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In the previous assignment, you learned about the Gini index of a country (a number measuring the country's income inequality) is closely related to the area under the country's Lorenz curve over the interval [0, 1]. Let's recall that if the point (ố0; 100) is on the Lorentz curve, then this means that the bottom a% of households receive 6% of the country's total income. In reality, we do not have a formula for the Lorenz curve but a collection of data. The following is data of Canadian households' (disposable) income in 2020. (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid%3D3610058701) Let's focus on the following 6 data points on the Lorenz curve LCanada. b. 100 0.2 0.4 0.6 0.8 1 LCanada (x)0 0.068 0.201 0.378 0.607 1 So, for example, the point (0.2,0.068) is on the Lorenz curve LCanada: This means that the bottom 20% of Canadian households received 6.8% of Canada's total (household disposable) income in 2020.

In the previous assignment, you learned about the Gini index of a country (a number measuring the country's income inequality) is closely related to the area under the country's Lorenz curve over the interval [0, 1]. Let's recall that if the point (ố0; 100) is on the Lorentz curve, then this means that the bottom a% of households receive 6% of the country's total income. In reality, we do not have a formula for the Lorenz curve but a collection of data. The following is data of Canadian households' (disposable) income in 2020. (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid%3D3610058701) Let's focus on the following 6 data points on the Lorenz curve LCanada. b. 100 0.2 0.4 0.6 0.8 1 LCanada (x)0 0.068 0.201 0.378 0.607 1 So, for example, the point (0.2,0.068) is on the Lorenz curve LCanada: This means that the bottom 20% of Canadian households received 6.8% of Canada's total (household disposable) income in 2020.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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4. In the previous assignment, you learned about the Gini index of a country (a number measuring the country's income inequality) is closely related to the area under the country's Lorenz curve over the interval [0, 1]. Let's recall that if the point (100, 100) is on the Lorentz curve, then this means that the bottom a% of households receive b% of the country's total income. In reality, we do not have a formula for the Lorenz curve but a collection of data. The following is data of Canadian households' (disposable) income in 2020. (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid%=D3610058701) Let's focus on the following 6 data points on the Lorenz curve LCanada. 0.2 0.4 0.6 0.8 1 LCanada () | 0 0.068 0.201 0.378 0.607 1 So, for example, the point (0.2,0.068) is on the Lorenz curve LCanada: This means that the bottom 20% of Canadian households received 6.8% of Canada's total (household disposable) income in 2020. (a) LCanada over the interval [0, 1] by L5, the left endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (b) LCanada Over the interval (0, 1] by R5, the right endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (c) LCanada Over the interval [0, 1] by T5, the Trapezoidal Rule. Use the data points above to approximate the area under the Lorenz curve (d) determine if T5 is an underestimate or an overestimates. It is known that Lorenz curves are always concave upward. Using this fact,
Transcribed Image Text:4. In the previous assignment, you learned about the Gini index of a country (a number measuring the country's income inequality) is closely related to the area under the country's Lorenz curve over the interval [0, 1]. Let's recall that if the point (100, 100) is on the Lorentz curve, then this means that the bottom a% of households receive b% of the country's total income. In reality, we do not have a formula for the Lorenz curve but a collection of data. The following is data of Canadian households' (disposable) income in 2020. (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid%=D3610058701) Let's focus on the following 6 data points on the Lorenz curve LCanada. 0.2 0.4 0.6 0.8 1 LCanada () | 0 0.068 0.201 0.378 0.607 1 So, for example, the point (0.2,0.068) is on the Lorenz curve LCanada: This means that the bottom 20% of Canadian households received 6.8% of Canada's total (household disposable) income in 2020. (a) LCanada over the interval [0, 1] by L5, the left endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (b) LCanada Over the interval (0, 1] by R5, the right endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (c) LCanada Over the interval [0, 1] by T5, the Trapezoidal Rule. Use the data points above to approximate the area under the Lorenz curve (d) determine if T5 is an underestimate or an overestimates. It is known that Lorenz curves are always concave upward. Using this fact,
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