The Gini coefficient varies over the interval. Gini coefficient in relation to sectors of the Russian economy
Assess the degree of wage differentiation among workers in each sector of the Russian economy, as well as the impact of the crisis on the redistribution of income within the industry.
Materials used
Rosstat data
Brief explanations
Equal distribution of income among all residents of the country is the basis of social stability.
The Gini coefficient is a statistical indicator of the degree of stratification of society along a certain basis. This indicator is often used to determine the uneven distribution of income among the world's population.
Using the methodology for calculating the Gini coefficient (it is presented in detail in the text of the study), we examined not the entire Russian economy, but its individual sectors.
Calculation of the Gini coefficient
A few words about how this indicator is calculated.
The values that the coefficient can take range from 0 to 1. Zero means complete equality of income among all residents (in this case, workers in a particular industry), one means complete inequality (an unrealistic situation when all wages in an industry are concentrated in the hands of one person ).
If the coefficient is presented as a percentage, then it is called the Gini index.
Let's illustrate with an example.
Let's assume that all residents of the country receive the same salary, in this case the graph will look like this:
10% of the population will receive 10% of total income, 20% of residents, respectively, 20% of total income, etc. This is a completely equal distribution of income.
In the opposite case, if we assume that one person receives a salary and everyone else works for free, the Gini coefficient will be equal to one, and the income concentration graph will look like this:
In reality, the income distribution usually looks like this:
The purple curve here is a graph of the shares of income of each group of residents (in our case, workers) in total income. For example, according to this graph, the lowest 10% of employees receive only 0.8% of total industry income, 90% of employees receive 60% of total income, which means that 40% of the income is in the hands of the top 10% of employees.
The figure formed by the intersection of the red straight line and the purple curve is the inequality of income distribution. The value of the Gini coefficient is the ratio of the area of this figure to the area of the entire triangle.
An example of calculating the Gini coefficient for one of the economic sectors
Let’s use Rosstat data “Distribution of the number of employees by size wages» by type economic activity and let's try to build a Lorenz curve based on these data and calculate the value of the Gini coefficient.
Table 1 (part 1). Distribution of the number of employees by wages and types of economic activity, in 2015 *
Agriculture, hunting and forestry | Fishing, fish farming | Mining | Manufacturing industries | Production and distribution of electricity, gas and water | Construction | |
---|---|---|---|---|---|---|
up to 5965.0 | 2,5 | 1,3 | 0,1 | 0,3 | 0,3 | 0,8 |
5965,1-7400,0 | 6,8 | 5,5 | 0,2 | 1,1 | 0,9 | 1,4 |
7400,1-10600,0 | 15,1 | 5,7 | 1,1 | 4,1 | 4,1 | 5,2 |
10600,1-13800,0 | 14,7 | 6,2 | 1,9 | 6,4 | 7,1 | 6,2 |
13800,1-17000,0 | 13,2 | 7,5 | 3,1 | 8,1 | 9,5 | 7 |
17000,1-21800,0 | 16 | 9,3 | 6,2 | 13,8 | 15,2 | 10,9 |
21800,1-25000,0 | 8,4 | 5,9 | 5,4 | 9,6 | 9,5 | 7,4 |
25000,1-35000,0 | 14,1 | 14,9 | 17 | 24,1 | 21,5 | 20,9 |
35000,1-50000,0 | 6,2 | 14,1 | 21,3 | 18,1 | 16,3 | 19,5 |
50000,1-75000,0 | 2,2 | 11,2 | 21,6 | 9,3 | 9,9 | 12,3 |
75000,1-100000,0 | 0,5 | 6 | 10,9 | 2,7 | 3,2 | 4,6 |
100000,1-250000,0 | 0,4 | 8,5 | 10,4 | 2,1 | 2,4 | 3,3 |
over 250000.0 | 0 | 4,2 | 0,9 | 0,3 | 0,2 | 0,4 |
Table 1 (part 2). Distribution of the number of employees by wages and types of economic activity, in 2015 *
*Data is published once every 2 years, in April.
Accrued wages | Wholesale and retail trade, repair of vehicles and motorcycles | Hotels and restaurants | Transport and communications | Financial activities | Operations with real estate, rental and provision of services | Research and development |
---|---|---|---|---|---|---|
up to 5965.0 | 1 | 1,3 | 1,4 | 0,4 | 1,1 | 0,4 |
5965,1-7400,0 | 2,5 | 3,2 | 1,6 | 0,6 | 2,5 | 1,1 |
7400,1-10600,0 | 8,2 | 10,5 | 4,9 | 1,4 | 5,9 | 2,4 |
10600,1-13800,0 | 9 | 10,8 | 6,1 | 2,3 | 7,2 | 3,6 |
13800,1-17000,0 | 10 | 11,7 | 6,8 | 3,7 | 8,2 | 4,8 |
17000,1-21800,0 | 14,2 | 14 | 11,1 | 8,5 | 10,9 | 7,9 |
21800,1-25000,0 | 9 | 8 | 7,7 | 7,3 | 6,7 | 6,2 |
25000,1-35000,0 | 19,1 | 18 | 20,9 | 21,5 | 16,6 | 19,2 |
35000,1-50000,0 | 12,6 | 13,2 | 19 | 21,1 | 16,2 | 22,1 |
50000,1-75000,0 | 7,4 | 5,6 | 12,4 | 15,7 | 12,5 | 18,3 |
75000,1-100000,0 | 2,8 | 1,7 | 4,2 | 6,8 | 5,3 | 6,8 |
100000,1-250000,0 | 3,3 | 1,8 | 3,4 | 9 | 6,1 | 6,3 |
over 250000.0 | 0,7 | 0,3 | 0,5 | 1,7 | 0,8 | 0,7 |
Table 1 (part 3). Distribution of the number of employees by wages and types of economic activity, in 2015 *
*Data is published once every 2 years, in April.
Accrued wages | Public administration, mandatory social Security, activities of extraterritorial organizations | Education | Health and social service provision | Providing utility, personal and social services | Of these, activities related to organizing recreation, entertainment, culture and sports |
---|---|---|---|---|---|
up to 5965.0 | 1 | 3,4 | 1,5 | 2,8 | 2,9 |
5965,1-7400,0 | 1,9 | 7,5 | 3,3 | 5,7 | 5,9 |
7400,1-10600,0 | 4 | 12,8 | 10,7 | 11,5 | 11,8 |
10600,1-13800,0 | 6 | 10,9 | 13,6 | 12,4 | 12,7 |
13800,1-17000,0 | 7 | 9,7 | 13 | 11,8 | 11,9 |
17000,1-21800,0 | 10,7 | 13,5 | 15,1 | 13,7 | 13,6 |
21800,1-25000,0 | 6,9 | 8 | 7,8 | 7,5 | 7,4 |
25000,1-35000,0 | 17,9 | 16,3 | 15 | 14,6 | 14 |
35000,1-50000,0 | 21,3 | 10,4 | 10,8 | 10,1 | 9,9 |
50000,1-75000,0 | 15,4 | 4,9 | 6,2 | 5,9 | 5,9 |
75000,1-100000,0 | 4,6 | 1,6 | 1,9 | 2 | 2,1 |
100000,1-250000,0 | 3,3 | 1 | 1,1 | 1,7 | 1,7 |
over 250000.0 | 0,2 | 0 | 0 | 0,4 | 0,4 |
To construct the Lorenz curve and calculate the Gini coefficient, data is needed on the share of income of each population group (in this case, industry workers) in total income. This data is in Table 1 are missing. In order to obtain such data, we will use a mathematical technique: we will multiply the average income for each interval (we define it as the middle of the interval) by the corresponding specific weights (shares) of the population, thereby obtaining the so-called percentage numbers of group incomes. Then, by calculating the shares of groups in total income and summing them up, we obtain a cumulative series of incomes, expressed as a percentage.
As an example, let’s carry out calculations for one of the industries, for example, agriculture, hunting and forestry.
Table 2. Estimated data for calculating the Gini coefficient for the industry "Agriculture, hunting and forestry"
Income | Middle of the interval | Specific gravity workers receiving an appropriate level of wages | Cumulative number of employees | Group income percentages | Share in total income | Cumulative income series |
---|---|---|---|---|---|---|
up to 5965.0 | 4000 | 2,5 | 2,5 | 10000 | 0,51 | 0,02 |
5965,1-7400,0 | 6200 | 6,8 | 9,3 | 42160 | 2,15 | 2,66 |
7400,1-10600,0 | 9000 | 15,1 | 24,4 | 135900 | 6,94 | 9,60 |
10600,1-13800,0 | 11950 | 14,7 | 39,1 | 175665 | 8,97 | 18,57 |
13800,1-17000,0 | 15150 | 13,2 | 52,3 | 199980 | 10,21 | 28,78 |
17000,1-21800,0 | 18600 | 16 | 68,3 | 297600 | 15,19 | 43,97 |
21800,1-25000,0 | 22600 | 8,4 | 76,7 | 189840 | 9,69 | 53,66 |
25000,1-35000,0 | 30000 | 14,1 | 90,8 | 423000 | 21,59 | 75,25 |
35000,1-50000,0 | 42500 | 6,2 | 97 | 263500 | 13,45 | 88,71 |
50000,1-75000,0 | 62500 | 2,2 | 99,2 | 137500 | 7,02 | 95,72 |
75000,1-100000,0 | 87500 | 0,5 | 99,7 | 43750 | 2,23 | 97,96 |
100000,1-250000,0 | 100000 | 0,4 | 100 | 40000 | 2,04 | 100,00 |
over 250000.0 | 250000 | 0 | 100 | 0 | 0,00 | 100,00 |
- Income
- Middle of the interval– the average wage level in each group of workers.
- Proportion of employees receiving the appropriate level of wages– Rosstat data (see Table 1).
- Cumulative number of employees– accumulated frequencies. In order to calculate the value of the i-series, it is necessary to sum up the shares of workers (column 3 of Table 2) from 1 to i inclusive.
- Group income percentages– calculated data used to determine the share of income of a particular group of workers in total income. They are calculated by multiplying the middle of the interval by the specific gravity (column 2 times column 3).
- Share in total income– the share of income of a particular group of employees in total income. The ratio of group income (column 5) to the sum of all income (sum of income in column 5).
- Cumulative income series– the sum of the shares of income to the corresponding group.
Let's build a diagram where the cumulative series of the number of employees will be plotted along the X-axis, and the cumulative series of income will be plotted along the Y-axis.
The area of the figure under the purple line can be calculated by summing up the areas of the trapezoids that make up the figure. Their total area is 3313.
The area of the figure with an absolutely uniform distribution of income is 5000 (the triangle under the straight line on Diagram 2).
Thus, the area of the figure reflecting the inequality of income distribution is 5000-3313=1687.
Therefore, the Gini coefficient for the industry Agriculture, hunting and forestry equal to 1687/5000=0.337
Gini coefficient for other sectors of the economy
Using the same model, we will calculate the values of the Gini coefficient for all 17 sectors of the economy that Rosstat takes into account.
Table 3. Gini coefficient for economic sectors in 2015
Industry | Gini coefficient |
---|---|
Agriculture, hunting and forestry | 0,337 |
Fishing, fish farming | 0,486 |
Mining | 0,314 |
Manufacturing industries | 0,331 |
Production and distribution of electricity, gas and water | 0,343 |
Construction | 0,355 |
Wholesale and retail trade, repair of vehicles and motorcycles | 0,395 |
Hotels and restaurants | 0,378 |
Transport and communications | 0,362 |
Financial activities | 0,355 |
Real estate transactions, rental and provision of services | 0,402 |
Research and Development | 0,334 |
Public administration, compulsory social security, activities of extraterritorial organizations | 0,349 |
Education | 0,384 |
Health and social service provision | 0,368 |
Providing utility, personal and social services | 0,412 |
Activities for organizing recreation, entertainment, culture and sports | 0,417 |
By ranking the data and presenting it in chart form, we can see that currently the greatest income equality is observed among employees in the mining sector, and the greatest inequality is in the fishing and fish farming sector.
To illustrate how different an inequality coefficient of 0.486 is from a coefficient of 0.314, here is a simple example. In fisheries and aquaculture, the top 12.4% of employees receive 40% of total income. But in the most “fair” sector from this point of view – the mining sector – a little more than 40% of the total income is already received by 22.1% of employees (see. Table 4).
Table 4
Fish farming, fish farming | Mining | ||
---|---|---|---|
Cumulative weight in total income | Cumulative number of employees | ||
0,11 | 1,3 | 0,01 | 0,1 |
0,83 | 6,8 | 0,03 | 0,3 |
1,91 | 12,5 | 0,22 | 1,4 |
3,46 | 18,7 | 0,65 | 3,3 |
5,85 | 26,2 | 1,53 | 6,4 |
9,49 | 35,5 | 3,71 | 12,6 |
12,29 | 41,4 | 6,01 | 18 |
21,69 | 56,3 | 15,63 | 35 |
34,29 | 70,4 | 32,70 | 56,3 |
49,01 | 81,6 | 58,16 | 77,9 |
60,05 | 87,6 | 76,14 | 88,8 |
77,92 | 96,1 | 95,76 | 99,2 |
100,00 | 100 | 100,00 | 100 |
The impact of the crisis on the differentiation of wages in economic sectors
By calculating the Gini coefficient for sectors of the economy in 2013 and comparing these values with the indicators for 2015, we will see how the crisis affected the differentiation of wages in a particular area.
Let's see if somewhere in the industry income has begun to be distributed more “fairly” among employees.
– rating of industries by growth of the Gini coefficient. The diagram shows that over the past 2 years, inequality in the distribution of wages has increased significantly in the areas of fishing, fish farming (+15.3%), hotel and restaurant business(+4.82%) and construction (+3.66%).
The distribution of wages became more “fair” in healthcare and the provision of social services (-3.47%), in the sphere of wholesale and retail motor vehicles (-2.27%), in the field scientific research and development (-2.16%).
In the fisheries and aquaculture sector in 2013, 8.2% of the highest paid employees had 23.56% of total income. In 2015, 22.08% of total income belonged to 3.9% of the highest paid employees. That is, in 2013, the top 1% of employees accounted for 2.87% of total industry income, and in 2015, each percent of these employees already accounted for 5.66% of total industry income.
Table 5
Fishing, fish farming | |||
---|---|---|---|
2013 | 2015 | ||
Cumulative weight in total income | Cumulative number of employees | Cumulative weight in total income | Cumulative number of employees |
0,03 | 0,3 | 0,11 | 1,3 |
1,25 | 7,1 | 0,83 | 6,8 |
3,21 | 14,7 | 1,91 | 12,5 |
6,40 | 24 | 3,46 | 18,7 |
10,93 | 34,4 | 5,85 | 26,2 |
15,10 | 42,2 | 9,49 | 35,5 |
20,88 | 51,1 | 12,29 | 41,4 |
33,64 | 65,9 | 21,69 | 56,3 |
47,92 | 77,6 | 34,29 | 70,4 |
65,88 | 87,6 | 49,01 | 81,6 |
76,44 | 91,8 | 60,05 | 87,6 |
100 | 100 | 77,92 | 96,1 |
100,00 | 100,00 |
conclusions
- The greatest income inequality among workers in sectors of the Russian economy is observed in the sphere fisheries and fish farming. The Gini coefficient for this industry is 0,486 .
- In the field fishing and fish farming 12.4% the highest paid employees receive 40% total income.
- Among the top three in terms of greatest income differentiation are: activities for organizing recreation, entertainment, culture and sports(Gini coefficient 0,417 ) And activities to provide utilities (0,412 ).
- The most “fair” distribution of income is in the sphere mining. There the income differentiation coefficient is equal to 0,314 , and a little more 40% total income already received 22,1% employees.
- In two last year(from 2013 to 2015) the degree of income stratification has changed in many areas of the economy.
- Inequality in wage distribution (as measured by the Gini coefficient) has increased significantly in the areas fishing, fish farming (+15,3% ), hotel and restaurant business (+4,82% ) And construction (+3,66% ).
- The distribution of wages has become more “fair” in healthcare and social services (-3,47% ), in the field wholesale and retail trade in motor vehicles (-2,27% ), in the field research and development (-2,16% ).
- The differentiation of employees by wages in such areas as manufacturing industries, mining, provision of utilities, education, activities for organizing recreation, entertainment, etc..
Gini coefficient
Gini coefficient- a statistical indicator of the degree of stratification of society in a given country or region in relation to any characteristic being studied.
Most often in modern economic calculations, the level of annual income is taken as the characteristic being studied. The Gini coefficient can be defined as a macroeconomic indicator that characterizes the differentiation of monetary incomes of the population in the form of the degree of deviation of the actual distribution of income from their absolutely equal distribution among the inhabitants of the country.
Sometimes a percentage representation of this coefficient is used, called Gini index.
Sometimes the Gini coefficient (like the Lorenz curve) is also used to identify the level of inequality in terms of accumulated wealth, but in this case a necessary condition becomes non-negativity net assets households.
Background
This statistical model was proposed and developed by the Italian statistician and demographer Corrado Gini (1884-1965) and published in 1912 in his work “Variability and Variability of a Character” (“Variability and Inconstancy”).
Calculation
The coefficient can be calculated as the ratio of the area of the figure formed by the Lorenz curve and the equality curve to the area of the triangle formed by the equality and inequality curves. In other words, you should find the area of the first figure and divide it by the area of the second. In case of complete equality, the coefficient will be equal to 0; in case of complete inequality it will be equal to 1.
Sometimes the Gini index is used - a percentage representation of the Gini coefficient.
or according to the Gini formula:
where is the Gini coefficient, is the cumulative share of the population (the population is pre-ranked by increasing income), is the share of income that the total receives, is the number of households, is the share of household income in total income, is the arithmetic mean of the shares of household income.
Benefits of the Gini Coefficient
- Allows you to compare the distribution of a characteristic in populations with different numbers of units (for example, regions with different populations).
- Complements data on GDP and per capita income. Serves as a kind of correction for these indicators.
- Can be used to compare the distribution of a trait (income) between different populations (for example, different countries). At the same time, there is no dependence on the scale of the economy of the countries being compared.
- Can be used to compare the distribution of a trait (income) across different population groups (for example, the Gini coefficient for the rural population and the Gini coefficient for the urban population).
- Allows you to track the dynamics of the uneven distribution of a characteristic (income) in the aggregate different stages.
- Anonymity is one of the main advantages of the Gini coefficient. There is no need to know who has what income personally.
Disadvantages of the Gini coefficient
- Quite often, the Gini coefficient is given without describing the grouping of the population, that is, there is often no information about exactly which quantiles the population is divided into. Thus, the more groups the same population is divided into (more quantiles), the higher the Gini coefficient value for it.
- The Gini coefficient does not take into account the source of income, that is, for a certain location (country, region, etc.) the Gini coefficient can be quite low, but at the same time some part of the population provides their income through backbreaking labor, and the other through property. For example, in Sweden the Gini coefficient is quite low, but only 5% of households own 77% of the shares of total number shares owned by all households. This provides these 5% with the income that the rest of the population receives through labor.
- The method of the Lorenz curve and the Gini coefficient in studying the uneven distribution of income among the population deals only with cash income, while some workers are paid wages in the form of food, etc.; The practice of issuing wages to employees in the form of options to purchase shares of the employer company is also becoming widespread (the last consideration is unimportant, the option itself is not income, it is only an opportunity to receive income by selling, for example, shares, and when the shares are sold and the seller receives money, this income is already taken into account when calculating the Gini coefficient).
- Differences in methods for collecting statistical data to calculate the Gini coefficient lead to difficulties (or even impossibility) in comparing the obtained coefficients.
Example of calculating the Gini coefficient
The preliminary coefficient in 2010 was 42% (0.420) The Gini coefficient in Russia in 2009 was 42.2% (0.422), in 2001 39.9% (0.399) In 2012, according to the Global Wealth Report, Russia is ahead of all major countries and has coefficient 0.84
see also
Notes
Wikimedia Foundation. 2010.
See what the “Gini Coefficient” is in other dictionaries:
- (Gini coefficient) Statistical indicator of inequality. For example, if уi is the income of the i th person, the Gini coefficient is equal to half the expected absolute difference between the incomes of two randomly selected people, i and j, divided by average income. On the… … Economic dictionary
- (Gini coefficient) See: Lorenz curve. Business. Dictionary. M.: INFRA M, Ves Mir Publishing House. Graham Betts, Barry Brindley, S. Williams and others. General editor: Ph.D. Osadchaya I.M.. 1998 ... Dictionary of business terms
A coefficient characterizing the differentiation of monetary incomes of the population in the form of the degree of deviation of the actual distribution of income from their absolutely equal distribution among all residents of the country. See t.zh. INCOME CONCENTRATION INDEX… Encyclopedic Dictionary of Economics and Law
GINI COEFFICIENT- an indicator characterizing the degree of deviation of the actual distribution of income from absolute equality or absolute inequality. If all citizens have the same income, then K.D. equal to zero, if we assume the hypothesis that all income... ... Large economic dictionary
Gini coefficient- income concentration index, showing the nature of the distribution of the entire amount of income of the population between its individual groups... Sociology: dictionary
Gini coefficient- indicator of population income concentration; The higher the inequality in a society, the closer it is to 1... Economics: glossary
Gini coefficient- a macroeconomic indicator characterizing the differentiation of monetary incomes of the population in the form of the degree of deviation of the actual distribution of income from their absolutely equal distribution among the inhabitants of the country... Dictionary of economic terms
Index of concentration of incomes, Income concentration index, Gini coefficient A macroeconomic indicator characterizing the differentiation of monetary incomes of the population in the form of the degree of deviation of the actual distribution of income from the absolute... ... Dictionary of business terms, I. G. Tsarev. The work models the distribution of income between economic entities in a closed loop. economic system. The equilibrium function of income distribution in society is calculated, its... eBook
What is inequality, how is it measured, what methodologies are used. Gini coefficient by country and other inequality coefficients.
Different inequality coefficients
- Quintile coefficient: the ratio of the average income of the richest 20% of the population to the average income of the poorest 20% of the population.
- Palma's attitude: The share of the richest 10% of the population in gross national income (GNI) divided by the share of the poorest 40%. Based on the work of José Gabriel Palma (2011), who found that middle-class incomes almost always account for about half of GNI, with the other half split between the richest 10% and the poorest 40%, but the shares of these two groups vary widely across countries .
- Gini coefficient: an indicator that characterizes the deviation of the actual distribution of income of individuals or households in a particular country from absolute equality. An index value of 0 corresponds to absolute equality, 1 to absolute inequality. (How to calculate)
The Gini and Palma indices are coefficients expressed as percentages, those multiplied by 100%.
The Office's calculations for the 2016 Human Development Report are based on World data Bank. With detailed data on the dynamics of changes in the Gini Index by year for individual countries can be found at.
I. Notation
2. Q - quantity
3. D – demand
4. S - sentence
5. Q D – quantity of demand
6. Q S – supply quantity
7. Q def – deficit (volume of deficit)
8. Sales Q – sales volume
9. Q ISP – volume of excess (surplus)
10. E DP – coefficient of price elasticity of demand
11. E SP – price elasticity coefficient of supply
12. I – income
13. E DI - coefficient of elasticity of demand by income
14. E DC - coefficient of cross elasticity of demand
15. TR – total income (seller’s revenue)
16. TC – total costs
17. P r – profit
18. P D – demand price
19. P S – offer price
20. P E – equilibrium price
II. Formulas:
1. y=k*x+b– equation describing the demand function
2. Q D = k*P+b– demand function
3. E DP = Δ Q D (%)/ΔP (%)– coefficient of price elasticity of demand
4. E DP = (Q 2 –Q 1): (Q 2 + Q 1)/ (P 2 –P 1): (P 2 + P 1)– midpoint formula, where P 1 is the price of the product before the change, P 2 is the price of the product after the change, Q 1 is the quantity of demand before the price change, Q 2 is the quantity of demand after the price change;
5. E DI = (Q 2 –Q 1): (Q 2 + Q 1)/ (I 2 –I 1): (I 2 + I 1)– formula for the elasticity of demand coefficient, where I 1 is the amount of income before the change, I 2 is the amount of income after the change, Q 1 is the amount of demand before the change in income, Q 2 is the amount of demand after the change in income;
6. E DC = (Q 2 –Q 1): (Q 2 + Q 1)/ (P 2 –P 1): (P 2 + P 1)– midpoint formula, where P 1 is the price of the second product before the change, P 2 is the price of the second product after the change, Q 1 is the quantity of demand for the first product before the price change, Q 2 is the quantity of demand of the first product after the price change;
7. TR = P*Q– formula for calculating the seller’s revenue
8. P r = TR – TC– formula for calculating profit;
9. Q D = k*P+b– supply function;
10. E SP = (Q S2 –Q S1): (Q S2 + Q S1)/ (P 2 –P 1): (P 2 + P 1)– supply coefficient formula, where P 1 is the price of the product before the change, P 2 is the price of the product after the change, Q S1 is the value of supply before the price change, Q S2 is the value of supply after the price change;
11. Q def = Q D - Q S– formula for determining the volume of the deficit;
12. Q def = Q S - Q D– formula for determining the volume of surplus
Formula for calculating the amount of money required for circulation:
1)
KD - mass of money;
Ect - the sum of prices of goods;
K - goods sold on credit;
SP - urgent payments;
VP - mutually extinguishable payments (barter transactions);
CO - turnover rate monetary unit(in year).
2)
Q is the quantity of products produced at constant prices.
Exchange equation:
M- money supply, in circulation;
V - velocity of money circulation;
P - average prices for goods and services;
Q is the quantity of products produced at constant prices.
This equation shows that total costs in monetary terms
equal to the value of all goods and services produced by the economy.
Formula for finding real income:
CPI - consumer price index.
Formula for finding the purchasing power of money:
Ipsd - purchasing power money;
Ic - price index.
Formula for finding the consumer price index:
Formula for calculating cost consumer basket:
P 1 - price of the first product;
P 2 - price of the second product;
P n - price of the nth product;
Q 1 - quantity of the first product;
Q 2 - quantity of the second product;
Q n - quantity of the nth product.
Formula for calculating the inflation rate:
Depending on the rate of inflation, there are several types of inflation:
1.Soft (creeping), when prices rise within 1-3% per year.
2.Moderate - with price increases of up to 10% per year.
3. Galloping - with prices rising from 20 to 200% per year.
4. Hyperinflation, when prices rise catastrophically - more than 200% per year.
Formula for calculation simple interest:
S - loan amount;
n - number of days;
i- annual interest in shares.
Formula for calculation compound interest:
P - amount of debt with interest;
S - loan amount;
n - number of days;
N - how many times is accrued per year.
Formula for calculating compound interest accrued over several years:
P - amount of debt with interest;
S - loan amount;
t - number of years;
i - annual percentage in shares.
Formula for calculating mixed interest for fractional years:
P - amount of debt with interest;
S - loan amount;
t - number of years;
i - annual percentage in shares;
n - number of days.
Formula for calculation bank reserves:
S is the required reserve ratio as a percentage;
R- total amount reserves;
D - the amount of deposits in the bank account.
Formula for calculating the unemployment rate:
Formula for calculating the employment level:
Formula for calculating cross price elasticity:
Formula for calculating the concept of elasticity:
Formula for calculating depreciation:
1)
2)
Formula for calculating household personal income:
Formula for calculating GNP by income:
Formula for calculating GNP based on expenses:
Formula for calculating NNP:
Formula for calculating average total costs:
1)
2)
Formula for calculating total costs:
Formula for calculating average fixed costs:
Formula for calculating average variable costs:
Formula for calculating revenue:
1)
2)
Formula for calculating accounting profit:
Calculation formula economic profit:
1)
2)
Formula for calculating product profitability:
Formula for calculating production profitability:
Formula for calculating business income:
Formula for calculating capital productivity:
Formula for calculating the value of cyclical unemployment:
Formula for calculating natural unemployment:
Formula for calculating labor productivity:
Formula for calculating arc elasticity by income:
Beginning of the form
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Gini coefficient
The shortest definition Gini coefficient – coefficient concentration of wealth. The higher it is, the higher the inequality. More complete definition– a measure of inequality of income distribution. An even more complete definition is the coefficient of deviation of the economy from absolute equality in income distribution.
Coefficient is displayed from the Lorentz curve and represents the ratio of the area between this curve and the line of absolute equality to total area below the line of absolute equality. The line of absolute equality is the bisector between the “share of households” and “share of income” axes. Coefficient can be calculated and according to the exact formula.
Maximum value coefficient is equal to one and this is - absolute inequality. The minimum is zero and this is absolute equality
Due to the socio-political significance of the estimates obtained on the basis of the coefficient, it is actively calculated, discussed and used for various levels of conclusions. One of the most active areas of use is comparative cross-country and time analysis. For example, the coefficient Genie for Russia in 1991 it was equal to 0.24, in 2008 it was 0.42. In the so-called “model” European and especially Northern European countries it is in the range from 0.2 to 0.3.
But direct conclusions from comparing the coefficient across countries and over time are hardly appropriate. He has limitations turning into disadvantages, which is explained by two circumstances. Firstly, the relative nature of this indicator. Secondly, its range asymmetry: one distribution can be more equal than another in one range, and less equal in another, with the same coefficient value for both distributions. Therefore, direct conclusions from comparisons of the coefficient in different countries and over time may lead to erroneous estimates.
Coefficient named after its author– Italian Corrado Gini, teacher of statistics, sociology and demography at the University of Rome. The coefficient was proposed by him in 1912 year, so the coefficient has a significant date - 100 years of practical use
Let's calculate the share of income of poor families.
Income of all families: 1.1 million * (0.15 * 200 thousand + 0.35 * 30 thousand + 0.5 * 10 thousand) = 1.1 million * (45.5 thousand).
This means the share of income of poor families = (1.1 million * (0.5 * 10 thousand)/(1.1 million * (45.5 thousand) = 0.11.
In the same way, we find the share of middle class income in total income (equal to 0.23).
This means the share of income of the poor and middle class in total income = 0.34.
I calculated the Gini index as the ratio of the area of the figure (S) enclosed between the curve of absolute equality and the Lorenz curve to the area of the figure enclosed between the curve of absolute equality and the curve of absolute inequality (San = 0.5)
S=0.5-S 1 -S 2 -S 3 -S 4 -S 5
S 1 , S 2 , S 3 , S 4 , S 5 can be easily found from the available data, which means the Gini index can also be found.
How to find data S1, S2, S3, S4, S5, what are they equal to? And what to do next, how to find exactly the Gini coefficient?
· S1, S3, S5 are right triangles, their area is equal to half the product of the legs
S2,S4 are rectangles, their area is the product of the sides
· Answer:
Four-dimensional cocktail
To make one serving of the Unstable Equilibrium, Economics Bar's signature cocktail, you need 1 Ingredient A, 2 Ingredients B, 3 Ingredients C, and 4 Ingredients D (ingredient names are a trade secret and will not be disclosed). However, the bar's owner, celebrity bartender and economist Sam Paulelson, has only limited resources to purchase expensive ingredients. So, for the ones he has cash he can buy either 100 units of ingredient A, or 200 units of ingredient B, or 300 units of ingredient C, or 400 units of ingredient D per day.
What is the maximum number of signature cocktails Sam can prepare in a day?
The first thing that came to my mind was a completely different solution - a logical one.
Let's note the fact that to buy any ingredient (A, B, C, D) for 1 serving of cocktail we need to spend 1/100 of all the money, that is, for 1 cocktail we spend 1/25 of all the money, so we can make 25 in total cocktails
The manual is presented on the website in an abbreviated version. This version does not include testing, only selected tasks and high-quality assignments are given, and theoretical materials are cut by 30%-50%. I use the full version of the manual in classes with my students. The content contained in this manual is copyrighted. Attempts to copy and use it without indicating links to the author will be prosecuted in accordance with the legislation of the Russian Federation and the policies of search engines (see provisions on the copyright policies of Yandex and Google).
14.2 Lorenz curve and Gini coefficient
Lorenz curve reflects the cumulative (accumulated) shares of the population's income. It is most convenient to consider the construction of the Lorenz curve using the following example:
Let's imagine an economy consisting of 3 agents: A, B, C. Agent A's income is 200 units, agent B's income is 300 units, agent C's income is 500 units.
To construct the Lorenz curve, we find the shares of individuals in total income. Total income is 1000. Then person A's share is 20%, B's share is 30%, C's share is 50%.
Individual A's share of the population is 33%. His income share is 20%.
Then we will include in the analysis a richer individual—individual B.
The combined share of A+B in the population is 67%. The joint share of A+B in income is 50% (20%+30%).
The combined share of A+B+C in the population is 100%. The joint share of A+B+C in income is 100% (20%+30%+50%).
Let us note the results obtained on the graph:
The line connecting the lower left point and the upper right point of the graph is called line of uniform income distribution. This is a hypothetical line that shows what would happen if income in the economy was distributed evenly. With an uneven distribution of income, the Lorenz curve lies to the left of this line, and the greater the degree of inequality, the stronger the bend in the Lorenz curve. And the lower the degree of inequality, the closer it is to the line of absolute equality.
In our case, the Lorenz curve looks like a piecewise linear graph. This happened because in our analysis we identified only three population groups. As the number of population groups considered increases, the Lorenz curve will look like this:
The Lorenz curve allows you to judge the degree of income inequality in the economy by its bend. To quantify the degree of income inequality along the Lorenz curve, there is a special coefficient - the Gini coefficient.
The Gini coefficient is equal to the ratio of the area of the figure bounded by the straight line of absolute equality and the Lorenz curve to the area of the entire triangle under the Lorenz curve.
If the Lorenz curve is depicted not in %, but in fractions, then the area of the large triangle is always equal to ½. The formula for the Gini coefficient for this case takes the form:
J = 2 * S A
The Gini coefficient can take values from 0 to 1. The closer the Gini coefficient is to zero, the smaller the bend in the Lorenz curve, and income is more evenly distributed. The closer the Gini coefficient is to one, the greater the bend in the Lorenz curve, and income is less evenly distributed.
Let's calculate the Gini coefficient for our example with three individuals. To do this, we will construct the Lorenz curve in fractions, and not in % 1.
The fastest way to calculate the area of the inner figure D is by subtracting the areas of figures A, B and C from the area of the large triangle.
In this case, the Gini coefficient will be equal to:
A special case of the Lorenz curve and the Gini coefficient: pairwise comparison.
As you know, any statistical indicator has its flaws. Just as the GDP indicator cannot judge the level of well-being of the economy, the Gini coefficient (and other indicators of the degree of inequality) cannot give a fully objective picture of the degree of income inequality in the economy.
This happens for several reasons:
- First, individuals' income levels are not constant and can change dramatically over time. The income of young people who have just graduated from university is usually minimal, and then begins to increase as the person gains experience and builds up human capital. People's income typically peaks between the ages of 40 and 50, and then declines sharply as the person retires. This phenomenon is called the life cycle in economics.
But a person has the opportunity to compensate for differences in income at different stages of the life cycle with the help of financial market– taking out loans or making savings. Thus, young people at the very beginning of their life cycle willingly take out loans for education or mortgage loans. People who are closer to the end of the economic life cycle are active savers.
The Lorenz curve and Gini coefficient do not take into account the life cycle, so this measure of the degree of income inequality in a society is not an accurate estimate of the degree of income inequality. - Second, individuals' incomes are affected by economic mobility. The US economy is an example of an economy of opportunity, where an individual from the bottom can, through a combination of hard work, talent and luck, become very successful person, and history knows many similar examples. But there are also cases of loss of large fortunes or even complete bankruptcies of quite wealthy entrepreneurs. Typically, in economies such as the United States, an individual household will move through several income distribution categories over the course of its lifetime. And this is due to high economic mobility. So, for example, a household may in one year be included in the group with the most low level income, and next year already in the middle income group. The Lorenz curve and the Gini coefficient also do not take this effect into account.
- Third, individuals can receive transfers in in kind, which are not reflected in the Lorenz curve, although they affect the distribution of individual income. Transfers in kind can be implemented in the form of assistance to the poorest segments of the population with food, clothing, but usually they are provided in the form of numerous benefits (free travel to public transport, free trips to sanatoriums and so on). Taking into account such transfers economic situation the poorest segments of the population are improving, but the Lorenz curve and the Gini coefficient do not take this into account. Not so long ago in Russia many benefits were monetized, and it became easier to calculate the objective incomes of the poorest segments of the population. Consequently, the Lorenz curve began to better reflect the real distribution of income in society.
These indicators are used to assess the degree of income inequality, and are included in the field of positive economic analysis. Let us recall that positive analysis differs from normative analysis in that positive analysis analyzes the economy objectively, as it is, and normative analysis is an attempt to improve the world, to make it “as it should be.” If the assessment of the degree of inequality is a positive economic analysis, then attempts to reduce inequality in the distribution of income belong to the field of normative economic analysis.
Normative economic analysis known for the fact that different economists can offer different, often diametrically opposed recommendations for solving the same problem. This does not mean who is more competent and who is less competent. This only means that economists start from different philosophical views on the concept of justice, and there is no unity on this issue.
We will first look at the different value systems that exist and then show how income can be distributed more equitably within each system.
The materials in this section are not published on the website, but are available in the full version of this manual, which I use in classes with students.
Taxes and tax system
The US economy of the 19th century can be said to be an ideal example of free capitalism. Adam Smith's ideals of minimal government intervention in the distribution of resources and the functioning of markets (remember the famous principle of laissez faire) were adopted at that time, government intervention in the market was minimal, government spending amounted to 7-8% of total expenses, and average rate taxation for US citizens was 5% of income. The entire 20th century passed under the banner of an active increase in the presence of the state in the economy, government spending increased to 25%-30% of total expenses, and the average tax rate increased to 35% of income.
The state now acts not only as an eliminater of market failures, which we actively discussed in the last chapter (externalities and the provision of public goods), but also as a stimulant of the economy when the economy is experiencing difficult times.
Taxes are the main source of government revenue. Any state has many taxes and fees, built on certain principles, as well as institutions for control over tax collection. All this amounts to state tax system.
Principles are used to evaluate the tax system efficiency and fairness. As we already know, the concept of justice is not precisely defined for economists. Depending on the system of moral values, justice can be established in one way or another. Economists are much more consistent in defining what efficiency is. The effective one is tax system, which least of all leads to distortion of incentives for market participants and, consequently, to the occurrence of deadweight losses.
Let us show how deadweight losses are associated with distorted incentives for market participants.
On the topic of market equilibrium, we remember that deadweight losses occurred when taxes and subsidies changed the position of the supply and demand curves, that is, they changed the economic behavior of people. The deadweight loss was that some buyers were unable to buy the good and some producers were unable to sell the good, compared to a situation where prices accurately reflected marginal costs.
Let's consider a simple example: individual A values the pleasure of consuming ice cream at 60 rubles, individual B - at 40 rubles. If the price of a glass of ice cream is 30 rubles, then each of them will buy it and enjoy it. The amount of consumer surplus will be equal to 40 rubles (30 rubles for individual A and 10 rubles for individual B). If we introduce a tax on ice cream consumption in the amount of 20 rubles per glass, then the situation on the market will change dramatically: individual A will still consume ice cream, but individual B will refuse to consume it. The total consumer surplus will now be equal to only 10 rubles (this is the surplus of individual A). Tax fees this will amount to 20 rubles (again, only individual A will pay them), and the state receives them. The amount of public benefits in this case will be 10 + 20 = 30 rubles, and it is 10 rubles lower than in a situation without taxation. Using this simple example, we were convinced that during taxation a permanent loss in the amount of 10 rubles arose. And they arise because individual B changed his economic behavior, completely abandoning the consumption of ice cream.
In the same way, any taxes lead to deadweight losses, so we can safely say that any taxes are ineffective in this sense. The task of economists is to find taxes that will minimally distort people's incentives, and therefore lead to minimal deadweight losses.
Taxes may apply differently depending on the amount of income. In order to do this, we will need two types of tax rates: average tax rate and marginal tax rate.
The average tax rate shows what percentage of tax an individual pays on average on income received
The marginal tax rate shows what percentage of tax an individual pays on additional income:
The average and marginal rates behave the same as any average and marginal values:
- When the marginal rate is higher than the average, the average rate increases
- When the marginal rate is lower than the average, the average decreases
Depending on the behavior of the average and marginal tax rates, there are 3 types of taxes: progressive, proportional, regressive.
Have a progressive tax The average tax rate rises as income increases, which means the marginal tax rate is higher than the average.
Examples of progressive taxes: income taxes in France, taxes in Sweden, car tax in Russia.
Have a proportional tax The average rate does not change with income growth, which means that the average tax rate coincides with the marginal tax rate.
Examples of proportional taxes: income tax in Russia 13%, profit tax in Russia 20%.
If an individual is offered the same tax rate while there is a certain tax-free minimum (or is provided tax deduction), then this tax system is no longer proportional, but progressive. At first, an individual does not pay taxes at all, and then, after exceeding the tax-free minimum, he begins to pay tax at the same rate.
Have regressive taxes The average rate falls as income rises, which means the marginal tax rate is lower than the average.
Examples of regressive taxes: excise taxes - since a person pays them when purchasing a product, regardless of his income. For example, from 10 to 30 rubles in the cost of each pack of cigarettes are excise taxes, and a person pays them regardless of the amount of income when purchasing each pack of cigarettes. Thus, for a poor person this tax constitutes a significant part of his income, but for a millionaire it will be insignificant.
Other examples of regressive taxes are any fixed taxes or duties. For example, in the Russian Federation, a person is forced to pay a fixed fee of about 1,000 rubles when registering a car license plate. This type of tax is regressive because the duty leaves more of the income for the poor person and less of the income for the rich person.
Which of these types of taxes is fairer? A popular point of view is that progressive taxes are more fair, and regressive ones are less fair. But this point of view is wrong. As we showed earlier, everything depends on within what system of moral values we will talk about justice.
Let's look at a simple example. Individual A receives an income of 10 rubles and pays tax at a rate of 10%. Individual B receives an income of 90 rubles and pays tax at a rate of 5%. The tax scale is regressive - the average rate falls as income rises. But is it unfair? Let's calculate the amount of tax paid by each individual. Individual A pays 1 ruble (=10*10%), individual B pays 4.5 rubles (=90*5%). As a result, an individual who earns more pays more tax. And where is the injustice here?
To assess the fairness of the tax system, the following postulates are highlighted:
- Principle of benefits received: individuals must pay taxes in accordance with the benefits they derive from government services. The idea that rich people should pay more taxes than poor people may be based on this principle. Because the government is the provider of public goods and the guarantor of property rights, rich people benefit more from the government than poor people because they have more property. This principle also justifies the idea of anti-poverty programs at the expense of the rich. We all want to live in a society that does not experience revolutions and social upheavals due to the unacceptable standard of living of the poorest segments of the population. Therefore, the idea of helping the poor at the expense of the rich seems justified.
- Solvency principles: horizontal equity and vertical equity. Horizontal equity means that individuals with the same income should pay the same taxes. Vertical equity means that individuals with higher incomes must pay higher taxes. As we saw from the example above, these principles can be met not only by a progressive taxation system, but also by a regressive one.
Depending on how taxes are collected in the state budget, distinguish direct and indirect taxes.
Direct taxes- These are taxes that are paid by the person who bears the tax. For example, income tax is a direct tax because it is paid by the firm that receives those profits. Income tax is a direct tax because it is paid by the individual who receives taxable income.
Indirect taxes- These are taxes paid by someone who is not a tax bearer. For example, excise taxes on alcohol and cigarettes are paid by firms. However, the bearer of the tax in this case is the consumer, because excise taxes “sit” in the price of goods purchased by the consumer. Indirect taxes in Russia are VAT (value added tax) and excise taxes. All indirect taxes are regressive with respect to the income of buyers.
Which taxes are more popular: direct or indirect? The answer is that indirect taxes are easier to collect because they are actually imposed on consumer spending. Direct taxes are more difficult to collect because they are imposed primarily on income, in which case individuals have incentives to evade taxes by hiding income. Therefore, indirect taxes are more popular in states with underdeveloped institutions, where individuals are able and willing to evade taxes.
Another effect that direct or indirect taxes have on the economy is to encourage individuals to save. Direct taxes are usually imposed on individuals' current income, so individuals have no incentive to save more. Indirect taxes encourage individuals to save because these taxes are imposed on consumption. By saving money rather than spending it now, individuals pay less in taxes now at indirect taxes, and pay more taxes now with direct taxes.
The Impact of Taxes on Income Inequality
The materials in this section are not published on the website, but are available in the full version of this manual, which I use in classes with students.