1. Consider a society where 4 individuals earn $10 each and 6 individuals earn $5 dollars each. (a) Build a table with the size distribution of income (also known as cumulative distribution of income).(b) Reshape the distribution of income in quintiles(c) What share of the total income did the top 40% get?
Question
- Consider a society where 4 individuals earn 5 dollars each. (a) Build a table with the size distribution of income (also known as cumulative distribution of income).(b) Reshape the distribution of income in quintiles(c) What share of the total income did the top 40% get?
Solution
(a) To build a table with the size distribution of income, we first need to list all individuals and their respective incomes.
| Individual | Income |
|---|---|
| 1 | $10 |
| 2 | $10 |
| 3 | $10 |
| 4 | $10 |
| 5 | $5 |
| 6 | $5 |
| 7 | $5 |
| 8 | $5 |
| 9 | $5 |
| 10 | $5 |
(b) To reshape the distribution of income in quintiles, we need to divide the population into 5 equal parts. Since we have 10 individuals, each quintile will contain 2 individuals.
| Quintile | Individuals | Income |
|---|---|---|
| 1 | 1, 2 | $20 |
| 2 | 3, 4 | $20 |
| 3 | 5, 6 | $10 |
| 4 | 7, 8 | $10 |
| 5 | 9, 10 | $10 |
(c) The top 40% of the population corresponds to the top two quintiles (quintiles 4 and 5). The total income of these quintiles is 10 + 60 (10 and 5). Therefore, the share of the total income that the top 40% get is 60 = 33.33%.
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