j$.$

II$.$ Problem $2-$ Measuring Inequality

See the Excel file titled "Homework $5-$ DATA" posted on Canvas.

III. Problem $2-$ Measuring Inequality

a$.$ Pick a country from those given in the Excel file titled "Practice Homework $4$ DATA". You will need to pick a country for which there is income decile data, obviously. Copy and paste the row of decile shares into a new worksheet. Add a zero to the left$-$hand end of the row and label the row "decile shares"; above this row add a row with the numbers $0$ to $100$ in steps of $10$ and label this row "deciles".

b$.$ Add a row to the bottom of your table with the cumulative share of income in each decile. You will need to think of a formula which adds the numbers as you move along the table. Label this row "Cumulative Share". This row will form the curved line in the Lorenz curve diagram.

c$.$ Add another row to the bottom of the table with the cumulative share of income associated with perfect equality. Label the row "Perfect Equality"$-$this will form the straight line in the Lorenz curve.

d$.$ Plot the Lorenz curve for your chosen country using a line chart.

e$.$ Calculate the Gini coefficient for your chosen country. You should add two additional rows to your table to calculate the area under the "Perfect Equality" line $(A+B)$ and the area under the "cumulative share" line $($B$).$ You will need to do a bit of simple geometry to work out the area under each curve$-$recall that the area of a trapezoid $=$ base height ${?}_1+$ height $\frac{\text{:}{?}_2}{2}.$ Using the totals of these two rows, calculate the Gini coefficient using its definition.

f$.$ Interpret your Lorenz curve and Gini coefficient. Is this a high level of inequality? How does it compare to$,$ say, the United States? What might explain any similarity or difference?