Social Security is funded through a payroll tax that is

Social Security is funded through a payroll tax that is separate from the federal income tax. It works in a way similar to the following example: For the first $1,800 in weekly earnings, the government charges a 15% wage tax but then charges no payroll tax for all earnings above $1,800 per week.
A: Suppose that a worker has 60 hours of leisure time per week and can earn $50 per hour.
(a) Draw this worker’s budget constraint with weekly leisure hours on the horizontal axis and weekly consumption (in dollars) on the vertical.
(b) Using the definitions given in exercise 3.16, what is the marginal and average tax rate for this worker assuming he works 30 hours per week? What if he works 40 hours per week? What if he works 50 hours per week?
(c) A wage tax is called regressive if the average tax rate falls as earnings increase. On a graph with weekly before-tax income on the horizontal axis and tax rates on the vertical, illustrate the marginal and average tax rates as income increases. Is this tax regressive?
(d) True or False: Budget constraints illustrating the tradeoffs between leisure and consumption will have no kinks if a wage tax is proportional. However, if the tax system is designed with different tax brackets for different incomes, budget constraints will have kinks that point inward when a wage tax is regressive and kinks that point outward when a wage tax is progressive.
B: Consider the more general case of a tax that imposes a rate t on income immediately but then falls to zero for income larger than x.
(a) Derive the average tax rate function a(I , t ,x) (where I represents weekly income).
(b) Derive the marginal tax rate function m(I , t ,x).
(c) Does the average tax rate reach the marginal tax rate for high enough income?

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