Lorenz Curve: Step by Step Calculation

 Lorenz Curve:

Lorenz Curve is a fairly widely used simple graphical method of comparing distribution on 2 dimensional surfaces. It is the graphical representation of disparity of wealth or income. It basically provides a visual idea of the cumulative distribution of income and wealth in relation to cumulative population distribution. It is basically a cumulative percentage curve which is drawn on a perfect square shaped Graph taking the percentage of population in X axis and cumulative percentage of wealth in Y axis.

Fig. 1 &2: Lorenz Curve (Line of equality and line of actual distribution)

The diagonal line of 45 degrees shows a line of equal distribution or line of perfect distribution. The degree of inequality in a distribution is directly proportional to the degree of conductivity of the actual distribution curve, that means the deviation of the actual distribution curve from the diagonal line. Equal distribution means everyone has an equal amount of income. For example, If each 10% of the people has 10% of the total income, then it will be represented along the diagonal line of the curve which is the line of equal distribution curve. This perfect equality is hypothetical and in reality such kind of equality hardly exists. Rather income distribution shows a kind of inequality or disparity or deviation from the diagonal line. Thus, in the Lorenz Curve, the gap between the diagonal line and the actual distribution line has more inequality in the distribution. 

Principle and characteristics:

The basic characteristics of Lorenz curve are as follows:

1. It is a graphical representation of inequality or disparity within the distribution.
2. Numerical expression of distribution is not obtained.
3. It helps visualise the inequality or disparity in the distribution, thus more useful to common people.

Example: 1

Table: Lorenz Curve of wealth (India, 2014)
Cumulative % of Population (Poorest to Richest)	Cumulative Wealth in %	Ideal wealth in %
10	0.2	10
20	0.6	20
30	1.4	30
40	1.7	40
50	2.5	50
60	5.1	60
70	8.9	70
80	14.6	80
90	24	90
100	100	100

Lorenz Curve can also be used to represent geographical data of different spatial units. For example, in a District the Block wise any demographic or other dataset can be represented in Lorenz Curve as cumulative percentage distribution. 

Example-2 (Geographic Data):

Table: Distribution of urban population

Distribution of Urban Population						Reorder of Districts
District	Total Population	Urban Population	% of Urban Pop	Rank (Ascending) as per % Urban Pop	Rank in ascending Reorder	Total Population	Urban Population	% of Total Pop to Regional Total	% of Urban Pop to Regional Total	Cumulative % Pop	Cumulative % Urban
A	250000	5000	2.0	1	1	250000	5000	7.6	0.5	7.6	0.5
B	200000	55000	27.5	5	2	150000	20000	4.5	2.0	12.1	2.5
C	450000	150000	33.3	6	3	200000	40000	6.0	4.0	18.2	6.5
D	1550000	555550	35.8	7	4	355550	95000	10.7	9.5	28.9	16.0
E	355550	95000	26.7	4	5	200000	55000	6.0	5.5	35.0	21.5
F	155000	80000	51.6	8	6	450000	150000	13.6	15.0	48.5	36.5
G	200000	40000	20.0	3	7	1550000	555550	46.8	55.5	95.4	92.0
H	150000	20000	13.3	2	8	155000	80000	4.7	8.0	100.0	100.0
Total	3310550	1000550				3310550	1000550	100.0	100.0

    Steps for calculation:

Step-1: Calculate % of urban population to total population for each district.

Step-2: Put the ranks % of urban population in either ascending or descending order (Here ascending order is used).

Step-3:  Reorder the rank. 

Step-4: Calculate the % of share of total population for each district to the regional total

Step-5: Calculate the % of share of urban population for each district to the regional total.

Step-6: find out cumulative percentage of total population as well as urban population.

        For more examples see the video