Advice 1: How to build the Lorenz curve

Curve Lorenz , in economic theory is called a curve showing the distribution of income and measures the degree of inequality in the distribution of national income. There are different ways of measuring income inequality. One of them is the Gini coefficient, characterizing the location of the Lorenz curve. The Gini coefficient shows the extent of the variation (inequality) of income distribution.
How to build the Lorenz curve
Instruction
1
To build the Lorenz curve you need the following statistics:

- the incomes of different population groups as a percentage of total incomes taken as 100% (percentage of income);

- the number of people in each group in percentage ratio to the whole quantity taken for 100% (share of population).
2
Take a sheet of paper, a pen or pencil and draw a coordinate axis. The X-axis is the population of the country (%), Y is national income (%).
3
Suppose the population is divided into 10 equal-sized groups, share of income of the first group (10% of the population) in national income is 3%, second group – 5%, the share of third at 7%, etc.
4
Graphically, the first point will be the point with coordinates x=10, y=3. The second point is obtained, by adding the percentage of income of the first group with the second income group (cumulative). Thus, the second point will have coordinates x=20, y=(3+5=8), the third coordinates, respectively, x=30, y=(8+7=15). On the same principle of counting all other points.
5
Indicate on your drawing the names of the points, e.g., A, b, C,...E. the Point on the X-axis, corresponding to 100% of the population identify as the point F.
6
Connect with a straight line points a and E, get the line that shows the distribution of income in conditions of absolute equality.
7
Then connect with a line the points O, A, b, C,...E. the Line can be broken or smooth.
8
Curve OABC...E is the cumulative Lorenz curve, which shows the share of total income goes to each of the groups, starting with the poorest and ending with the group with the largest income. Unlike direct FIRST, it reflects the actual distribution of income.
9
Stroke segment of the figure formed by these two lines. Segment OABC...E characterizes the degree of inequality as the ratio of the area OABC, segment...E to the area of the triangle ОЕF. This ratio is called the Gini coefficient. Income inequality the deeper, the more this coefficient.

Advice 2 : How to calculate the Gini coefficient

Data on GDP per capita and the average income of the population of the state may not be enough to determine his well-being. This applies particularly to cases where the state is strong stratification between rich and poor. The coefficient of Gini to determine the degree of this bundle and add to the General picture of the welfare of citizens.
How to calculate the Gini coefficient
You will need
  • formula brown's formula Gini
Instruction
1
The coefficient of the Gini can take values from 0 to 1. It can also be expressed in percent.
To calculate the Gini coefficient can be the brown formula: G = |1-?(X{k}-X{k-1})(Y{k}-Y{k+1})|. In this formula, G is the Gini coefficient, X{k} - cumulate proportion of the population, Y{k} is the proportion of income which, in aggregate, receives X{k}. ? the summation sign. The summation is conducted according to the index k from k = 1 to k = n, where n is the number of households.
2
Also, the Gini coefficient can be calculated according to the formula of the Gini: G = ?(?|y{i}-y{j}|)/(2*(n^2)*||y||), y{k} is the proportion of household income in the total income ||y|| arithmetic average share of household income. The first sign of summation leads to the summation over index i from i = 1 to i = n, the second (in brackets) is the index j from j = 1 to j = n, where n is the number of households as in formula brown.
3
The smaller the Gini coefficient, the less stratification among selected groups. To calculate the Gini coefficient not only in the framework of the entire state. For example, it is possible to calculate the Gini coefficient for different groups of the population - residents of the city and the village; employees of private and state enterprises, etc.Ratio of the Gini one set may differ depending on the conditions of the calculation. The greater the number of (groups of) quantiles, which divided the totality in the calculation, the greater the Gini coefficient.It is also important to remember that the Gini coefficient does not take into account sources of income.

Advice 3 : How to build the Lorenz curve

Curve Lorenz , in economic theory is called a curve showing the distribution of income and measures the degree of inequality in the distribution of national income. There are different ways of measuring income inequality. One of them is the Gini coefficient, characterizing the location of the Lorenz curve. The Gini coefficient shows the extent of the variation (inequality) of income distribution.
How to build the Lorenz curve
Instruction
1
To build the Lorenz curve you need the following statistics:

- the incomes of different population groups as a percentage of total incomes taken as 100% (percentage of income);

- the number of people in each group in percentage ratio to the whole quantity taken for 100% (share of population).
2
Take a sheet of paper, a pen or pencil and draw a coordinate axis. The X-axis is the population of the country (%), Y is national income (%).
3
Suppose the population is divided into 10 equal-sized groups, share of income of the first group (10% of the population) in national income is 3%, second group – 5%, the share of third at 7%, etc.
4
Graphically, the first point will be the point with coordinates x=10, y=3. The second point is obtained, by adding the percentage of income of the first group with the second income group (cumulative). Thus, the second point will have coordinates x=20, y=(3+5=8), the third coordinates, respectively, x=30, y=(8+7=15). On the same principle of counting all other points.
5
Indicate on your drawing the names of the points, e.g., A, b, C,...E. the Point on the X-axis, corresponding to 100% of the population identify as the point F.
6
Connect with a straight line points a and E, get the line that shows the distribution of income in conditions of absolute equality.
7
Then connect with a line the points O, A, b, C,...E. the Line can be broken or smooth.
8
Curve OABC...E is the cumulative Lorenz curve, which shows the share of total income goes to each of the groups, starting with the poorest and ending with the group with the largest income. Unlike direct FIRST, it reflects the actual distribution of income.
9
Stroke segment of the figure formed by these two lines. Segment OABC...E characterizes the degree of inequality as the ratio of the area OABC, segment...E to the area of the triangle ОЕF. This ratio is called the Gini coefficient. Income inequality the deeper, the more this coefficient.
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