Question

The following table represents the annual income for the five citizens of Sodor.

Thomas           $20,000                       James $12,000           Gordon            $50,000

Percy               $4,000                         Clara   $14,000

a) Draw a Lorenz curve for the above situation and Label it A.

b) President Yang has decided all citizens shall receive $5000 per year from the government. The tax for this transfer will come from the citizens who make more than $20,000 per year. Draw a new Lorenz curve after the tax and distribution and Label it B.

            c) What has been the effect of this policy on the Gini coefficient? Explain your answer.

Answer 1

a)To draw a Lorenz curve you have to find out what percentage of income every individual earn

Like Percy earns 4,000, the total income of odor is 100,000. His income share is 4%.

Now Percy is 20% of the population of the area. So on X-axis, we will have 20% and on Y-axis we will have 4%

Same for everyone in the area

Its Lorenz curve will look like this.

The red line is the line of equality.

The Blue line is Lorenz curve A.

b) Now that president has decided to give everyone $5,000 and the tax for this will come from everyone whole income is more than $20,000. Only one person has an income of more than $20,000 and that is Gordon.

Gordon will pay Tax of $25,000 and that will be distributed equally among 5 i.e $5,000 each. Or we could say that Gordon will pay $5,000 to everyone. As a result, Gordon's income becomes 50,000-25,000+5000 = 30,000

It's Lorenz curve looks like this

The yellow line is Lorenz curve B.

c). We can see that the Lorenz curve B sags less than Lorenz curve A. It means the income distribution is now more equal than it was before. Now Percy has 9% of income compared to 4% that it was before this policy. The Gini coefficient condenses the income inequality of a country by a single number between 0 and 1. The higher the number, the higher the inequality. Gini coefficient is derived by dividing the area between the line of equality and Lorenz curve with total area under Line of equality. So the more area Lorenz curve covers, the more the Gini coefficient and the more the income inequality.

As a result of this policy, the Gini coefficient has been deceased.

Lorenz curve Income Percentage of population 1.00 0.75 0.50 0.25 0.00 0.00 0.25 0.50 0.75 1.00

Lorenz curve Income Percentage of population New income 1.00 0.75 0.50 0.25 0.00 0.00 0.25 0.50 0.75 1.00