Optimal mixed taxation, credit constraints, and the timing of income tax reporting

We study optimal income and commodity tax policy with credit-constrained low-income households. Workers receive an even flow of income during the tax year, but report their incomes and make tax payments (receive transfers) at the end of the year. They spend their disposable income on multiple commodities over the year. We show that differentiated subsidies on commodities can be optimal even if the Atkinson-Stiglitz Theorem conditions apply. When the optimal policy leaves low-income households with binding credit constraints, it may be optimal to subsidize differentially the good that they consume in higher proportion. Uniform subsidies would also relax the credit constraint, but would be more costly to the government since they would equally benefit unconstrained households. Numerical examples suggest that commodity tax differentiation increases with basic needs and with the interest rate at which government borrows.