Question $1.(20$ points$)$

The Gini coefficient $($index$)$ is a measurement of income inequality. Its value ranges between $0$ and $1,$ where $0$ indicating perfect equality and $1$ as perfect inequality. To calculate the Gini coefficient, we need the Lorenz Curve which graphically shows the distribution of income. It is usually represented as the portion of income $($Y$-$axis$)$ to the percentage of population $($X$-$axis$).$ Here we name the Lorenz Curve as the C$-$Line, and the Gini coefficient as $($Gamma$).$ With the information given, try to finish the following questions.

$(1)$ To calculate Gamma, we also need a $45-$degree diagonal line within the diagram of income distribution. Suppose we label this diagonal line as D$-$Line. What the D$-$Line represent for?