Measuring inequality and fiscal choices
導入済み| English | 意味 |
|---|---|
| Gini coefficient/ˈdʒiːni ˌkəʊɪˈfɪʃənt/ | ジニ係数 |
| progressive tax/prəˈɡresɪv tæks/ | 累進税 |
A decision you can investigate
- Two economies produce the same output, but in one the richest tenth hold half of all income.
- Are they equally well off?
Build the explanation
- The Lorenz curve plots the cumulative share of income against the cumulative share of households, poorest first; the Gini coefficient 基尼系数 is the area between the curve and perfect equality divided by the whole triangle, Gini = A/(A+B), from 0 (perfect equality) to 1.
- A fiscal deficit is one year’s shortfall of revenue against spending, while the national debt is the accumulated stock of past deficits. A progressive tax 累进税 takes a rising share of higher incomes; a regressive tax, like most sales taxes, takes a falling share.
Work through the evidence
- Four people earn 5, 15, 30 and 50 (total 100). Cumulative income shares, poorest first, are 5%, 20%, 50%, 100%: the richest quarter holds 50% and the poorest half just 20%.
- If every income doubles to 10, 30, 60, 100, every share is unchanged, so the Gini is unchanged even though everyone is richer: level and distribution are separate questions.
Four people earn 5, 15, 30, 50 (total 100). What share does the richest quarter hold?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The richest single earner holds 50 of 100, so the top quarter holds 50% of income.
Test the limits
- Inequality can sharpen incentives and enterprise, but wide gaps cut the poor’s access to education and health and can weaken trust and demand; development may widen gaps before narrowing them.
- The Laffer curve is a hypothesis about shape, since revenue is zero at 0% and at 100%, not a measurement of where any real economy sits; high debt shifts costs to future taxpayers, an intergenerational question.
If every income doubles, the Gini coefficient falls.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Every share is unchanged when all incomes scale together; the Gini measures distribution, not level.
Growth always reduces measured inequality.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The doubling case shows growth can leave every share untouched; distribution needs its own argument.
Apply and explain your answer
- Incomes double from 5, 15, 30, 50 to 10, 30, 60, 100. What happens to the Gini coefficient?
- Nothing: every income doubled, so every share is unchanged; growth without redistribution leaves relative inequality intact.
A deficit is best described as…
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The stock is the national debt; the flow is the deficit.
Use the terms precisely
- Gini coefficient: The ratio A/(A+B) from the Lorenz diagram; 0 is perfect equality.
- progressive tax: A tax taking a rising share of income as income rises.
Match the terms to their meanings.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Use each term for its stated economic relationship.
Four people earn 5, 15, 30 and 50 (total 100). Cumulative income shares, poorest first, are 5%, 20%, 50%, 100%: the richest quarter holds 50% and the poorest half just 20%. If every income doubles to 10, 30, 60, 100, every share is unchanged, so the Gini is unchanged even though everyone is richer: level and distribution are separate questions.
Inequality can sharpen incentives and enterprise, but wide gaps cut the poor’s access to education and health and can weaken trust and demand; development may widen gaps before narrowing them. The Laffer curve is a hypothesis about shape, since revenue is zero at 0% and at 100%, not a measurement of where any real economy sits; high debt shifts costs to future taxpayers, an intergenerational question.
The Lorenz curve plots the cumulative share of income against the cumulative share of households, poorest first; the Gini coefficient is the area between the curve and perfect equality divided by the whole triangle, Gini = A/(A+B), from 0 (perfect equality) to 1.