Question

There are 20 people living in Jalle town. Eight (8) residents are farmers, each of whom earns$200 per year. Six (6) of them are fishermen, each of whom earns $300 per year. Four (4) of the residents own small shops, each of whom earns $600 per year. Two (2) residents are mechanics and each of them earns an annual income of $1000. The total annual income of Jalle town is, therefore, $7,800.

a) Based on the information given above, fill out the table below

Population Quintiles	% of Income Received)
Poorest 0 %
Poorest 20%
Poorest 40%
Poorest 60%
Poorest 80%
Poorest 100%

b) Graph the Lorenz curve of Jalle town and compute the Gini coefficient.

Answer 1

A town has a population of 20 people.

The total income of the population is $7,800.

There are eight farmers with an income of $200/year each.

There are six fishermen with an income of $300/year each.

The town also has four shop-owners with an income of $600/year each and two mechanics with an income of $1,000/year each.

1. The table given below shows the percentage share of total income held by different quintiles of the population.

Population Quintiles	No. of people in quintile	Their income	Percentage of income received
Poorest 0%	0	0	0
Poorest 20%	4	4*200=800	(800/7,800) *100 =10.25%
Poorest 40%	8	8*200=1,600	(1,600/7,800) *100 =20.5%
Poorest 60%	12	8*200+4*300=2,800	(2,800/7,800) *100 =35.89%
Poorest 80%	16	8*200+6*300+2*600=4,600	(4,600/7,800) *100 =58.97%
Poorest 100%	20	8*200+6*300+4*600+2*1,000=7,800	(7,800/7,800) *100 =100%

2. Lorenz curve is a tool that is used to graphically represent inequalities in income. This method was given by American economist Max Lorenz. It represents the percentage of the population from the poorest to the richest on the horizontal axis.

The percentage share of income is represented on the vertical axis.

The line of equality shows perfect income equality. This means 20% of the population holds 20% share of income.

The Lorenz curve shows the actual distribution of income. The difference between the Lorenz curve and the line of equality represents disparity in income.

Gini index or Gini coefficient is a statistical measure used to represent income inequality. It was given by Italian statistician Corrado Gini. The value of the Gini coefficient ranges from 0 to 1 or 0% to 100%. Perfect income equality is represented by 0 and perfect inequality is represented by 1.

Fraction of Income	Fraction of population	% of population that is richer	Score
0.205	0.4	0.6	0.205(0.4+2*0.6) =0.328
0.23	0.3	0.3	0.23(0.3+2*0.3) =0.207
0.31	0.2	0.1	0.31(0.2+2*0.1) =0.124
0.26	0.1	0	0.26(0.1+2*0) =0.026
			Total: 0.685

Gini Coefficient = 1-0.685=0.315

So, the Gini coefficient is 0.315.