Atkinson's inequality index can be derived by assuming a consumer evaluates income distributions from behind a veil of ignorance without knowing their own income. The consumer maximizes expected usefulness by integrating a utility function over the income distribution density. Atkinson's inequality index is defined as the relative cost of inequality and is the ratio of the average income to the equivalent certain income that yields the same total utility. Atkinson assumes the consumer has a constant relative risk aversion utility function, from which an expression for Atkinson's inequality index can be derived.