The Theil Index is a measure of economic inequality that takes into account the distribution of income across the entire population.

The formula for the Theil Index is $$T = \frac{1}{\mu}\sum_{i=1}^{n}(y_i - \mu)\ln\left(\frac{y_i}{\mu}\right)$$, where $$y_i$$ is the income of individual $$i$$, $$\mu$$ is the mean income, and $$n$$ is the total number of individuals.

The Theil Index ranges from 0 to 1. A value of 0 indicates perfect equality, while a value of 1 indicates perfect inequality.

The Theil Index is interpreted as follows: a higher Theil Index indicates higher inequality, while a lower Theil Index indicates lower inequality.

One of the limitations of the Theil Index is that it is sensitive to outliers. This means that a small number of very high or very low incomes can have a significant impact on the value of the Theil Index.

The Theil Index is used to measure inequality in different countries, regions, and income groups. It is also used to track changes in inequality over time.

South Africa has the highest Theil Index, indicating the highest level of inequality.

Denmark has the lowest Theil Index, indicating the lowest level of inequality.

The Theil Index has increased in the United States over the past 50 years, indicating that inequality has increased.

The Theil Index has increased in China over the past 50 years, indicating that inequality has increased.

There are a number of policies that can be implemented to reduce inequality, including progressive taxation, minimum wage laws, and social safety nets.

There are a number of challenges to reducing inequality, including political opposition, economic constraints, and social resistance.

It is not possible to eliminate inequality completely. There will always be some degree of inequality in any society.

The goal of reducing inequality is to create a more just and equitable society, improve economic efficiency, and promote social stability.

It is impossible to predict the future of inequality. There are a number of factors that could influence the future of inequality, including economic growth, technological change, and political developments.