Inequality in economics is the measurement of the allocation of scarce resources among a population. Inequality is measured by comparing the resources of citizens both relatively and against the quantity of total resources available.
The Gini coefficient is one method of measuring inequality within a population. The advantage of the Gini is its simplicity in summarizing statistical data. Possible Gini scores range from 0 - 1. The higher the coefficient, the more inequality there is in a given set.
Gini coefficient, after taxes and transfers
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- The idea that a poor person gets more utility per dollar than a rich person does
- Since the utility of every dollar for a rich person is lower compared to the poor person, it is believed that is the person with more money gives the dollar to someone who is less well off, total social welfare will increase. 
John Rawls described his theory on inequality in his book A Theory of Justice He believes society must be arranged so that the least advantaged in society should be helped and that offices and positions should be open to everyone on the condition of fair and equal opportunity.
Rawls proposes a thought experiment whereby people are considered to be behind a "veil of ignorance," that doesn't allow them to see where they will end up in life or what types of characteristics they will have. We are to judge the equity of a nation by how well we would fare if we were the worst off person in the population. Putting ourselves behind the theoretical veil of ignorance forces us to look at the possibility of our future as the lowest person in society. The most equitable nation, according to this theory, is the nation where the worst off person fares the best in comparison to the worst of person in other nations.