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Economists use Lorenz curves to illustrate the distribution of income in a country. Letting x represent the percent of families in a country and y the percent of total income, the model y = x would represent a country in which each family had the same income. The Lorenz curve, y = f(x), represents the actual income distribution. The area between these two models, for 0 ≤ x ≤ 100, indicates the "income inequality" of a country. In 2013, the Lorenz curve for a country could be modeled by y = (0.00067x² + 0.0160x + 1.723)2, 0 ≤ x ≤ 100 where x is measured from the poorest to the wealthiest families. (a) Find the income inequality (in dollars) for that country in 2013. (Round your answer to two decimal places.) $ (b) Use the Lorenz curve to complete the table, which lists the percent of total income earned by each quintile in the country in 2013. (Round your answers to three decimal places.) Quintile Lowest Percent 2nd 3rd 4th Highest

Economists use Lorenz curves to illustrate the distribution of income in a country. Letting x represent the percent of families in a country and y the percent of total income, the model y = x would represent a country in which each family had the same income. The Lorenz curve, y = f(x), represents the actual income distribution. The area between these two models, for 0 ≤ x ≤ 100, indicates the "income inequality" of a country. In 2013, the Lorenz curve for a country could be modeled by y = (0.00067x² + 0.0160x + 1.723)2, 0 ≤ x ≤ 100 where x is measured from the poorest to the wealthiest families. (a) Find the income inequality (in dollars) for that country in 2013. (Round your answer to two decimal places.) $ (b) Use the Lorenz curve to complete the table, which lists the percent of total income earned by each quintile in the country in 2013. (Round your answers to three decimal places.) Quintile Lowest Percent 2nd 3rd 4th Highest

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 43E
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Economists use Lorenz curves to illustrate the distribution of income in a country. Letting x represent the percent of families in a country and y the percent of total income, the model y = x would represent a country in which each family had the same income. The Lorenz curve, y = f(x), represents the actual income distribution. The area between these two models, for 0 ≤ x ≤ 100, indicates the "income inequality" of a country. In 2013, the Lorenz curve for a country could be modeled by y = (0.00067x² + 0.0160x + 1.723)2, 0 ≤ x ≤ 100 where x is measured from the poorest to the wealthiest families. (a) Find the income inequality (in dollars) for that country in 2013. (Round your answer to two decimal places.) $ (b) Use the Lorenz curve to complete the table, which lists the percent of total income earned by each quintile in the country in 2013. (Round your answers to three decimal places.) Quintile Lowest Percent 2nd 3rd 4th Highest
Transcribed Image Text:Economists use Lorenz curves to illustrate the distribution of income in a country. Letting x represent the percent of families in a country and y the percent of total income, the model y = x would represent a country in which each family had the same income. The Lorenz curve, y = f(x), represents the actual income distribution. The area between these two models, for 0 ≤ x ≤ 100, indicates the "income inequality" of a country. In 2013, the Lorenz curve for a country could be modeled by y = (0.00067x² + 0.0160x + 1.723)2, 0 ≤ x ≤ 100 where x is measured from the poorest to the wealthiest families. (a) Find the income inequality (in dollars) for that country in 2013. (Round your answer to two decimal places.) $ (b) Use the Lorenz curve to complete the table, which lists the percent of total income earned by each quintile in the country in 2013. (Round your answers to three decimal places.) Quintile Lowest Percent 2nd 3rd 4th Highest
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