2. The Goal of work

The main goal of work is to analyze the present situation in education system in Ukraine by Cobb-Douglas, to indicate the problems and aspects that need to be resolved . Also Basing on available information to do statistical calculations and to propose the problem solutions and the ways of implementation it in real life.

3. Statement of the problems

By education index Ukraine occupies 18-th place (0,795), leaving behind, in particular, such countries, as Spain (22th place with education index 0,781), Great Britain (24th place; 0,766), France (27th; 0,751), Poland (30th; 0,728), Italy (32th; 0,706), Belarus (35th; 0,683), Portugal (th41; 0,670), the Russian Federation (53th; 0,631). And the average education index in the world — 0,436, which mean that Ukraine exceeds it in 1,8 times.

The Quantity of educational establishments in the world:

Meanwhile on an indicator of gross domestic product (GDP) per capita at par purchasing capacity in US dollars Ukraine occupies 90th place among 169 countries, with the amount of 6535 dollars, — against 29661 dollars in Spain (the GDP per capita is in 4,5 times more than in Ukraine), 35087 dollars in Great Britain (in 5,4 times more), 34341 dollars in France (in 5,3 times more), 17803 dollars in Poland (in 2,7 times more) etc. On the average indicator of gross domestic product per capita in the world equals to 10631 dollars that in 1,6 times more than in Ukraine.

Thus, there is a question: if the statement, that the education is one of the major factors in economic development is true then why Ukraine with such high amount of educated people have such low indexes of economic development one of which is GDP? The difference between these indices is extremely high, but why? It is a big question which we have to resolve.

The quantity of the persons studied in educational institutions on the beginning of 2009/10 academic years, equaled to 7 million 518 thousand, from them 4 million 495 thousand — at schools, 424 thousand — in colleges, 2 million 599 thousand — in high schools. In comparison with 2000/01 academic year, the total amount of pupils has decreased for 18,1 %, from them at schools — has decreased on 33,5 %, in colleges — on 19,3 %, and in high schools — has increased on 34,6 %.

In 2010, Ukraine occupied 134 place in annual rating of perception of corruption (Corruption Perceptions Index). According the survey made by fund «Democratic initiatives», the size of a bribe in various high schools of the country varies from 50 to 4800 grivnas, and the average sum makes 300 grivnas.

The comparative analysis of the most important quantitative parameter —” durations of the education”, made by the Ukrainian researchers K.Korsak and O.Zubritsyka, testifies that in overwhelming majority of member countries of the European Union there is an appreciable increase in duration of secondary education (12—13 years to volume of 9-11 thousand astronomical hours). In Ukraine full duration of secondary education an average is 7000-7600 astronomical hours, which means on 30 % less than in countries of EU. According to the European experts concerning development of education, the main disadvantage of the Ukrainian education — small duration of education which is one of the reasons of non-recognition in Europe certificates and diplomas of the Ukrainian origin. Interesting fact for economists is that in case of less duration of education is working bigger amount of professors and teachers.

In Ukraine during the period of 2000-2007 the State expenditure on education was equal to 5,3% from gross domestic product, whereas in Germany — 4,4, Japan — 3,4, Spain — 4,4, Italy — 4,3, the USA — 5,5, France and Great Britain — 5,6 %. That's mean that the state financing of educational activity is in Ukraine is on the level of the most developed countries in the world, and even exceeds it.

Also interesting data gathered by World poll Gellapa, where the main question was «Are you satisfied by quality of an education system and schools in city or area in which you live?» showed such results: the percentage of people who answered yes in Ukraine equals to 38 %, when in Belarus to 47%, 42% — in Russian Federation, 70% — in USA, 71% — in Canada, 59% —in Germany, 53% — in Japan, 70% —in France, 70% — in Great Britain, 66% —in Poland.

Also one of the approval of unsatisfactory situation in our education system is the fact that none of our educational establishment is included in TOP 500 best universities in the world. And even without polls and surveys we have a lot of questions on which still can't find the answers, such as: why power consumption of our gross domestic product in times exceeds indicators of the developed countries; Why the death rate in Ukraine from noninfectious illnesses on 100 thousand population almost in 1,5-2 times exceeds corresponding indicators of the European countries; why, despite a considerable quantity of engineers of a different profile, in our markets practically there are no qualitative domestic goods? Why at not too big, in comparison with other countries, loading of professors and teachers, the index of distribution of alcoholism, a tobacco smoking, a narcotism among our youth exceed corresponding indicators of the European countries, what are reasons of unsatisfactory educational work?

Perhaps, one of the main reasons of discrepancy between high quantity indicators of educational sphere and indicators of economic development, in particular such indicator as gross domestic product, first of all speaks poor quality of educational activity, or, in other words, low labor productivity of participants of educational process.

4. 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	2008	2008	2008	2008
Vinnitsa	1344	7,2	1397	7,24
Volynsk	850	6,75	1167	7,06
Dnipropetrovsk	2935	7,98	4078	8,31
Donetsk	3699	8,22	5587	8,63
Jytomyr	1059	6,97	1557	7,35
Zakarpattya	982	6,89	1105	7,01
Zaporijia	1589	7,37	2289	7,74
Ivano-Frankivsk	1162	7,06	1438	7,27
Kyiv	5873	8,68	6847	8,83
Kyiv region	1463	7,29	1649	7,41
Kirovograd	858	6,75	974	6,88
Crimea	1566	7,36	2209	7,7
Lugansk	1699	7,44	2030	7,62
Lviv	2489	7,82	3360	8,12
Mykolaiv	1002	6,91	1472	7,29
Odessa	2218	7,7	7949	8,98
Poltava	1230	7,11	1689	7,43
Rivne	1044	6,95	1269	7,15
Sevastopol	418	6,04	363	5,89
Sumy	986	6,89	1583	7,37
Ternopil	950	6,86	1179	7,07
Harkiv	3118	8,04	3632	8,2
Herson	964	6,87	1227	7,11
Hmelnytsk	1236	7,12	1802	7,5
Cherkasy	1095	7	1526	7,33
Chernivetska	788	6,67	1445	7,28
Chernigiv	903	6,81	1110	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	2008	2008	2008	2008	2008
Vinnitsia	1295	64,9	1009	6,92	-0,05
Volynsk	1292	43	667	6,5	-0,07
Dnipropetrovsk	1488	118,6	2118	7,66	-0,09
Donetsk	1417	128,9	2192	7,69	0,09
Jytomyr	1347	52	841	6,73	-0,11
Zakarpattya	1354	46,5	756	6,63	-0,06
Zaporijia	1443	62,7	1086	6,99	0,02
Ivano-Frankivsk	1399	54	907	6,81	-0,09
Kyiv	2180	119,7	3131	8,05	0,18
Kyiv region	1434	60,3	1038	6,94	0
Kirovograd	1293	36,9	573	6,35	0,1
Crimea	1442	65,4	1132	7,03	-0,04
Lugansk	1379	68,2	1129	7,03	0,05
Lviv	1429	104,9	1799	7,49	-0,07
Mykolaiv	1352	43,1	699	6,55	0,03
Odessa	1359	94,7	1544	7,34	-0,08
Poltava	1389	52,6	877	6,78	0
Rivne	1330	47,1	752	6,62	0
Sevastopol	1513	16,7	303	5,71	0,09
Sumy	1344	44	710	6,56	0
Ternopil	1274	47,4	725	6,59	-0,05
Harkiv	1553	109,6	2043	7,62	0,02
Herson	1290	41,4	641	6,46	0,09
Hmelnytsk	1305	53,4	836	6,73	0,05
Cherkasy	1334	50,4	807	6,69	-0,03
Chernivetska	1371	33,9	558	6,32	0,02
Chernigiv	1298	42,1	656	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	27
dispersion analysis
	df	SS	MS	F	F-value
Regression	2	8,04106	4,020532	755,6216	2,13E-22
remained	24	0,1277	0,005321
total	26	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	2008
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	0
Kirovograd	0,1
Crimea	-0,04
Lugansk	0,05
Lviv	-0,07
Mykolaiv	0,03
Odessa	-0,08
Poltava	0
Rivne	0
Cevastopol	0,09
Sumy	0
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.