The land of Nod has the income distribution curve y = 0.2x³+0.6x²+0.2x, where y(x) is the percentage of the national income earned by the lowest-earning x-100% of the population. The coefficient of income-inequality in Nod is ... O...y = 0.25 O...y = 0.45 O...y=0.35 O...y = 0.3
The land of Nod has the income distribution curve y = 0.2x³+0.6x²+0.2x, where y(x) is the percentage of the national income earned by the lowest-earning x-100% of the population. The coefficient of income-inequality in Nod is ... O...y = 0.25 O...y = 0.45 O...y=0.35 O...y = 0.3
MATLAB: An Introduction with Applications
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![### Income Distribution and Inequality in Nod
**Problem Statement**
The land of Nod has the income distribution curve given by the equation:
\[ y = 0.2x^3 + 0.6x^2 + 0.2x, \]
where \( y(x) \) represents the percentage of the national income earned by the lowest-earning \( x \times 100 \% \) of the population.
The task is to determine the coefficient of income-inequality (γ) in Nod, based on the given income distribution curve.
**Options:**
- \[
\cdot \quad \gamma = 0.25
\]
- \[
\cdot \quad \gamma = 0.45
\]
- \[
\cdot \quad \gamma = 0.35
\]
- \[
\cdot \quad \gamma = 0.3
\]
### Explanation of Income Distribution Curve
An income distribution curve such as this helps illustrate how income is shared among different proportions of the population. In this context:
- When \( x = 1 \) (i.e., the whole population is considered), the equation will give the total percentage of the national income.
- The curve \( y(x) \) provides a way to analyze the distribution by showing the share of income earned by the lowest-earning fraction of the population.
The coefficient of income-inequality, commonly known as the Gini coefficient (γ), quantifies the inequality across the distribution. It ranges from 0 to 1, where:
- 0 indicates perfect equality (everyone earns the same).
- 1 indicates maximal inequality (all income is earned by a single individual).
The solution involves determining which of the provided options accurately represents this inequality coefficient based on the given distribution curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb215e6b-9552-449e-af55-e4170ca85711%2F59bd23af-9a1f-4cfb-a4d0-04bed23109a4%2Feajtjen_processed.png&w=3840&q=75)
Transcribed Image Text:### Income Distribution and Inequality in Nod
**Problem Statement**
The land of Nod has the income distribution curve given by the equation:
\[ y = 0.2x^3 + 0.6x^2 + 0.2x, \]
where \( y(x) \) represents the percentage of the national income earned by the lowest-earning \( x \times 100 \% \) of the population.
The task is to determine the coefficient of income-inequality (γ) in Nod, based on the given income distribution curve.
**Options:**
- \[
\cdot \quad \gamma = 0.25
\]
- \[
\cdot \quad \gamma = 0.45
\]
- \[
\cdot \quad \gamma = 0.35
\]
- \[
\cdot \quad \gamma = 0.3
\]
### Explanation of Income Distribution Curve
An income distribution curve such as this helps illustrate how income is shared among different proportions of the population. In this context:
- When \( x = 1 \) (i.e., the whole population is considered), the equation will give the total percentage of the national income.
- The curve \( y(x) \) provides a way to analyze the distribution by showing the share of income earned by the lowest-earning fraction of the population.
The coefficient of income-inequality, commonly known as the Gini coefficient (γ), quantifies the inequality across the distribution. It ranges from 0 to 1, where:
- 0 indicates perfect equality (everyone earns the same).
- 1 indicates maximal inequality (all income is earned by a single individual).
The solution involves determining which of the provided options accurately represents this inequality coefficient based on the given distribution curve.
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