Imagine an economy with only two people. Larry earns $30,000 per year, while Rog
ID: 1209791 • Letter: I
Question
Imagine an economy with only two people. Larry earns $30,000 per year, while Roger earns $270,000 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. a. Calculate the Gini ratio for this two-person economy using the geometric formulas for the area of a triangle (= ½ × base × 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.) Instructions: Round your answer to one decimal place. Gini ratio = b. What would the Gini ratio be if the government taxed $30,000 away from Roger and gave it to Larry? (Hint: The figure will change.) Instructions: Round your answer to one decimal place. Gini ratio = c. Start again with Larry earning $30,000 per year and Roger earning $270,000 per year. What would the Gini ratio be if both their incomes doubled? Instructions: Round your answer to one decimal place. Gini ratio = How much has the Gini ratio changed from before the doubling in incomes to after the doubling in incomes? The ratio has
Explanation / Answer
The gini coefficient is the measure of inequality in income distribution which ranges from 0 to1 where 0 implies perfect equality and 1 implies perfect inequality.
Here we have 3 different cases where gini ratios are changing as income changes.
a) When Larry earns $30,000 per year and Roger earns $270,000 per year, the gini ratio is .7
b) now when $30,000 is taxed away from roger and gave it to Larry their income became $60,000 and 240,000 respectively.
thus gini ratio became .65 and rounded off to .6.
Here we can say the income inequality is a bit better than the original case as some amount is taken from Roger and given to Larry.
c) again when both their income doubled ie Larry earning $60,000 and roger earning $540,000 per year
the new gini ratio is .7 only.
Thus we can say even when their income is changed the income inequality remains the same.