Question

4. The following income distribution data are for a hypothetical developing country. (20 points) Ọuintile Lowest 20% Second quintile Third Fourth quintile Highest 20% Highest 10% Percent Share 2.4% 5.7% 10.7% 18.6% 62.6% 46.2% quintile a) Carefully graph the Lorenz curve, labeling the axes. (5 points) b) This country's national income is about $300 billion. What is the dollar income of the bottom 20 percent? Bottom 40 percent? (5 points) c) Using the same income data specified in (ii), assume that this country's population is 150 million. Suppose that each household earns the average income for its quintile. How many people in this country are poor if the poverty line is S400 per capita? How much will it take to lift the poor out of poverty? (10 points)

Answer 1

a)

Population	Perfect equality distribution	Actual Income	Cumulative distribution
0%	0%	0.00%	0.00%
20%	20%	2.40%	2.40%
40%	40%	5.70%	8.10%
60%	60%	10.70%	18.80%
80%	80%	18.60%	37.40%
100%	100%	62.60%	100.00%

$w88BPW1mnSQGAAAAABJRU5ErkJggg==$

b)

National Income=NI=$300 billion

Dollar income of 20% population =2.40% of NI=300*2.4%=$7.2 billion

Dollar income of 40% population =8.10% of NI=300*8.1%=$24.3 billion

c)

Population	Population, million	Actual Income f	$ income= f*300000 million	Income per capita
Lowest 20%	30	2.40%	7200	240
Second Quintile	30	5.70%	17100	570
Third Quintile	30	10.70%	32100	1070
Fourth Quintile	30	18.60%	55800	1860
Highest 20%	30	62.60%	187800	6260

We find that Lowest 20% population is below poverty level income of $400 per capita.

No. of persons in this category are 30 million.

Amount needed to uplift this population=(400-240)*30=$4800 million or say $4.8 billion