Mathematic modeling and forecasting the number of population and labor resources in the republic of Uzbekistan

The economy of Uzbekistan has achieved a notable success in further enhancing national economy, conducting adherence to market economy requirement, furnishing the industry with new technology and equipment, increasing the welfare of the nation, creating comfortable investing environment, steadily developing small business, private entrepreneur and service, all under the circumstance of modernization. Certainly, the current demographic situation of the country is important. The population of Uzbekistan, the population of cities and villages, their dynamic changing procedures indicate the scale of socio-economic development, its current situation and perspective. At the beginning of 2013, the regular population of Uzbekistan was 29993.5 people. [1]

During the years of independence, the population of the country has exceeded 9.4million or every year 427 thousand people added to it. In fact, the population of Uzbekistan is unevenly distributed in throughout its territory. The main part of the population (28.1 %) lives in the regions situated in Fergana valley. Likewise, Kashkhadaryo and Surkhandaryo are considered as the regions which include significant number of citizens. Meantime, other regions which indicate large population of the country are Samarkhand (22.2 %) and Tashkent (9,2 %). Demographic capacity of Tashkent city, Republic of Khorakhalpakstan, Navaiy and Syrdaryo regions is declined in the period of this research.

The change in the population and labor resources of Uzbekistan is a main factor indicating the scale of socio-economic development, its current situation and perspective.

These factors add its contribution to the development of our country. That’s why, mathematical modeling and forecasting of the population and labor recourses with investigating is scientifically-practically significant. Nowadays, there are a lot of demographic statistics which can define forecasting the number of populations and labour recouses now and in the future. These include parabolic indicators, logical and the worst quadratic methods of mathematical modelling. These models are based on mathematic functions in defining future demographic and economic ratios ([2]- [5]).

Increase in the population and labor resources in the Republic of Uzbekistan and its regions is calculated by using the worst quadratic method in the demographic statistics and mathematical statistics and making it a “function” in relation to “time”.

In this case, the mathematic model is searched in the following way,

where, t=x-1991, a and k are uncertain parameters, e is a domain of the natural logarithm. The parameter k, here, of this formula is said to be the natural increasing coefficient of population and labor forces. By using the worst quadratic method, we can construct the following equations:

In order to make the regression equation of increase in the population and labour recources in the Republic of Uzbekistan, we use the current statistics.

As a result, we will get coefficents a and k for the number of the population.

k=0.0157, a=21015266.12

Furthermore, for the labor recourse, we will have k=0.0471, a=9856159.81

Then, the mathematic model which expresses the number of the population is as the following.

.

where is t=0,1,2,…,30

By using these formulas, we get the following mathematic model which describes increase in the number of population in the Republic of Uzbekistan and its regions

The regression equations of increasing of the number of the population in Republic of Uzbekistan and its regions

The table above shows that the number of the population in the Republic of Uzbekistan and its regions can be forecasted till any needed years. The table also presents that the number of the populations of Republic has increased by 145.5 percent during the years of independence. Rates of increase have been observed in all the researched regions. Increase in the number of the population of regions in Uzbekistan may be divided into 4 groups:

-                   The first group includes rate of increase is very high (natural increase coefficient is 0.0221 and high) including Surkhandarya and Kashkadarya.

-                   The second group includes Bukhara, Djizzakh, Namangan, Fergana, Andidjan and Samarkand. In those countries, the rate of natural increase changes from 0.0153 to 0.0192

-                   The third group includes the regions of Syrdarya, Navaiy, Tashkent, Karakalpakstan where the rate of increase in population slightly lower (the rate of natural increase changes from 0.0102 to 0.0119).

-                   The fourth group includes only Tashkent city where natural rate of increase in population is 0.0035

Now, we will look at mathematic modeling of increase in labor forces.

where t = 0, 1, 2, …, 30.

The analyzed mathematic models are essence with 0.95propability in Fisher statistics. By using these formulas, we get the following mathematic models which show the increase of the number of labor resource in Republic of Uzbekistan and its regions.

The regression equations of increasing of the number of labor resource in Republic of Uzbekistan and its regions

The graph indicates that the rate of increase in labor recourses in the regions Surkhandarya, Kashkadarya, Andidjan, Namangan, Fergana, Khorezm regions of the country is higher than overall Republic level. This in term shows that new employment opportunities should be launched.

References:

1.      Ата-Мирзаев О. Современные тенденции развития народонаселения Узбекистана и демографический прогноз // Методологические вопросы разработки стратегий долгосрочного развития: материалы V Форума экономистов/ под общей редакцией д. э.н.Садыкова А. М./Ташкент:IFMR,

2.      Ғофуров М.,Холмуродов М., Хусанов К. Иқтисодий-математик усуллар ва моделлар. –Т.: АГНИ, 2001. — 100 б.

3.      Замков О. О. и др. Математические методы в экономике. Учебник. –М.: Изд-во «Дело и сервис», 2004. — 368 с.

4.      Шодиев Т. Ш. ва бошқалар. Иқтисодий-математик усуллар ва моделлар. –Т.: 2000. — 96 б.

5.      Орлов А. И. Новая парадигма математической статистики // Материалы республиканской научно-практической конференции «Статистика и еѐ применения — 2012». Под редакцией проф. А. А. Абдушукурова. Ташкент: НУУз, 2012.