In a society with 240,000 households, 10,000 households earn $4 each, 4,000 households earn $2 each, 10,000 households earn $10 each, and the rest earn $1 each.What is the income share of the third quintile?

To answer this question, we first need to understand what a quintile is. A quintile is a statistical value of a data set that represents 20% of a given population, so the third quintile represents the 40th to 60th percentile of the population.

Step 1: Calculate the total income of the society.

• 10,000 households earn $4 each, so they earn a total of 10,000 *$4 = $40,000.
• 4,000 households earn $2 each, so they earn a total of 4,000 *$2 = $8,000.
• 10,000 households earn $10 each, so they earn a total of 10,000 *$10 = $100,000.
• The rest of the households (240,000 - 10,000 - 4,000 - 10,000 = 216,000 households) earn $1 each, so they earn a total of 216,000 *$1 = $216,000.
• The total income of the society is $40,000 +$8,000 + $100,000 +$216,000 = $364,000.

Step 2: Calculate the income of the third quintile.

• The third quintile represents the 40th to 60th percentile of the population, so it represents 20% of the population. 20% of 240,000 households is 48,000 households.
• Since the households are not equally distributed among the income levels, we cannot simply take 20% of the total income. We need to calculate the income of these 48,000 households.
• The lowest income level is $1, and there are 216,000 households in this level. So, all the households in the third quintile are in this level.
• The income of the third quintile is therefore 48,000 * $1 =$48,000.

Step 3: Calculate the income share of the third quintile.

• The income share of the third quintile is the income of the third quintile divided by the total income of the society.
• The income share of the third quintile is therefore $48,000 /$364,000 = 0.131868 or 13.19% when rounded to two decimal places.