Question

3) A country with a population of 100,000,000 has the following income distribution: - Everyone in the first quintile earns exactly $200/month. - Everyone in the second quintile earns exactly $350/month. - Everyone in the third quintile earns $600/month - Everyone in the fourth quintile earns $1000/month - Everyone in the fifth quintile earns $2000/month Assume the poverty line is at $400/month a) Draw the Lorenz curve for this country b) Calculate the headcount ratio c) Calculate the average proportional income gap and the Poverty gap index (P1)

Answer 1

3.a.solution:

Per head income	population	total income in that quintile	percentage of the total income	cumulative percentage	cumulative percentage of the population
200	200000000	40000000000	4.819277108	4.819277108	20
350	200000000	70000000000	8.43373494	13.25301205	40
600	200000000	1.2E+11	14.45783133	27.71084337	60
1000	200000000	2E+11	24.09638554	51.80722892	80
2000	200000000	4E+11	48.19277108	100	100
total	1000000000	8.3E+11	100

b. solution:

poverty line=400

total population under income 400(total headcount)=400000000

hence headcount ratio=400000000/1000000000=0.40

c. solution:

average income gap

=total poverty gap/total poor

={200000000(400-350)+200000000(400-200)}/400000000

=125

the poverty gap index=

(as 400 is the poverty line)

=1/1000000000{200000000(400-200)/400+200000000(400-350)/400}

=0.625x200000000/1000000000

=125000000/1000000000

hence the poverty gap index=0.125

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