Question

There's been a fair amount of talk about income inequality in the U.S. Or more to the point, talk about how inequality has been increasing. So has it? And to what extent? Let's take a look at income shares. We can take the income earned by every U.S. resident and add them all up. That's total or aggregate income. Then we can divide households up according to their incomes. Let's think that we put households on a "ladder" according to their incomes. We put the household with the lowest income on the bottom rung, the household with the next lowest income on the next rung, and so on, until we have every household on the ladder, with the household with the highest income on the top rung. Now let's put the 20% of the households at the bottom of the ladder into one group. The next 20% of households in a second group. The next 20% in a third group. The next 20% in a fourth group. The final 20% in a fifth group. So we have 5 groups with 20% of the households in the U.S. in cach. These groupings are called income quintiles. OK, let's see what the average incomes of the members of these quintiles were in 2016: Bottom 20% 2nd 20% 3rd 20% 4th 20% Top 20% $12,943 $34,504 $59,149 $95,178 $213,941 Note that in 2016 there were 126,224,000 households in the U.S. Because each of these 5 groups have the same number of households in them (20% of the total number), we can figure out aggregate income by 1) averaging these five incomes and 2) multiplying that average by 126.224 million. Do that and put that number in 1) on the answer sheet. Note if you multiply using 126.224, the number you get is in millions of dollars. Keep that in mind when you're figuring total inconc. We can figure out the income share of each group by taking the total income of each group and dividing that by aggregate income. The U.S. Census does that and publishes the result. Here are the income shares of each of these income quintiles, in 1980 and 2016. Bottom 20% 2nd 20% 3rd 20% 4th 20% Top 20% share, %, 2016 3.1 8.3 14.2 22.9 51.5 share, %, 1980 16.8 24.7 44.1 For example, in 2016, households in the bottom 20% of the income distribution received 3.1% of aggregate income. How much was that? Put that amount in 2) on the answer sheet. 10.2 In 3), put in the number of percentage points of income cach quintile gained or lost from 1980 to 2016. I'll get you started. The bottom 20% lost 1.1% of total income (so you put - 1.1 under bottom 20%). In other words, that much of total income was paid to those households in 1980 but in 2016, that income went to households in other quintiles

Answer 1

1) Aggregate income = Average of x 126.224 millia - 5 incomes of the quintiles -- = (12943+34504 +59149 +95178 +213941x4126-a1824 mila 5 = $83143) (126.224 million) _10494642-032 million dollars 2) Aggregate income of bottom 20% of the income distribution. Total number of households = 126224000 Each of the 5 groups have the same number of households hence we can get the number of households in one group by dividing total number of hodseholds by s. o Number of households = 126224ooo in bottom 20% - 5 = 25244800 73= 25.2448 million

Мm Бе» 9, hоughоtо — in bottom 20% тоогцо 5 - = 25244800 729=25.2448 million Aggregate income Two methods of calculating of bottom 20% " Number of households X in bottom 20% - average income of the members of bottern -20%. = 25.2448 million X $ 12943 = 326 743.4464 million dollars w) Share of bottom 20%. Aggregate income. in aggreate income . ) 3.1% of 10494642-032 million dollars 100 - 31 x 10494642.032 million dollars = 325333.902992 million dollars Hence answer for (2) can be 32 5333.902992 3) gain(t)/ bottom 20% and quin 3rd quin 4th quin top 20%. dossi) -11 -1.91 -26 -1.80 +7.4 I gain(t)/ loss (-) given by this formula :- (Her(-) = % Share in 2016 - r. share in 1980

4) 1:17, 9 agaregate income in 2016 from (1) we got the = 10494642 032 million aggregate income as dollars f 1% of 10494642 .032 b e tal x10494642-032 Ls 115441.062352 million dollare. 5) 20% of best U.S households in - 25244800 o 2016 [Already calculated in question (2)]

6 het income of all households belonging to the bottom 20%. bracket in 1980 be 6x J we know from (3) that bottom 20% lost 1:16 number of percentage points of income from 1980 to 2016.1 from (2) we have aggregate income of button 201 as 32 5333.9029 million dollars

x can be found by :- X H több = 325333-9029 million dollars X = 325333.9029 X 100 - 98.9 X = 3289 52.3790 million dollars hoss = x - 325333.9029 = 3618.4761 million dollars Income clost by a household in the bottom | 20% of the income distribution on average can be given by dividing the loss by the number of households in the bracket 2 36 18·4761 25:2448 =143: 3355 dollars Ape