# Problem Set 1 Answer Key - Problem Set#1 Answer Key 1 a HCR...

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Problem Set #1 Answer Key 1. a. HCR = #in poverty/total population. So, HCR = 30/40 = ¾ PGR = (1/n)Σ(z-y i )/z *I(z>y i ), where n is the total population, z is the poverty line, y is the ith person’s income, and I(z>y i ) means we only include the term in the sum if z>y i . So, PGR = (1/40)*[((550-500)/550)*10 + ((550-400)/550)*10 + ((550-250)/550)*5 + ((550-200)/550)*5] = 0.2386 PGR2 = (1/n)Σ((z-y i )/z ) 2 *I(z>y i ). So, PGR2 = (1/40)*[((550-500)/550) 2 *10 + ((550- 400)/550) 2 *10 + ((550-250)/550) 2 *5 + ((550-200)/550) 2 *5] = 0.10847 b. HCR = 10/40 = ¼ PGR = (1/40)*[((275-250)/275)*5 + ((275-200)/275)*5] = 0.04545 PGR2 = (1/40)*[((275-250)/275) 2 *5 + ((275-200)/275) 2 *5] = 0.01033 c. If you are using the HCR, the best redistributive policy would be to take money from the rich (doesn’t matter who) and give it to the poor who are closest to the poverty line. We are only considering whether they are below the line or not with this measure, not with how far below they are. If you are using the PGR, the best policy would be to give the money in equal amounts to the poor. It doesn’t actually matter to whom you give the money (as long as they are below the poverty line) as it will have the same effect on the measure, but giving it out equally seems to be fair, since you have no reason to prefer one poor person over another (remember, the goal is just to reduce poverty according to the given measure). If PGR2 was being used, I would want to give the money to the most poor, because the square on the term would then give that change a bigger effect. Adjusting the poverty line will adjust the initial measure, but what we are worried about is

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Problem Set 1 Answer Key - Problem Set#1 Answer Key 1 a HCR...

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