If a country had perfect income equality what would the Lorenz curve look like?

Perfect income equality means that every individual in the population has the same income. In this case, if we take any subset of the population, the share of income will be exactly proportional to the share of the population. For example, the poorest 20% of the population would have 20% of total income, the poorest 50% would have 50% of total income, and so on.

The Lorenz curve is a graphical representation of income distribution in a population. It is plotted using the cumulative percentage of total income (along the vertical axis) and the cumulative percentage of the population (along the horizontal axis). The curve helps understand the level of inequality by comparing it to a perfectly equal distribution, which is represented by a straight diagonal line called the Line of Equality.

Since in a country with perfect income equality, each subset of the population has an income share proportional to its size, the Lorenz curve will coincide with the Line of Equality. That is, it will be a straight diagonal line starting at the origin (0,0) and ending at the point (100%, 100%).

To visualize the Lorenz curve for perfect income equality, draw a two-dimensional graph with the horizontal axis representing the cumulative percentage of the population and the vertical axis representing the cumulative percentage of income. Plot a straight diagonal line starting at the origin (0,0) and extending to the point (100%, 100%). The resulting line will represent the Lorenz curve for perfect income equality. In conclusion, for a country with perfect income equality, the Lorenz curve will be a straight diagonal line from the origin to the point (100%, 100%), coinciding with the Line of Equality. The curve demonstrates that, in a perfectly equal distribution, the proportion of income held by any subset of the population is equal to its proportion within the overall population.