8. In 2004, the distribution of net worth within the United States was as given in the following table: 1 PERCENTAGE OF POPULATION 0.4 0.6 0.8 0.9 0.95 0.99 0.002 0.04 0.153 0.287 0.41 0.656 1 PERCENTAGE OF WEALTH (Source: Prof. E. N. Wolff, Levy Institute of Economics at Bard College, 2007.) a) According to the table, what percentage of net worth was held by the top 1% ? (Hint: What percentage did the other 99% hold?) b) Use regression to fit an exponential function g(x)= a b* to these data. c) Determine the area between the line of equality and the graph of g(x) over the interval [0,1]. (Hint: Integrate a b* using formula 11 from Table 1 in Section 4.7.) d) Determine the Gini coefficient and the Gini index. (Note: E. N. Wolff calculated the Gini coef- ficient as 0.829.) e) What percentage of the net worth was held by the lowest 50% of the population? f) What percentage of the net worth was held by the top 15% of the population?
8. In 2004, the distribution of net worth within the United States was as given in the following table: 1 PERCENTAGE OF POPULATION 0.4 0.6 0.8 0.9 0.95 0.99 0.002 0.04 0.153 0.287 0.41 0.656 1 PERCENTAGE OF WEALTH (Source: Prof. E. N. Wolff, Levy Institute of Economics at Bard College, 2007.) a) According to the table, what percentage of net worth was held by the top 1% ? (Hint: What percentage did the other 99% hold?) b) Use regression to fit an exponential function g(x)= a b* to these data. c) Determine the area between the line of equality and the graph of g(x) over the interval [0,1]. (Hint: Integrate a b* using formula 11 from Table 1 in Section 4.7.) d) Determine the Gini coefficient and the Gini index. (Note: E. N. Wolff calculated the Gini coef- ficient as 0.829.) e) What percentage of the net worth was held by the lowest 50% of the population? f) What percentage of the net worth was held by the top 15% of the population?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Only need d e and f
![In 2004, the distribution of net worth within the United States was as given in the following table:
| PERCENTAGE OF POPULATION | 0.4 | 0.6 | 0.8 | 0.9 | 0.95 | 0.99 | 1 |
|--------------------------|------|------|------|------|------|------|------|
| PERCENTAGE OF WEALTH | 0.002| 0.004| 0.0153 | 0.287 | 0.606 | 0.656 | 1 |
(Source: Prof. E. N. Wolff, Levy Institute of Economics at Bard College, 2007.)
a) According to the table, what percentage of net worth was held by the top 1%? (Hint: What percentage did the other 99% hold?)
b) Use regression to fit an exponential function \( g(x) = a \cdot b^x \) to these data.
c) Determine the area between the line of equality and the graph of \( g(x) \) over the interval \([0, 1]\). (Hint: Integrate \( a \cdot b^x \) using formula 11 from Table 1 in Section 4.7.)
d) Determine the Gini coefficient and the Gini index. (Note: E. N. Wolff calculated the Gini coefficient as 0.829.)
e) What percentage of the net worth was held by the lowest 50% of the population?
f) What percentage of the net worth was held by the top 15% of the population?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9090cee2-e90d-4a10-833f-9f95651c436f%2Fd4827d13-6217-4e10-a159-839d54a4a940%2Fo650nii_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In 2004, the distribution of net worth within the United States was as given in the following table:
| PERCENTAGE OF POPULATION | 0.4 | 0.6 | 0.8 | 0.9 | 0.95 | 0.99 | 1 |
|--------------------------|------|------|------|------|------|------|------|
| PERCENTAGE OF WEALTH | 0.002| 0.004| 0.0153 | 0.287 | 0.606 | 0.656 | 1 |
(Source: Prof. E. N. Wolff, Levy Institute of Economics at Bard College, 2007.)
a) According to the table, what percentage of net worth was held by the top 1%? (Hint: What percentage did the other 99% hold?)
b) Use regression to fit an exponential function \( g(x) = a \cdot b^x \) to these data.
c) Determine the area between the line of equality and the graph of \( g(x) \) over the interval \([0, 1]\). (Hint: Integrate \( a \cdot b^x \) using formula 11 from Table 1 in Section 4.7.)
d) Determine the Gini coefficient and the Gini index. (Note: E. N. Wolff calculated the Gini coefficient as 0.829.)
e) What percentage of the net worth was held by the lowest 50% of the population?
f) What percentage of the net worth was held by the top 15% of the population?
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