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%. On a single graph, draw the worker's original budget line and her budget line under the negative income tax. page 75Show that the worker will choose to work fewer hours if the negative income tax is adopted. Will the worker's utility be greater under the negative income tax?

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Suppose a single parent can work up to 16 hours per day at a wage rate of$10 per hour. Various income maintenance programs have been developed to assurea minimum level of income for low-income families. Aid to Families withDependent Children (AFDC) was established with the Social SecurityAct of 1935. The family was given an income subsidy depending on family size. Under this program, the family’s benefi t was reduced by $1 forevery dollar earned. Suppose the maximum daily subsidy for the singleparent described in this problem is $40.a. Draw the daily budget constraint without program participation forthe single parent described in this problem.b. On the same graph, draw the daily budget constraint under AFDC forthe single parent described in this problem.c. What effect does this program have on the incentive to work? Explain.

One proposal for reforming the welfare system is to create a negative income tax. Under the negative income tax, each person is entitled to a grant of G dollars permonth. For every dollar the person earns, the grant is reduced by t dollars. a. Suppose G = 200 and t = 0.40. Consider an individual whose hourly wage = $10. There are 30 days in a month, so the total allotment of T = 720. Sketch the budgetconstraint before and after the introduction of the negative income tax. b. Would people work more or less with the implementation of this system? c. What if t = 100%? Explain!