Question

The following income distribution data are for Brazil.

Quintile Percent Share

Lowest 20% 2.5%

Second quintile 7.4%

Third quintile 11.8%

Fourth quintile 20.9%

Highest 20% 57.4%

Highest 10% 43.0%

(i) Brazil’s national income is about $300 billion. What is the approximate dollar income of the bottom 20%? Bottom 40%?

(ii) Suppose one percent of national income were transferred from the richest 20% of households to the poorest 20% of households. In the context of the Lorenz curve, would we see an increase in the Lorenz curve or a decrease? Briefly explain you answer.

(iii) Given the information in the table above, calculate the Kuznets ratio for Brazil.

Answer 1

(i) National income = 300 Bn$

Dollar income of bottom 20% = 2.5% of national income = 2.5%*300 = $7.5 BN

Dollar income of bottom 40% = Lowest quintile + Second quintile = (2.5% + 7.4%)*300 = $29.7 BN

(ii) One percent of national income = 3 BN$

See below the old and new income distribution:

Income % share	Actual income ($ BN)	New income	New income %	Cumulative old income %	Cumulative new income %
2.50%	7.5	10.5	3.50%	2.50%	3.50%
7.40%	22.2	22.2	7.40%	9.90%	10.90%
11.80%	35.4	35.4	11.80%	21.70%	22.70%
20.90%	62.7	62.7	20.90%	42.60%	43.60%
57.40%	172.2	169.2	56.40%	100.00%	100.00%
100.00%	300	300	100.00%

See below the lorenz curve:

The new lorenz curve increases. The curve moves a bit towards the line of equality as the income share of highest quintile reduces and the lowest quintile increases with the redistribution.

(iii) Kuznets ratio = Income of the highest quintile / lowest quintile

Kuznets ratio (old) = 172.2 / 7.5 = 22.96

New ratio = 169.2/10.5 = 16.11