jytomyr		6,97		7,35
Zakarpattya		6,89		7,01
Zaporijia		7,37		7,74
Ivano-Frankivsk		7,06		7,27
Kyiv		8,68		8,83
Kyiv region		7,29		7,41
Kirovograd		6,75		6,88
Crimea		7,36		7,7
Lugansk		7,44		7,62
Lviv		7,82		8,12
Mykolaiv		6,91		7,29
Odessa		7,7		8,98
Poltava		7,11		7,43
Rivne		6,95		7,15
Sevastopol		6,04		5,89
Sumy		6,89		7,37
Ternopil		6,86		7,07
Harkiv		8,04		8,2
Herson		6,87		7,11
Hmelnytsk		7,12		7,5
Cherkasy				7,33
Chernivetska		6,67		7,28
Chernigiv		6,81		7,01

So from this table we can see that the highest GVA among all regions is in such regions as: Kiev City, Donetsk, Harkiv, Dnopropetrovsk and Lviv. In comparison with all results extremely high GVA has Kiev City. We can explain it as Kiev is the capital of Ukraine and it is normal that there is higher coefficient in this area. And the lowest GVA have such regions as: Sevastopol, Volynsk, Kirovograd and Chernigiv. We can explain as the result of low employment in this segment, low population and not high salary. Because of such conditions many people try to move from this area or work in another segment. The highest capital have such regions: Odesa, Kiev City, Donetsk, Dnipropetrovsk and Harkiv. Very interesting that Odesa has the highest amount of capital but has one of the lowest GVA. That’s show inefficient usage of capital. And The lowest capital is in such regions as: Sevastopol (this also can explain the low GVA), Kirovograd, Zakarpattia and Chernigiv.

Table #2

Average monthly salary W (in a calculation on one regular worker, Uah), employed N (thousand of persons), average annual salary L=12*N*W (million Uah) in education segment of regions of Ukraine, remains value .

	W	N	L	lnL	lnY-lnY'
Region
Vinnitsia		64,9		6,92	-0,05
Volynsk				6,5	-0,07
Dnipropetrovsk		118,6		7,66	-0,09
Donetsk		128,9		7,69	0,09
Jytomyr				6,73	-0,11
Zakarpattya		46,5		6,63	-0,06
Zaporijia		62,7		6,99	0,02
Ivano-Frankivsk				6,81	-0,09
Kyiv		119,7		8,05	0,18
Kyiv region		60,3		6,94
Kirovograd		36,9		6,35	0,1
Crimea		65,4		7,03	-0,04
Lugansk		68,2		7,03	0,05
Lviv		104,9		7,49	-0,07
Mykolaiv		43,1		6,55	0,03
Odessa		94,7		7,34	-0,08
Poltava		52,6		6,78
Rivne		47,1		6,62
Sevastopol		16,7		5,71	0,09
Sumy				6,56
Ternopil		47,4		6,59	-0,05
Harkiv		109,6		7,62	0,02
Herson		41,4		6,46	0,09
Hmelnytsk		53,4		6,73	0,05
Cherkasy		50,4		6,69	-0,03
Chernivetska		33,9		6,32	0,02
Chernigiv		42,1		6,49	0,01

In educational segment the highest salaries are in such regions as: Kiev City, Harkiv, Sevastopol and Dnipropetrovsk and in the same time the lowest salaries are in such regions as: Ternopil, Herson, Volynsk and Vinnitsia. The highest employment is in such regions as: Donetsk, Kiev city, Dnipropetrovsk and Harkiv. The highest employment in Kiev city because Kiev is the capital. As about eastern part of Ukraine, the high level of employment in such segment it is because teaching is one of the spread profession for women in that area. The lowest employment is in such regions as: Sevastopol, Chernivetska, Kirovograd and Herson. But the problem with salaries is not so far from Kiev city. Near the capital of Ukraine, in Fastiv region nowadays teachers don’t achieve salary during several months. and Today 21 November 2011 people from that area tried to protest and to achieve their salary but still get nothing and even more the government of that area didn’t tell the direct answer when the teachers will get their salaries.

Next step to analyse more deeper that main coefficient in educational segment, lets make a Regression analysis for education segment of Ukraine. Regression is used for the influence analysis on a separate dependent variable of values of one or more independent variables.

Then using the MS Excel function “Regression” we calculate the parameters a, b, c:

Coefficient of determination- A measure used in statistical model analysis to assess how well a model explains and predicts future outcomes. It is indicative of the level of explained variablity in the model. The coefficient, also commonly known as R-square, is used as a guideline to measure the accuracy of the model. That’s mean that with the coefficient of determination can be explained by the regression equation. Every sample has some variation in it (unless all the values are identical, and that's unlikely to happen). The total variation is made up of two parts, the part that can be explained by the regression equation and the part that can't be explained by the regression equation. The ratio of the explained variation to the total variation is a measure of how good the regression line is. If the regression line passed through every point on the scatter plot exactly, it would be able to explain all of the variation.

Regression statistics
multiple R	0,992153
R-square	0,984367
normed R-sq	0,983065
standard Error	0,072944
observations
dispersion analysis
	df	SS	MS	F	F-value
Regression		8,04106	4,020532	755,6216	2,13E-22
remained		0,1277	0,005321
total		8,16876
	coefficient	Stand.Error	t-statistics	P-value	lower 95%	upper 95%	lower 95,0%	upper 95,0%
Y-intercestion	-0,22393	0,19744	-1,134188	0,267918	-0,631424	0,1835603	-0,6314239	0,183560322
variable X 1	0,05067	0,05898	0,85912	0,398774	-0,071057	0,1723973	-0,0710569	0,172397317
variable X 2	1,028288	0,0761	13,51321	1,03E-12	0,871236	1,1853406	0,8712359	1,185340644

From this table we find out that

Also from the following table we obtain the next coefficients:

lnc= - 0,22

a= 0,05

b= 1,03

So with such coefficients we get such equation:

,

where a value in curves means standard deviation. Both got dependences testify or about the low role of capital for GVA of education, or about the question of measuring of capital in such special industry, as education.

And if to transfer it to its normal form we have:

Y=0,802K^0,05L^1,03

Where c=1.385 is a total factor productivity

If to analyze the coefficients separately we can say this:

R^2>0,98 is very close to 1 which is positive result.

By the rule the sum of a and b should equal to 1 (a + b = 1)

the production function has constant returns to scale: Doubling capital K and labor L will also double output Y. As well as that the level of effectiveness of resources does not depend from the scale of production. This is the perfect situation, but we have a little deviation, and in our case a+b=1.08 which is very close to 1, but still a little more. This means that returns to scale are increasing (if we increase the scale of production – mean expenses of recourses will increase as well).

The higher is the ‘a’ the higher is the dependence. Which means, for instance, that the higher is the wage the higher is the labor productivity. That is the core that gives us a chance to make some conclusions and give some proposals. Also we can analyze the remainders, by comparing the estimated values of GVA and observed ones:

	lnY-lnY'
Region
Vinnitsa	-0,05
Volynsk	-0,07
Dnipropetrovsk	-0,09
Donetsk	0,09
Jytomyr	-0,11
Zakarpattya	-0,06
Zaporijia	0,02
Ivano-Frankivsk	-0,09
Kyiv	0,18
Kyiv region
Kirovograd	0,1
Crimea	-0,04
Lugansk	0,05
Lviv	-0,07
Mykolaiv	0,03
Odessa	-0,08
Poltava
Rivne
Cevastopol	0,09
Sumy
Ternopil	-0,05
Harkiv	0,02
Herson	0,09
Hmelnytsk	0,05
Cherkasy	-0,03
Chernivetska	0,02
Chernigiv	0,01

Analyzing these data, we can say that when Y- >0 the estimation of GVA is lower than the observation of GVA, that is not good, because it makes it harder to estimate and predict values.

After making analyzes of these data, as well as the interpretations of the Cobb-Douglas production formula, we can make some proposals, and estimate them.

Дата добавления: 2015-11-14