In the US, Everyone Has to Pay Social Security Taxes on Labor

Essay

In the U.S., everyone has to pay social security taxes on labor income until pre-tax income reaches a certain amount after which no additional taxes are due.Consider the case of workers A, B and C who have 60 hours of leisure per week and who earn an hourly wage of $40.Suppose the social security tax is 50% up to a pre-tax weekly income of $1,200 and then falls to zero for any income above $1,200 per week.Assume tastes are homothetic.
a.Worker A is observed to work 40 hours per week under this tax system.Is he working more or less than he would if the system were abolished?
b.Worker B is observed to work 30 hours a week under this tax system.Is he working more or less than he would if the system were abolished?
c.Worker C is observed to work 20 hours per week under this system.Is he working more or less than he would if the system were abolished?
d.Could any of the three workers above share exactly the same tastes?
e.For which of these workers is there no deadweight loss from the tax?