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2. In a given country, there are 5 people that earn $1 per year and 5 people that earn $ 3 per year.(a) Draw the Lorenz curve for this country.(b) On the diagram indicate (using the areas) how you would calculate the Gini coefficient

Question

  1. In a given country, there are 5 people that earn 1peryearand5peoplethatearn1 per year and 5 people that earn 3 per year.(a) Draw the Lorenz curve for this country.(b) On the diagram indicate (using the areas) how you would calculate the Gini coefficient
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Solution

(a) The Lorenz curve is a graphical representation of the distribution of income or distribution of wealth. It is often used to represent inequality. Here's how you would draw it for this country:

  1. First, you need to order the population from the poorest to the richest. In this case, we have 5 people earning 1and5peopleearning1 and 5 people earning 3.

  2. Next, on the x-axis of your graph, you represent the cumulative percentage of the population. This should range from 0% (the poorest) to 100% (the richest).

  3. On the y-axis, you represent the cumulative percentage of total income earned by the bottom x% of the population.

  4. Now, plot the points. The first point would be (0,0). The next point would be (50%, 25%) because the bottom 50% of the population (the 5 people earning $1) have 25% of the total income. The next point would be (100%, 100%) because all of the population has all of the income.

  5. Connect the points with a line. This is your Lorenz curve.

(b) The Gini coefficient is a measure of inequality represented by the area between the Lorenz curve and the line of perfect equality (a straight diagonal line from (0,0) to (100%, 100%)).

  1. To calculate the Gini coefficient, first calculate the area between the Lorenz curve and the x-axis. This is done by integrating the Lorenz curve function from 0 to 1.

  2. Next, calculate the area under the line of perfect equality. This is a simple triangle with an area of 0.5.

  3. The Gini coefficient is then 1 minus twice the area between the Lorenz curve and the x-axis.

  4. In this case, the Gini coefficient would be 1 - 2*(0.25) = 0.5. This indicates a moderate level of inequality.

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