Imagine an economy with only two people. Larry earns $20,000 per year, while Roger earns $80,000 per year. As shown in the following figure, the Lorenz curve for this two-person economy consists of two line segments. The first runs from the origin to point a, while the second runs from point a to point b. Percentage of income (cumulative) 100 80 60 40 20 a Lorenz curve for Larry and Roger 10 20 30 40 50 60 70 80 90 100 Percentage of population (cumulative) Instructions: Enter your answers rounded to 1 decimal place. a. Calculate the Gini ratio for this two-person economy using the geometric formulas for the area of a triangle (= ½ x base x height) and the area of a rectangle (= base x height). (Hint. The area under the line segment from point a to point b can be thought of as the sum of the area of a particular triangle and the area of a particular rectangle.) b. What would the Gini ratio be if the government taxed $20,000 away from Roger and gave it to Larry? (Hint. The figure will change.) c. Start again with Larry earning $20,000 per year and Roger earning $80,000 per year. What would the Gini ratio be if both their incomes doubled? How much has the Gini ratio changed from before the doubling in incomes to after the doubling in incomes? (Click to select) wwwwwwww
Imagine an economy with only two people. Larry earns $20,000 per year, while Roger earns $80,000 per year. As shown in the following figure, the Lorenz curve for this two-person economy consists of two line segments. The first runs from the origin to point a, while the second runs from point a to point b. Percentage of income (cumulative) 100 80 60 40 20 a Lorenz curve for Larry and Roger 10 20 30 40 50 60 70 80 90 100 Percentage of population (cumulative) Instructions: Enter your answers rounded to 1 decimal place. a. Calculate the Gini ratio for this two-person economy using the geometric formulas for the area of a triangle (= ½ x base x height) and the area of a rectangle (= base x height). (Hint. The area under the line segment from point a to point b can be thought of as the sum of the area of a particular triangle and the area of a particular rectangle.) b. What would the Gini ratio be if the government taxed $20,000 away from Roger and gave it to Larry? (Hint. The figure will change.) c. Start again with Larry earning $20,000 per year and Roger earning $80,000 per year. What would the Gini ratio be if both their incomes doubled? How much has the Gini ratio changed from before the doubling in incomes to after the doubling in incomes? (Click to select) wwwwwwww
Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter20: Income Inequality And Poverty
Section: Chapter Questions
Problem 5PA
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I need help with the first three sections please.
Transcribed Image Text:Imagine an economy with only two people. Larry earns $20,000 per year, while Roger earns $80,000 per year. As shown in the
following figure, the Lorenz curve for this two-person economy consists of two line segments. The first runs from the origin to point a,
while the second runs from point a to point b.
Percentage of income (cumulative)
100
80
60
40
20
0
b
Lorenz curve for
Larry and Roger
S
1
10 20 30 40 50 60 70 80 90 100
Percentage of population (cumulative)
Instructions: Enter your answers rounded to 1 decimal place.
a. Calculate the Gini ratio for this two-person economy using the geometric formulas for the area of a triangle (= ½ x base x height) and
the area of a rectangle (= base height). (Hint. The area under the line segment from point a to point b can be thought of as the sum of
the area of a particular triangle and the area of a particular rectangle.)
b. What would the Gini ratio be if the government taxed $20,000 away from Roger and gave it to Larry? (Hint: The figure will change.)
c. Start again with Larry earning $20,000 per year and Roger earning $80,000 per year. What would the Gini ratio be if both their
incomes doubled?
(Click to select)
How much has the Gini ratio changed from before the doubling in incomes to after the doubling in incomes?
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