Coefficients characterizing the concentration of the trait under study in certain groups Herfindahl coefficient. What is the decile ratio? How to determine the decile coefficient of income differentiation

Statistics studies the differentiation and concentration of incomes of the population.

To study the features of population differentiation by income level, structural characteristics of distribution series are used, such as fashion, median, quartiles, deciles, etc.

Deciles are income levels that divide the population into ten equal parts.

The first (bottom) decile characterizes the maximum average per capita monetary income of 10% of the poorest population:

The ninth (top) decile characterizes the minimum per capita money income of 10% of the wealthiest population:

where x d [ and x dl) - the lower boundaries of the intervals containing the lower and upper deciles, respectively;

C and c - the values ​​of the intervals containing the lower and upper deciles;

If,- the total amount of frequencies;

Srfj-i and S d the accumulated frequencies of the intervals preceding the intervals containing the lower and upper deciles, respectively;

D and D are the frequencies of the intervals containing the lower and upper deciles.

To assess the degree of differentiation of the population by the size of average per capita money income, the decile coefficient of differentiation is used:

where d 9 ndi- respectively the upper and lower deciles.

Example 2. According to the table. 20.2 determine the average per capita monthly income; modal and median income; lower and upper deciles; decile coefficient of income differentiation of the population.

Distribution of the population of the Krasnodar Territory in terms of average per capita cash income, 2012

Table 20.2

Solution.

1. Let's build an auxiliary table. 20.3.

Auxiliary table for calculating indicators

Table 20.3

Population group by average per capita money income, rubles / month	Middle interval,	The population of the group,% of the total	Product of parameters	Accumulated population frequency,%
Over 45,000

2. Let's define the average per capita monthly income:

3. Let's calculate the modal average per capita monthly income:

Thus, in 2012, in the Krasnodar Territory, the most common level of per capita monthly income was equal to 13,111 rubles.

4. Let's define the median per capita monthly income:

Consequently, one half of the population of the region in the year under study had an average per capita income below 15 387 rubles, and the other half - above this value.

5. Calculate the bottom decile:

Thus, the maximum per capita income of 10% of the poorest population of the Krasnodar Territory in the study year amounted to 5578 rubles. per month, which is below the average living wage for this administrative region by 588 rubles.

6. Let's define the top decile:

So, the minimum per capita income of 10% of the richest population of the Krasnodar Territory in 2012 amounted to 42,826 rubles. per month, which exceeded the subsistence minimum by 6.9 times.

7. The decile coefficient of differentiation was:

Consequently, in 2012, the minimum income of 10% of the richest population in the region was 7.7 times higher than the maximum income of 10% of the poorest population.

To assess the uniformity of the distribution of the population by income, the Lorenz coefficient is determined:

where y, - is the share of income concentrated in the i-th social group of the population;

Xj- the share of the population that belongs to the i-th social group in the total population.

The value of the Lorenz coefficient, close to zero, means the even distribution of the population by income.

The degree of inequality in the distribution of income of the population is also characterized by the Gini income concentration coefficient, which is calculated using the following formula

where NS- the number of social groups;

situ, is the cumulative (accrued) share of income.

The Gini coefficient varies from 0 to 1. With an equal distribution, this coefficient tends to zero, and the higher the polarization of income in society, the closer it is to unity.

The assessment of the degree of concentration of the population by the value of the average per capita money income can also be carried out using the Herfindahl coefficient:

The advantage of this indicator is its high sensitivity to changes occurring in the structure of the distribution of the total volume of monetary income for certain groups of the population.

Example 3. According to the table. 20.4 we will determine the indicators of the concentration of incomes of the population of the Krasnodar Territory.

Solution.

1. Let's build an auxiliary table. 20.5.

Distribution of the total cash income of the population of the Krasnodar Territory, 2012

Table 20.4

Auxiliary table for calculating odds

Table 20.5

Social group of the population	population	Share in total cash INCOME U /	Estimated indicators
						X 1-yA
First (with the lowest incomes)
Fourth
Fifth (highest earning)

2. Let's calculate the coefficient of concentration of Gini's income:

Since, by condition, the total amount of money income is distributed between equal-sized groups of the population (i.e. x - xi - xs = x 4 = = x 5 = 0.2), the original formula for calculating the Gini coefficient can be transformed as follows:

In our case, we have:

Since the Gini coefficient exceeded 0.3 points, we can talk about a fairly high degree of uneven distribution of the population by income level.

3. Let's calculate the Lorentz coefficient:

The obtained value of the Lorenz coefficient also indicates a fairly significant degree of socio-economic stratification of the population of the Krasnodar Territory in 2012.

4. The Herfindahl coefficient was 0.311 points ( K g= 0.310956, see table. 20.5). Its value exceeded 0.2 points, which indicates a rather significant level of concentration of the population's income in one of the groups, namely, in the fifth group. In the year under study, 47.5% of all incomes of the population of the Krasnodar Territory were concentrated in it.

The state exists primarily for the people. Therefore, the main task of management should be to address the issue of improving the living standards of the population and the well-being of each individual. And for this, you first need to analyze the distribution of material wealth between different social strata. One of the indicators that make it possible to do this is the decile coefficient of income differentiation. It is on its basis that the structure of the welfare of the population is often compiled.

Social inequality graph

Economists calculate the difference in the total income of various segments of the population using a number of indicators. Among them, the main ones are the Gini index and the decile coefficient of differentiation. Graphically, social inequality is displayed using the Lorentz curve. The degree of inequality characterizes the angle of deviation of the broken line from the bisector. If the incomes are equal, then the Lorentz curve completely coincides with it. This situation means that any 10% of the population has a similar percentage of the total national material resources. If someone alone has appropriated all the income, then the Lorentz curve will first go along the abscissa axis, and then rise vertically. From the resulting graph, you can calculate the Gini index.

Decile coefficient of income differentiation

The distribution of material resources between representatives of different social classes within a country without plotting a graph in sociology is measured using a number of instruments. The decile factor is one of them. It represents the ratio of the average income of the richest 10% of the population in the state to the same percentage of the poorest. The smaller the result, the more stable the situation in society. It is believed that a coefficient value greater than 10 means a hypothetical possibility of civil unrest and the beginning of a coup d'état. This is due to the fact that the difference in assets belonging to different "castes" is so great that the injustice of the structure of society is immediately apparent.

Decile factor calculation

The analysis of social stratification begins with dividing the population into groups. This can be done both using statistical programs and manually. To do this, you need to collect information about the level of income of the population, and then arrange it in descending order. There should be ten groups. The first will include the richest people, the tenth - the needy citizens. The decile coefficient will be equal to the ratio of the average income of the last group to the income of the most wealthy. To facilitate memorization, you can draw up a mathematical formula, designating all the components with letters. Let d 1 and d 10 be the incomes of 10% of the richest and the poorest residents, and K d is the decile coefficient. In this case, the formula will look like this: K d = K 10 / K 1.

Practical value of the indicator

The decile coefficient of income differentiation shows the differences between the incomes of the richest and the poorest segments of the population. It indicates the concentration of income in one hand. If the value of this coefficient is equal to ten, it means that the richest group makes 10 times more profit than the similarly poor group. Thus, the decile coefficient shows the difference between different segments of the population and is a tool for economic analysis. It is on the basis of calculating such indicators that competent public administration should be formed.

The value of the indicator in the countries of the world

Consider the countries of the world in terms of income inequality between rich and poor based on UN and CIA data. In Europe, the lowest values ​​are in Denmark, Sweden and Finland. In these countries, the incomes of the rich and the poor differ 3 times. In countries such as Germany and France, this figure is three times higher on average. At the same time, these countries are implementing programs aimed at reducing social tension, so income inequality tends to decrease. The highest rates are found in Namibia, Bolivia, Sierra Leone, Honduras, Haiti, Botswana and Brazil (75 on average).

The generalized decile coefficient in the countries of the European Union is 6 (the smallest - in the Scandinavian countries - about 4), in the USA - 15, in Japan - 6, in North Africa - 6.

Decile factor in Russia

Income inequities are a notorious situation in our society. Since the 90s of the last century, the decile coefficient in the Russian Federation has only been growing. The gap between social groups has reached such proportions that the problem is visible to the naked eye. And what kind of justice can we talk about in this case? The richest 10% have 20 times more tangible assets than a similar group of the poor. However, the situation was not always so sad.

At the beginning of the last century, the decile coefficient did not exceed 6, while in the United States it exceeded 18. By the standards of Western countries, even the royal family lived in poverty. This proves once again that the Bolshevik revolution of 1917 was caused by political reasons, not economic ones. It is believed that any kind of disorder can arise if the indicator exceeds 10.

Social differentiation in tsarist Russia

According to the research of Professor B. Mironov, to the poorest strata of the population in 1901-1904. belonged to the following categories of people:

• The marginals.
• Agricultural workers.
• Day laborers.
• Women and children employed in factories.

The income of the poorest 10% of the population was 6.5 rubles per month, or about 78 per year.

The assessment of the wealth of the country's richest people was carried out by the Commission for the Imposition of Income Tax, created under the Ministry of Finance in 1905. She calculated that their average income was 2130 rubles per year, or 178 per month. But this is only 1% of the tenth group. The remaining 9% of the wealthy received only 320.5 rubles a year. Thus, the average income of the tenth decile group is 493 rubles, and the differentiation coefficient is 6.3.

Threats of uneven distribution

Low-income families are the most vulnerable segment of the population. They don't have enough savings to weather cyclical economic crises. The presence of such groups of the population not only provokes conflicts and unrest, but also forces the state to spend significant funds on their maintenance. At the same time, subsidizing is not a solution to the problem, but only delays the escalation of the situation. A much more rational way is to create new jobs and introduce progressive taxation.

Solution:

First, let's define the serial numbers:

Medians = (100 + 1) / 2 = 50.5;

1st quartile = 100/4 = 25;

3rd quartile = 3/4 * 100 = 75;

1st decile = 1/10 * 100 = 10;

9th decile = 9/10 * 100 = 90.

Let's calculate the median:

Me = (XMe + IMe) / (0.5Sf-SMe-1) / fMe, where

Me is the median;

ХМе - lower border of the median interval;

IMe - the value of the median interval;

Sf is the sum of the frequencies of the series;

SMe-1 - the sum of the accumulated frequencies of the series preceding the median interval;

fМе is the frequency of the median interval.

To calculate the median, let us determine the median interval - this is the interval in which 50.5% of the population is located. In our example, the interval is 800 - 1000. Substitute the values ​​into the formula:

Me = 800 + 200 * (0.5 * 100-40.7) / 16.5 = 912.8 rubles,

those. half of the population has an average per capita income of less than 912.8 rubles.

First quarter (Q1):

Q1 = XQ1 + I * (Sf / 4- S Q1-1) / f Q1.

Third Quartel

(Q3): Q3 = XQ3 + I * (3 * Sf / 4- S Q3-1) / f Q3, where

XQ1, XQ3 - lower boundaries of quarterly intervals, respectively, of the first and third;

I is the value of quarterly intervals;

S Q1-1, S Q3-1 - accumulated frequencies of the interval preceding the quartile;

f Q1, f Q3 - the frequency of the quartile interval.

Q1 = 600 + 200 * (25-22.1) / 18.6 = 631.2 rubles,

those. per capita income of 25% of the population does not exceed this amount.

Q3 = 1200 + 400 * (75-69.9) / 15.6 = 1330.8 rubles,

those. only 25% of the population has an average per capita income exceeding 1,330.8 rubles.

First decile:

(D1): D1 = HD1 + I * (Sf / 10- S D1-1) / f D1;

Ninth decile (D9):

D9 = XD9 + I * (9 * Sf / 10- S D9-1) / f D9, where

HD1, HD9 - the lower boundaries of the decile intervals, respectively, of the first and ninth;

I - accumulated frequencies of the interval preceding the decile;

S D1-1, S D9-1 - accumulated frequencies of the interval preceding the decile;

f D1, f D9 - frequency of the decile interval.

D1 = 400 + 200 * (10-6.4) / 15.7 = 445.8 rubles,

therefore, 10% of the population has an average per capita income of less than 445.8 rubles, and 90% more than this amount.

D9 = 1600 + 400 (90-85.5) / 7.5 = 1840.0 rubles,

and only 10% of the population has an average per capita income exceeding 1840.0 rubles.

The decile coefficient of income differentiation of the population (CD): CD = D9 / D1 = 1840.0 / 445.8 = 4.1.

The decile coefficient of income differentiation of the population shows that the average per capita monetary income, above which the income of 10% of the population of the region, in 2001 exceeded the level of income by 4.1 times, below which the income of 10% of the population had.

Task 12. Calculate:

1) Structural means: median, first and third quartiles, first and ninth deciles;

Decile coefficient of income differentiation of the population.

There is data on the distribution of the city's population by average per capita money income for the IV quarter of 2006, presented in the table:

Average per capita income per month, rubles	Population,% of the total	Accumulated frequencies
Up to 1000	6,4	6,4
1000,1 - 6000	15,7	22,1
6000,1 - 8000	18,6	40,7
8000,1 - 10000	16,5	57,2
10000,1 - 12000	12,7	69,9
12000,1 – 16000	15,6	85,5
16000,1 - 20000	7,5	93,0
Over 20,000	7,0	100,0
Total	100,0

The differentiation indicators also cover the income concentration ratios of Lorenz and Gini. They refer to a system of estimates known as the Pareto-Lorenz-Gini methodology, which is widely used in foreign social statistics.

The Italian economist and sociologist V. Pareto (1848 - 1923) summarized the data of some countries and found that there is an inverse relationship between the level of income and the number of their recipients, called the Pareto Law in the literature.

The American statistician and economist O. Lorenz (1876 - 1959) developed this law, proposing its graphical representation in the form of a curve, called the "Lorentz curve".

Task 13. Draw the Lorenz curve, which clearly shows the degree of differentiation of incomes of different groups of the population. If we divide the population of Russia into 10 equal in number groups, then the share of each group in the total income of the population in 2014 was approximately:

The Lorentz curve is a curve of the concentration of individual elements of the statistical population by groups. On the Lorenz graph, in the case of an even distribution of income, the pairwise shares of the population and income should coincide and be located on the diagonal of the square, which means the complete absence of concentration of income. Segments of straight lines connecting the points corresponding to the accumulated parts and the growing percentages of income form a broken line of concentration (Lorentz curve). The more this line differs from the diagonal (the more its concavity), the more uneven the distribution of income, and accordingly the higher its concentration.

Task 14. Is it possible in real life a case of absolute equality or absolute inequality in the distribution of income among the population? What does absolute inequality mean?

The Gini coefficient (G), named after its author, the Italian statistician and economist C. Gini (1884 - 1965), is calculated as follows:

G = 1-2SXiCUMYi + SXiYi, where

CUMYi is the cumulative share of income.

Having supplemented the initial data with some calculated indicators, we get the following table:

Social group of the population	Share of population Xi	Share in total income Yi	Estimated indicators
CUMYi	XiYi,	ХiCUMYi
	0,20	0,05	0,05	0,010	0,010
	0,20	0,10	0,15	0,020	0,030
	0,20	0,20	0,35	0,040	0,070
	0,20	0,20	0,55	0,040	0,110
	0,20	0,45	1,00	0,090	0,200
Total	1,00	1,00	-	0,200	0,420

The coefficient G varies in the range from 0 to 1. The closer the value of G is to 1, the higher the level of inequality (concentration) in the distribution of total income; the closer it is to 0, the higher the level of equality.

Task 15. Determine the coefficient of concentration of Gini incomes by year and the dynamics of inequality in the distribution of monetary incomes of the population of the region. The table contains data on the distribution of the total cash income of the region's population (based on the materials of a sample survey of household budgets, in percent):

Task 16. Plot the Lorenz curve and calculate the Gini coefficient for a given economy. In some country, 20% of the poorest people receive 10% of the total income of society, and 20% of the wealthiest citizens receive 50% of the total income. After a while, the state introduced a 20% tax, which only rich families pay, and then it returned all this money to the poorest in the form of transfers.

Task 17. How will the Lorentz curve and the Gini coefficient change?

Savings of the population

Savings of the population occupy a special place among economic phenomena, since they are at the intersection of the interests of citizens, the state and organizations.

On the one hand, savings are the most important indicator of the standard of living, directly related to consumption, income and expenditures of the population.

Task 18. Explain why?

On the other hand, the savings of the population are a valuable resource for the economic development of a country or region.

Task 19. Explain why?

In the world, the savings of the population occupy about 80% of the total volume of investment capital, and in Russia - only 16%. Therefore, to revive the Russian economy, raising funds from the population is one of the priority measures. In this regard, it is necessary to solve two problems: firstly, the development of new forms of savings of individuals, and, secondly, the protection of savings of the population.

Task 20. Suggest new forms of organized savings for the development of the savings market in Russia.

Task 21. What measures to protect the savings of citizens should be taken by the state?

Personal income taxation

In tax practice, the problem of tax shifting is solved simply: it is assumed that direct taxes are fully paid by the owners of taxable income and property; indirect taxes are fully covered by the final consumers of the products.

The payment of income tax in order to pay off the employee's obligations to the state refers to mandatory deductions from the employee's wages.

In accordance with subparagraph 6 of paragraph 1 of Article 208 and paragraph 1 of Article 209 of the Tax Code of the Russian Federation (Tax Code of the Russian Federation), remuneration for the performance of labor duties is recognized as an object of taxation for personal income tax. According to paragraph 1 of Article 206 of the Tax Code of the Russian Federation, the organization from which the employee received income is obliged to calculate, withhold and pay the amount of personal income tax. In this case, taxation is carried out at a rate of 13% (clause 1 of article 224 of the Tax Code of the Russian Federation).

Task 22. Explain why the increase in taxes on individual income reduces both consumer spending and savings?

Task 23. Calculate the available wages of the company's employees for the year (minus taxes and mandatory payments), taking into account the collection of alimony from each: Ivanov I.I. - for one child, Sidorov S.AND. - for two children, Petrov P.I. - for three children. These workers had no other income.

Table - Indicators for calculating available wages

Month	Ivanov I.I.	Sidorov S.I.	Petrov P.I.
The salary	Tax and payments	The salary	Tax and payments	The salary	Tax and payments
January
February
March
April
May
June
July
August
September
October
November
December
Total income

Task 24. What taxes on personal income are direct taxes, and which are indirect?

Task 25. Which of the following benefits are enjoyed by those citizens who do not pay for them directly, but pay them indirectly? Give reasons for your answer.

25.1. Protection from criminals by the police.

25.2. Public health care.

25.3. Mail services.

25.4. State television.

25.5. Fire brigade.

25.6. Education at a public school.

Shadow income

At any time, among economists-researchers there is a constant interest in the shadow economy, that is, in that part of the economy that is not reflected in official statistics, eludes taxation, etc. Structurally consists of criminal and non-criminal sectors.

The first of them includes purely criminal activities: drug business, prostitution, arms trade, racketeering, corruption, making counterfeit money, laundering dirty money, etc.

The non-criminal sector includes economic activities that are not included in the reporting (or reflected in it with distortions) and are not recorded in contracts. We are talking about housekeeping, tutoring, private carriage, construction of summer cottages, repair of equipment, renting out housing, private medical practice, car maintenance, etc.

Task 26. What is the difference between the income of a racketeer and a seamstress who is not registered with the tax office?

Considering the problem of the structure and formation of income, it is necessary to distinguish between labor and unearned income. Earned income is associated with work, and unearned income, therefore, includes income from capital (from property, interest, winnings ...), various types of assistance, gifts, inheritance, etc.

Task 27. Explain why legal unearned income is an integral part of a market economy?

Inflation

Inflation (from the Latin inflation - swelling) - overflow of the sphere of circulation with excess money supply in the absence of an adequate increase in the mass of commodities, which causes a depreciation of the monetary unit. Inflation manifests itself in the form of an increase in prices for goods and services, not due to an increase in their quality, which reduces the level of real incomes.

Task 28. Some economists argue that inflation does not reduce real incomes for all segments of the population. What is your point of view?

Task 29. Which of the following people is most likely to benefit from inflation? Why?

A. Someone who borrowed money at a fixed interest rate.

B. Someone who lives on an allowance whose value does not change.

C. Someone saving money at home.

Task 30. Inflation occurs in the country when (A) income grows faster than (B) income. Which of the following definitions of "monetary" or "real" should be inserted in (A) and which in (B)?

Task 31. Determine in which year the inflation rate was the highest? The table below shows the retail price index in one of the countries:

Task 34. Explore what happens to the ratio of the incomes of the most and the poorest population in Russia over this period of time? What social consequences did this process lead to? The income ratio of 10% of the most and the poorest population in Russia at the end of the 20th century is characterized by the following data (times):

4,4	4,5	8,0	11,2	15,1	12,5	15,1

The price index is calculated using the formula:

SI = S (Pi1 * Qi) / S (Pi0 * Qi), where

Pi1 / Pi0 - the price of the i-th product in the given year / base year;

Qi - the quantity of the i-th product in the given and base year.

Task 35. What is the inflation rate for the year? Suppose the consumer price index takes into account only two commodities: food and housing. The share of food products is 0.33, and that of housing is 0.67. Food prices rose 20% and housing prices fell 2%. Exercise

Task 36. Calculate the price index for 1991 (base year - 1972) using the data in the table:

Living wage

Living wage, a socio-economic category that characterizes the minimum means of subsistence, physically necessary to support the life of the worker and restore his workforce.

Living wage- the cost estimate of the consumer basket, as well as mandatory payments and fees.

Consumer basket- a minimum set of food products, as well as non-food products and services, the cost of which is determined in relation to the cost of a minimum set of food products, necessary to preserve human health and ensure his life.

The consumer basket for the main socio-demographic groups of the population in the whole of the Russian Federation and in the constituent entities of the Russian Federation is determined at least once every five years.

On January 1, 2013, a new consumer basket came into force, which will be valid until 2018.

The consumer basket primarily includes food products, which make up about 50% of its cost (for comparison, in Western Europe, this figure does not exceed 20%). It is worth mentioning that the majority of Russian families also spend more than half of the family budget on food.

The second group includes non-food items - clothing, footwear, hats, underwear, medicines.

Well, the third group of the consumer basket consists of services: utilities, transport costs, cultural events, and so on.

So, if you look at the table below, which presents the products and services included in the consumer basket for 2014, then you will see that, according to the government's calculations, an able-bodied citizen consumes 100.4 kg per year. potatoes, 114.6 kg. vegetables, 60 kg. fresh fruit, 126.5 kg. bread and bakery products, 58.6 kg. meat and 18.5 kg of fish products, respectively. Cultural services account for 5% of the total monthly expenses.

What does this mean per person per day? And this means that an ordinary average citizen of the Russian Federation for a normal existence should consume 300 g of bread, potatoes - 280 g, vegetables - 300 g, fresh fruits - 160 g, sweet - 60 g, milk and dairy products per day. food - 800 g, vegetable oils and fats - 40 g. And also 1 time in 2 days to eat one egg, be content with 160 g of meat per day, well, eat 350 g of fish per week. As for cultural development, here an able-bodied Russian citizen has a chance to go to the cinema or theater once a month for his living wage, for more money for these purposes is not provided.

1. Food

Name	unit of measurement	Consumption (average per person per year)
Able-bodied population	pensioners	children
Bread products (bread and pasta in terms of flour, flour, cereals, legumes)	kg	126,5	98,2	76,6
Potato	kg	100,4	80,0	88,1
Vegetables and melons	kg	114,6	98,0	112,5
Fresh fruits	kg	60,0	45,0	118,1
Sugar and confectionery products in sugar terms	kg	23,8	21,2	21,8
Meat products	kg	58,6	54,0	44,0
Fish products	kg	18,5	16,0	18,6
Milk and dairy products in terms of milk	kg	290,0	257,8	360,7
Eggs	thing	210,0	200,0	201,0
Vegetable oil, margarine and other fats	kg	11,0	10,0	5,0
Other products (salt, tea, spices)	kg	4,9	4,2	3,6

2. Non-food items

Name	Measurement unit / wear life
able-bodied population	pensioners	children
Upper coat group	pieces / years	3/7,6	3/8,7	3/2,6
Upper costume and dress group	pieces / years	8/4,2	8/5,0	11/2,0
Linen	pieces / years	9/2,4	10/2,9	11/1,8
Hosiery	couples / years	7/1,4	4/1,9	6/1,3
Hats and haberdashery	pieces / years	5/5,0	4/5,6	4/2,8
Shoes	couples / years	6/3,2	6/3,5	7/1,8
School supplies	pieces / years	3/1,0	3/1,0	27/1,0
Linens	pieces / years	14/7,0	14/7,0	14/7,0
Cultural and household goods	pieces / years	19/10,5	19/10,5	19/10,5
Essentials, Sanitation and Medicines	percent of total spending on non-food items per month

Name	unit of measurement	Consumption (average per person)
able-bodied population	pensioners	children
Lodging	sq. m total area
Central heating	Gcal per year	6,7	6,7	6,7
Cold and hot water supply and sewerage	l per day
Gas supply	cub. m per month
Electricity	kWh per month
Transport service	trips per year
Cultural services
Other types of services	percent of the total cost of services per month

Living wage- the minimum level of income that is considered necessary to ensure a certain standard of living in a particular country. In practice, the cost of living in developed countries is generally higher than in developing countries.

The size of the subsistence minimum represents a cost estimate of the consumer basket, which includes the minimum sets of food, non-food products and services necessary to preserve human health and ensure his life, as well as mandatory payments and fees.

The consumer basket in the constituent entities of the Russian Federation is established by the legislative (representative) bodies of the constituent entities of the Russian Federation.

The subsistence minimum is set separately per capita, for the able-bodied population, for pensioners, for children every quarter.

For the II quarter of 2014

Per capita - 8192 rubles.

For the able-bodied population - 8834 rubles.

For pensioners - 6717 rubles.

For children - 7920 rubles.

A generalized assessment of the degree of structuring of the phenomenon as a whole is usually carried out according to the formula concentration level(or Herfindahl coefficient), which is more sensitive to changes in the proportion of groups with the highest specific gravity as a result, determined by the formula:

where is the share j-th group in the total result of the studied value of the attribute; m - the number of groups identified in the aggregate.

The maximum value of the coefficient is 10,000 (if fractions are in percent) or 1 (if fractions are in numbers). The closer the coefficient value to the maximum, the higher the concentration of the studied trait in one or more groups. The minimum value of the coefficient is 100 (if the share is in percent) or 0.01 (if the shares are in numbers).

Effective number of groups

The inverse of the Herfindahl index is effective number of groups in the structure, which shows the number of groups without taking into account groups with negligible shares, is determined by the formula:

E = 1 / H.

Production per person	number of people	group average (middle of the interval)	working out per group

Herfindahl coefficient , which indicates an insignificant concentration of the studied trait (production) in one or more groups.

The number of effective groups E = 1 / H = 1 / 0.179 = 5.6. This indicator shows that the studied trait is concentrated in 6 groups out of 7 available. This again confirms the relatively even distribution of output among the groups of workers.

1. Coefficients characterizing the differentiation of the studied trait in the aggregate

On the basis of quantiles, various coefficients of differentiation of the trait under study are calculated: decile (quartile, percentile) coefficient, fund coefficient, Ginny coefficient. These coefficients characterize the uneven distribution of the trait in the studied population. For example, inequality in the distribution of income (how much the income of the wealthiest group differs from the income of the least wealthy group).

Decile coefficient of differentiation,

This coefficient shows how many times the smallest attribute value among the 10% of observation units with the highest attribute values ​​(the lowest income of the 10% of the most affluent) is greater than the largest attribute value among the 10% of observation units with the lowest attribute values ​​(the largest income is 10 % of the poorest).

Quartile coefficient of differentiation,

This coefficient shows how many times the smallest attribute value among the 25% of observation units with the highest attribute values ​​(the lowest income of the 25% of the most affluent) is greater than the largest attribute value among the 25% of observation units with the lowest attribute values ​​(the largest income is 25 % of the poorest).

Funds ratio- the ratio of the average value of the studied trait in the tenth decile group to the average value of the studied trait in the first decile group

This coefficient shows how many times the average value of the trait among 10% of observation units with the highest values ​​of the trait (average income of 10% of the most affluent) is greater than the average value of the trait among 10% of observation units with the smallest values ​​of the trait (average income of 10% of the poorest) ...

The first decile group is the range of values ​​from the minimum to the first decile. The tenth decile group is the range of values ​​from the ninth decile to the maximum value. The average for a range of values ​​is the midpoint of the range.

Hence,

;

The more important these coefficients take, the greater the inequality in the distribution of benefits (responsibilities) between the tenth decile group and the first decile group.

Let's take a look at these coefficients using an example.

Information about the production of workers for October

		Production of one worker					number of people		accumulated frequency
						meaning
					16+ (22-16) × ((612/10) -5) / 110 =
					40+ (46-40) × (9 × (612/10) -567) / 60 =
1 quartile					22+ (28-22) × ((612/4) -115) / 182 =
3 quartile					34+ (40-34) × (3 × (612/4) -417) / 90 =

The values ​​of the coefficients allow us to draw the following conclusions: the smallest output of the 10% of the best workers exceeds the best output of the 10% of the most unproductive workers by 2.3 times.

The lowest output of the 25% of the best workers exceeds the best output of the 25% of the most unproductive workers by 1.6 times.

To calculate the fund ratio, you need to find the average value of the 1st and 10th decile groups.

=;

This coefficient allows us to conclude that the average output of the best workers is 3.3 times that of the lowest productive workers.

Which is very clearly visible in the example of the richest and poorest inhabitants of the country. Differences in incomes and opportunities that citizens have pose a serious challenge to the entire state body. But the solution to this problem is better left to politicians and citizens with an active position and consider property inequality from the point of view of economics.

What is the decile ratio

The decile coefficient of inequality of income distribution is understood as the coefficient of values ​​that are taken from the richest and poorest inhabitants of the country (the same number of both). The decile ratio shows the gap between their level of well-being. The values ​​can be percent of GDP, total welfare, or another indicator that measures the standard of living. And the ratio of wealth that, say, 10% of the richest in society and the poorest have, is called the decile coefficient. The percentage of society may be different - 1.3 or 20, but in most cases it is 10 that is used. The decile ratio in Russia is about 15: 1, which is evidence of the uneven distribution of income and social tension in the country.

Distribution of income

How is it that the distribution is so unequal? In this case, it depends on two components: the civil liability of entrepreneurs and government levers of regulation. Moreover, to a large extent, everything depends on the first factor: after all, entrepreneurs may want to evade taxes. In addition, they can voluntarily support schools, scientific developments, promising public initiatives. In turn, the state deals with the issue of the infrastructure for the distribution of income, as well as the search and punishment of those who evade their debt to the country.

Problems related to unequal distribution of income

The number of problems that may arise due to uneven distribution of income is very large. The size of the article will not allow describing all of them, but some, the most basic, should still be described:

1. The growth of social tension. The fact that most of the funds are concentrated in the hands of a small number of people creates a fertile ground for social upheavals due to the fact that a significant part of citizens are dissatisfied with this state of affairs in the state.
2. Slowing down the development of the state. If a significant amount of money accumulates in a limited circle of people, then it becomes problematic for the rest to provide their children with a quality education or to raise money to start their own business, which leads to a drop in the standard of living and the possibility of implementation, and when this phenomenon takes on massive features, then the possibilities of the state decrease. ...
3. Weakness in the foreign policy field. This situation follows from the two previous ones: when the state begins to weaken from within, it becomes more difficult for it to achieve external goals.
4. The threat of the collapse of the state. If life becomes very difficult, especially after a period of relative stability and prosperity, then hotbeds of rebellion or national strife may arise, which may ultimately result in the creation of a separate state.

Decile factor calculation

Well, now it is clear what the decile coefficient is. How to calculate it and make sure personally that the data that you met somewhere was not taken from the ceiling? You can navigate by the following example.

It is necessary to calculate the decile coefficient, taking as a basis 10% of citizens - 5% of the richest and the poorest. The richest have assets worth 200 billion rubles at their disposal. Whereas the poorest are only 10 billion. In this case, it is necessary to divide 200 billion by 10, and we get the decile coefficient, which in this case will be 20. That is, the gap between the richest and the poorest will be twenty times. If you are interested in the meaning of other groups, you can choose them too; you just need to substitute new numbers in the already solved example. The decile coefficient, the formula and the calculation method are not so difficult, so that a person with mathematical knowledge at the school level cannot calculate it.

Public welfare

The decile coefficient of income differentiation is important from the point of view of the use of public goods. So, if it reaches significant values ​​(more than 10), the state needs to think about regulating the position, even if by force. One of these is the redistribution of wealth in favor of socially unprotected segments of the population.

Social protection as one of the solutions to the problem of uneven distribution of income

Social protection is used as a way to reduce social tensions. This mechanism is based on the collection of taxes from the rich and the distribution of the collected among the poor. When using it, it should be borne in mind that too little taxation will not allow meeting the needs in the required amount, and too high will cause discontent and capital flight from the country, which will further complicate the situation in the future. But for all its conveniences in the modern world, social protection can reduce the difference by just a few points. All other options are more brutal and, as a rule, are used almost nowhere.