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Homework answers / question archive / 1) Income inequality and the poverty rate The following table summarizes the income distribution for the town of Perkopia, which has a population of 10,000 people
1) Income inequality and the poverty rate
The following table summarizes the income distribution for the town of Perkopia, which has a population of 10,000 people. Every individual within an income group earns the same income, and the total annual income in the economy is $500,000,000. Suppose that in 2004, the poverty line is set at an annual income of $26,800 for an individual.
Note: This question uses quintiles, which are a statistical value of a data set that includes 20% of the population. This means that the population has been divided into fifths, where the first quintile is the lowest 20% of the values of the variable of interest, and so on to the fifth quintile, which is the highest 20% of the values.
Share of Total Income in Perkopia
Year Lowest Quintile Second Quintile (Percent) Middle Quintile Fourth Quintile Highest Quintile 1998 4.0 10.0 16.5 23.0 46.5 2004 3.8 9.6 15.2 22.9 48.5 2010 3.4 9.0 14.9 22.4 50.3 2016 3.2 8.0 14.0 21.6 53.2
The data in the table suggest that there was ? income inequality from 1998 to 2016.
Complete the following table to help you determine the poverty rate in Perkopia in 2004. 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 26800.
Share of Income in 2004 Total Income Individual Income Quintile (Percent) (Dollars) (Dollars) Below Poverty Line? Lowest 3.8 19,000,000 9,500 1 v.
Second
9.6
48,000,000
24,000
Middle
15.2 76,000,000
38,000
Fourth 22.9 I I 57,250
Highest
48.5 242,500,000
Using the information in the previous table, the poverty rate in Perkopia in 2004 is .
Suppose that the government introduces a welfare program in which any individual with an income of less than $26,800 per year receives a lump-sum transfer payment of $3,000 from the government. Assume that, in the short run, there is no change in labour supply behaviour among the people in Perkopia.
In the year 2004, the poverty rate after the introduction of the welfare program in Perkopia is v .
Again, suppose the government introduces a welfare program in which any individual with an income of less than $26,800 receives a lump-sum transfer payment of $3,000 from the government. Poornima, a resident of Perkopia who currently earns an income of $26,000, has the opportunity to work overtime and earn an additional $1,500 this year.
Which of the following statements are correct? Check all that apply. O Poornima would gain more income by turning down the overtime than she would if she accepted the overtime. O Poornima may accept the overtime if she feels that taking it will increase the chances of her receiving a significant promotion. O The $3,000 in aid presents a disincentive for Poornima to make more than
$26,800 per year.
The data in the table suggest that there was( An increase )income inequality from 1998 to 2016.
Population of Each Quantile = 1/5*10000 = 2000
Quintile | Share | Total Income (Share*500000000/100) | Individual Income (Total Income / 2000) | Below Poverty level (Individual Income is lower than or equal to $26,800) |
Lowest | 3.8 | 19000000 | 9500 | Yes |
Second | 9.6 | 48000000 | 24000 | Yes |
Middle | 15.2 | 76000000 | 38000 | No |
Fourth | 22.9 | 114500000 | 57250 | No |
Highest | 48.5 | 242500000 | 121250 | No |
From the table It is observed that 2 out of 5 quantiles falls below poverty line. So, the poverty rate in Perkopia in 2004 is as follows:
Poverty Rate = 2/5 = 40%
After introducing the welfare program,
Individual Income of Lowest Quantile = $9,500+$3,000 = $12,500
Lowest Income of Second Quantile = $24,750+$3,000 = $27,750
After the lump sum payment of 3000, the second quintile will come out of the poverty so, poverty rate after the welfare payment: Poverty Rate = 1/5*100 = 20%
The annual income of a random individual in 2004 is 26,000. When the individual receives the welfare program amount, the income he obtains for the year 2004 is
Individual Income = $26,000+$3000 = $29,000
When the individual works for overtime an additional amount of $1100 is earned then their annual income is
Individual Income = $26,000+$1,500 = $27,500
In both cases the individual reaches above the poverty line with annual income more than 26,800.
So, All the given options are correct.