Suppose that a family’s tax liability equalled its income multiplied by one half, minus €10,000. Under this system, some families would pay taxes to the government, and some families would receive money from the government through a ‘negative income tax’.

a. Consider families with pre-tax incomes of €0, €10,000, €20,000, €30,000 and €40,000. Make a table showing pre-tax income, taxes paid to the government or money received from the government, and after-tax income for each family.

b. What is the marginal tax rate in this system (i.e. out of every €1 of extra income, how much is paid in tax)? What is the maximum amount of income at which a family receives money from the government?

c. Now suppose that the tax schedule is changed, so that a family’s tax liability equals its income multiplied by one quarter, minus €10,000. What is the marginal tax rate in this new system? What is the maximum amount of income at which a family receives money from the government?

d. What is the main advantage of each of the tax schedules discussed here?