1. Optimal income taxation for purposes of determining vertical equity and accounting for behavioral responses has the following condition: the ratio of marginal utility of income for each person (i) in the system to the marginal tax revenue from each person (i) is equal across individuals.
a) Suppose the marginal utility of income is a constant value (100) for all incomes and all individuals. Using the above relationship between marginal utility and marginal revenue, does a constant marginal utility of income imply to a progressive or regressive income tax system?
[Hint: In thinking about solving this problem, use an example with two people with different incomes. For example, person (1) has $50,000 and person (2) has $100,000. Increase the income tax by 1 percentage point for each individual. Check the optimal condition. What are the implications?]