Question

use the lorenz curve diagram to answer the questions.
a. did the distribution of income become more equal in 2020 than it was in 2019, or less equal?
it became less equal in 2020.
b. if area ( a = 2,150 ), area ( b = 250 ), and area ( c = 2,600 ), calculate the gini coefficient for 2019 and the gini coefficient for 2020.
the gini coefficient for 2019 is ( square ). (enter your response rounded to two decimal places.)

Explanation:

Step1: Recall the formula for Gini coefficient

The formula for the Gini coefficient \( G=\frac{A}{A + B}\) (where \(A\) is the area between the line of perfect equality and the Lorenz curve, and \(A + B\) is half of the area of the square in the Lorenz curve diagram, \(A + B=\frac{100\times100}{2}=5000\) in a standard Lorenz - curve - based Gini calculation. But if we are given areas \(A\) and \(B\) directly (assuming the standard Lorenz - curve - square setup where the total area \(A + B+C\) is \(5000\) (since \(2150 + 250+2600=5000\))), the formula \(G=\frac{A}{A + B}\) holds.

Step2: Calculate the Gini coefficient for 2019

We know that for 2019, \(A = 2150\) and \(B = 250\). Substitute these values into the formula \(G=\frac{A}{A + B}\).

$$G=\frac{2150}{2150 + 250}=\frac{2150}{2400}$$

$$G=\frac{2150\div10}{2400\div10}=\frac{215}{240}\approx0.8958\approx0.90$$

Answer:

\(0.90\)