Try the fastest way to create flashcards
Question

# 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 twoperson 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.

Solutions

Verified
Step 1
1 of 2

$\textbf{a.}$ We know that the Gini ratio is:

\begin{align*}\text{Gini ratio} = \dfrac{\text{Area between Lorenz curve and diagonal}}{\text{Total area below the diagonal}}\end{align*}

The total area below the diagonal is:

\begin{align*}\dfrac{1}{2} \cdot (100) \cdot (100) = 5,000\end{align*}

The area below the Lorenz curve is:

\begin{align*}(\dfrac{1}{2} \cdot (50) \cdot (20)) + (\dfrac{1}{2} \cdot (50) \cdot (80)) + (50\cdot20) = 3,500\end{align*}

Thus, the Gini ratio is:

\begin{align*}\dfrac{5,000 - 3,500}{5,000} = \textbf{0.3}\end{align*}

$\textbf{b.}$ The area below the Lorenz curve when $\20,000$ taxed away from the Roger and given to the Larry:

\begin{align*}(\dfrac{1}{2} \cdot (50) \cdot (40)) + (\dfrac{1}{2} \cdot (50) \cdot (60)) + (50\cdot40) = 4,500\end{align*}

Thus, the Gini ratio is:

\begin{align*}\dfrac{5,000 - 4,500}{5,000} = \textbf{0.1}\end{align*}

$\textbf{c.}$ When the income doubled, the Larry income becomes $\40,000$ and Rodger income becomes $\160,000$:

\begin{align*}(\dfrac{1}{2} \cdot (50) \cdot (20)) + (\dfrac{1}{2} \cdot (50) \cdot (80)) + (50\cdot20) = 3,500\end{align*}

Thus, the Gini ratio is:

\begin{align*}\dfrac{5,000 - 3,500}{5,000} = \textbf{0.3}\end{align*}

The Gini ratio stays the same even though the income is doubling.

## Recommended textbook solutions

#### Microeconomics

20th EditionISBN: 9780077660819Campbell R. McConnell, Sean M. Flynn, Stanley L. Brue
623 solutions

#### Economics: Principles, Problems, and Policies

20th EditionISBN: 9780078021756Campbell R. McConnell, Sean M. Flynn, Stanley L. Brue
967 solutions

#### Krugman's Economics for the AP Course

3rd EditionISBN: 9781319370169David Anderson, Margaret Ray
2,138 solutions

#### Krugman's Economics for AP

2nd EditionISBN: 9781464122187David Anderson, Margaret Ray
1,672 solutions