# In the U.S., the social security system is funded by a payroll (wage) tax of 12.4% that

## Question:

In the U.S., the social security system is funded by a payroll (wage) tax of 12.4% that is split equally between employer and employee; i.e. the statutory incidence of the social security tax falls half on employers and half on employees.
A. In this exercise we consider how this split in statutory incidents impacts the labor market. Assume throughout that labor supply is upward sloping.
(a) Illustrate the labor supply and demand graph and indicate the market wage w∗ and employment level l∗ in the absence of any taxes.
(b)Which curve shifts as a result of the statutory mandate that employers have to pay the government 6.2% of their wage bill? Which curve shifts because of the statutory mandate that employees pay 6.2% of their wages in social security tax?
(c) Suppose the wage elasticity of labor demand and supply are equal in absolute value at the pre-tax equilibrium. Can you illustrate how the market wage at the post-tax equilibrium— when both parts of the social security tax are taken into account—might be unchanged from the initial equilibrium wage w∗?
(d) In your graph, illustrate what the imposition of the 2-part social security tax means for the take home wage ww for workers. What does it mean for the real cost of labor wf that firms incur?
(e) How would the equilibrium wage in the market change if the government imposed the entire 12.4% tax on workers (and let employers statutorily off the hook)? How would it change if the government instead imposed the entire tax on employers?
(f) What happens to the take-home wage for workers and the real labor cost of firms as a result of the two statutory tax reforms raised in part (e)?
(g) Does any of this analysis depend on whether there are wealth effects in the labor market?
B. Suppose, as in exercise 19.6, that labor demand and supply in the absence of taxes are given by ld = (A−w)/α and ls = (w −B)/β.
(a) Determine the equilibrium employment level l∗ and the equilibrium wage w∗ .
(b) Now suppose the government imposes a per-unit tax t on workers and a second per-unit tax t on employers. Derive the new labor demand and supply curves that incorporate these (as you would when you shift demand and supply curves in response to statutory tax laws).
(c) Determine the new equilibrium wage and employment level. Under what condition is the new observed equilibrium wage unchanged as a result of the two-part wage tax? Is there any way that employment will not fall?
(d) Determine the take-home wage ww for workers and the real labor cost wf for firms.
(e) Suppose you did not know the statutory incidence of the wage tax but simply knew the total tax was equal to 2t . How would you calculate the economic incidence—i.e. how would you calculate ww and wf ?