Question 5.29 Choose the correct answerConsider a 2-person economy, where the owner of a firm pays 40% of the total output to the worker. What is the Gini coefficient in this economy?

Question

BlackTom AI · Accepted Answer

For a two-person economy the Gini coefficient can be obtained directly from the two incomes: it measures the relative difference between the two incomes as a fraction of total income. With incomes y1 and y2, a convenient closed-form expression is G = |y1 − y2| / (y1 + y2).

Step-by-step reasoning and calculations:
1. Relevant concepts:
   - The Gini coefficient is a summary measure of inequality between 0 (perfect equality) and 1 (maximum inequality for a large population). For simple two-person cases it reduces to a ratio of the income gap to total income.
2. Identify the two incomes:
   - The worker receives 40% of total output: y1 = 0.40 (we can call this the poorer income).
   - The owner receives the remaining 60%: y2 = 0.60.
3. Compute the absolute difference:
   - |y2 − y1| = |0.60 − 0.40| = 0.20.
4. Compute total income (sum):
   - y1 + y2 = 0.40 + 0.60 = 1.00.
5. Plug into the two-person formula:
   - G = |y1 − y2| / (y1 + y2) = 0.20 / 1.00 = 0.20.
6. Express as a fraction:
   - 0.20 = 1/5.

Why this answer is correct:
- With only two individuals, the whole distribution is determined by the single gap between their incomes; expressing that gap as a share of total income gives the Gini for this simple case. The computed value 0.20 (1/5) precisely measures that relative gap.

Why the other choices are incorrect:
- a. 3/5 (0.60): far too large given the small 0.20 gap between shares.
- b. 2/5 (0.40): twice the correct gap share.
- d. 4/5 (0.80): much larger and incompatible with the given 40/60 split.

Conclusion: The Gini coefficient for this two-person economy is 0.20, i.e., 1/5, matching the provided answer.

Question 5.29 Choose the correct answerConsider a 2-person economy, where the owner of a firm pays 40% of the total output to the worker. What is the Gini coefficient in this economy?Single choice

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