Question

The following income distribution data are for Brazil.

Quintile	Percent Share
Lowest 20%	3.0%
Second quintile	6.9%
Third quintile	14.8%
Fourth quintile	19.6%
Highest 20%	55.7%
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) The national income is 300 billion so we have the dollar income of:

lowest 20% of population as 3% which is 3%*300 = $9 billion

lowest 40% as 9.9%*300 = $29.7 billion.

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

See below the old and new income distribution:

Income % share	Actual income ($ BN)	New income	New income %	Cumulative old income %	Cumulative new income %
3.00%	9.00	12.00	4.00%	3.00%	4.00%
6.90%	20.70	20.70	6.90%	9.90%	10.90%
14.80%	44.40	44.40	14.80%	24.70%	25.70%
19.60%	58.80	58.80	19.60%	44.30%	45.30%
55.70%	167.10	164.10	54.70%	100.00%	100.00%
100.00%	300.00	300.00	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) = 167.10 / 9 = 18.57

New ratio = 16410/12 = 13.68