Question

A group of 10 people have the following annual incomes: \(24,000, \)18,000, \(50,000, \)100,000, \(12,000,

\)36,000, \(80,000, \)10,000, \(24,000, \)16,000. Calculate the share of total income that each quintile receives from this

income distribution. Do the top and bottom quintiles in this distribution have a greater or larger share of total income than the top and bottom quintiles of the U.S. income distribution?

Short answer

Compared to the top and bottom quintiles of the U.S. income distribution, the bottom quintile in this distribution has a greater share of total income and the top quintile in this distribution has a smaller share of the total income.

Step-by-step solution

Step 1. Given information

A group of 10 people have the following annual incomes: $24,000, $18,000, $50,000, $100,000, $12,000,

$36,000, $80,000, $10,000, $24,000, $16,000.

Step 2. Calculation of quintiles

Incomes	Incomes in the ascending order	Five groups of income	Quintiles	Share of total income
$24,000	$10,000
$18,000	$12,000	$10,000+$12,000	$22,000	6%
$50,000	$16,000
$100,000	$18,000	$16,000+$18,000	$34,000	9.2%
$12,000	$24,000
$36,000	$24,000	$24,000+$24,000	$48,000	13%
$80,000	$36,000
$10,000	$50,000	$36,000+$50,000	$86,000	23.2%
$24,000	$80,000
$16,000	$100,000	$80,000+$100,000	$180,000	48.6%
TOTAL			$370,000

We can see from the above table that compared to the top and bottom quintiles of the U.S. income distribution, the bottom quintile in this distribution has a greater share of total income and the top quintile in this distribution has a smaller share of the total income, that is, income inequality is lower in this income distribution comparing to that of the US income distribution.