Consider a person who can work up to 80 hours each week at a pre-tax wage of $20 per hour but faces a constant 20% payroll tax. Under these conditions, the worker maximizes her utility by choosing to work 50 hours each week. The government proposes a negative income tax whereby everyone is given $300 each week and anyone can supplement her income further by working. To pay for the negative income tax, the payroll tax rate will be increased to 50%.
(a) On a single graph, draw the worker's original budget line and her budget line under the negative income tax.
(b) Show that the worker will choose to work fewer hours if the negative income tax is adopted.
(c) Will the worker's utility be greater under the negative income tax?