2. Poverty and Inequality Consider the following income distribution for a 10-person economy with a poverty line of $11. Fill in the missing information, rounding to 1 decimal place where necessary: Person Income ($) % Cumulative % Cumulative Population Income 10 1.5 20 3.8 5 30 7.5 6 40 12.0 10 50 19.5 12 60 28.6 15 70 39.8 18 80 53.4 22 90 69.9 10 40 100 100.0 a. Compute the following measures of poverty and inequality for this economy. Show your work in the boxes below the table. i . Headcount Index 0.5 ii. Income Gap Ratio 52.7% iii. FGT1 26.4% iv. FGT2 17.1% 1) HCI = poor people / total population = 5/10 = 0.5 ii) IGR = [(z - y)/(2*HC) = ((11-2) + (11-3) + (11-5) + (11-6) + (11-10))/(11*5) = 29/55 ili) FGT1 = (1/N)*[((z-yi)/z) = (1/10)*((11-2) + (11-3) + (11-5) + (11-6) + (11-10))/11 = 29/110 IV) FGT2 = (1/N)*[(z-yi)/2)*2 = (1/10)*((11-2)-2 + (11-3)^2 + (11-5)-2 + (11-6)-2 + (11-10)-2)/(11*2) = 207/1210b. The headcount index does not reflect the depth of poverty below the poverty line. 1 . Describe a specific income transfer within this economy, including which people and how much will be transferred, that demonstrates this limitation of the headcount index. 11. Compute the headcount index after the transfer. iii. Discuss how this transfer demonstrates the limitations of the headcount index as a measure of poverty. c. You have just been given $8 of foreign aid. Consider all measures of poverty and inequality we discussed in class. i. To reduce the share of the population in poverty, which measure would you target? 1i. How would you distribute the aid to reduce the share of the population in poverty as much as possible? Be specific about how much would go to which individuals. What is the new value of the measure you identified in (i) after this aid distribution?ili. To reduce the severity of poverty in this economy, which measure would you target? iv . How would you distribute the aid to reduce the severity of poverty? Be specific about how much would go to which individuals. What is the new value of the measure you identified in (iii) after this aid distribution? V. To reduce the amount of society's resources (total money in the society) required to eliminate poverty, which measure would you target? vi. How would you distribute the aid to accomplish this goal? Be specific about how much would go to which individuals. What is the new value of the measure you identified in (v) after this aid distribution