1) The data in the table suggest that there was (an increase/no change/a decreas

Question

1) The data in the table suggest that there was (an increase/no change/a decrease/no evidence of)   income inequality from 1994 to 2012.

2) Complete the following table to help you determine the poverty rate in Perkopia in 2000. To do this, begin by determining the total income of all individuals in each quintile using the fact that total annual income in the economy is $500,000,000. Next, determine the income of an individual in each quintile by dividing the total income of that quintile by the number of people in that quintile. (Hint: Recall that Perkopia has a population of 10,000 people.) Finally, determine whether the individual income for each quintile falls below the poverty line of $27,400.

3) Using the information in the previous table, the poverty rate in Perkopia in 2000 is (10/20/30/40/50/60%) .

Suppose that the government introduces a welfare program in which any individual with an income of less than $27,400 per year receives a lump-sum transfer payment of $6,000 from the government. Assume that, in the short run, there is no change in labor-supply behavior among the people in Perkopia.

4) In the year 2000, the poverty rate after the introduction of the welfare program in Perkopia is (10/20/30/40/50/60%) .

Again, suppose the government introduces a welfare program in which any individual with an income of less than $27,400 receives a lump-sum transfer payment of $6,000 from the government. Kevin, a resident of Perkopia who currently earns an income of $27,102, has the opportunity to work overtime and earn an additional $1,600 this year.

5) Which of the following statements are correct? CHECK ALL THAT APPLY

____ The $6,000 in aid creates a disincentive for Kevin to earn more than $27,400 per year.

____ Kevin would gain more income by turning down the overtime than he would if he accepted the overtime.

Share of Total Income in Perkopia (Percent,) Year Lowest Quintile Second Quintile Middle Quintile Fourth Quintile Highest Quintile 1994 2000 2006 2012 5.0 3.9 3.5 3.2 11.0 9.9 8.8 7.6 16.0 15.2 14.6 14.0 25.0 22.9 22.0 21.5 43.0 48.1 51.1 53.7

Explanation / Answer

Solution :

1) As we move from 1994 to 2012, we can see that the share of total income for lowest quintile is decreasing (implying poor are becoming poorer) and share of total income of highest quintile is increasing (implying that rich are becoming richer), thus clearly, there was an increase in income inequalityfrom 1994 to 2012.

[Another way to check for the income inequality : you can use the Lorenz curve (using the cumulative share of total income and population. Since the whole population is divided into 5 quintiles, each quintile consists of 100/5 = 20%, or 0.20, population. The curve which lies farthest to the perfect equality line (45 degree line) gives most unequal outcome (likewise, the one lying nearest gives least unequal outcome). You'll see that 1994 curve lies nearest to the perfect inequality line while 2012 lies farthest]

2) Total income in Perkopia = $500,000,000 or $500 million (say $500m). Then, total income for each quintile is = income share (of that quintile)*500m. Since total population in Perkopia = 10,000 people. We already saw for each quintile, there is 20%of population. Thus, in each quintile, there are 0.2*10000 = 2000 people. If individual income lies below $27,400, that person lies below poverty line.

Then, using the given data, table for year 2000 can be formed as follows:

3) Poverty rate = total number of people lying below poverty line/ total population

Poverty rate = total population in first 2 quintiles/total population

Poverty rate = (2000 + 2000/10000 = 0.40 or 40%

4) Now there is a lumpsum transfer of $6,000 from government to people below poverty line. Thus, each individual in 1st quintile has now income = 9750 + 6000 = $15,750; and each individual in 2nd quintile has now income = 24750 + 6000 = $30,750. So, now 1st quintile people still lie below poverty line (as 15750 < 27400), while 2nd quintile people have now moved above the poverty line (as 30750 > 27400).

So, now only 2000 people lie below poverty line, poverty rate now = 2000/10000 = 0.2 or 20%

5) If Kevin works overtime, earning = 27102 + 1600 = $28,702, so he has moved above the poverty line and will not receive $6,000 grant from government. But if Kevin doesn't work overtime, he will earn $27,102 (which is less than $27,400), and will remain below poverty line, ending up receiving $6,000 from government every as well. So, now he can get total income of 27102 + 6000 = $33,102, which is greater than $28,702.

So, we can conclude that

True, that the $6,000 in aid creates a disincentive for Kevin to ern more than $27,400 per year.

True, Kevin would gain more income by turning down the overtime than he would if he accepted the overtime.

Quintile Income share Total income Individual income BPL? Lowest 3.9% = 0.039 0.039*500m = $19.5m 19.5m/2000 = $9,750 Yes Second 9.9% = 0.099 0.099*500m = $49.5m 49.5m/2000 = $24,750 Yes Middle 15.2% = 0.152 0.152*500m = $76m 76m/2000 = $38,000 No Fourth 22.9% = 0.229 0.229*500m = $114.5m 114.5m/2000 = $57,250 No Highest 48.1% = 0.481 0.481*500m = $240.5m 240.5m/2000 = $120,250 No

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