Revisiting the optimal linear income tax with categorical transfers

- Linear/piecewise-linear income tax finances categorical transfers to unable group.
- Inequality in average marginal value of income across unable and able groups.
- This inequality may persist at optimum: depends on unable group size/rev requirement.
- Optimal tax expressions can be written more generally to allow for this.
- Numerical results provide examples where this arises under both types of tax system.

When individuals differ in both productivity and some categorical attribute, optimal linear/piecewise-linear tax expressions are written to capture cases where it is suboptimal to eliminate inequality in the average social marginal value of income between categorical groups. Simulations provide examples.