1. (42 points) In his influential work on the impact of taxes on labor supply, Jerry
Hausman assumed desired (or optimal) annual hours followed this formula:
.
Assume a two-bracket tax on annual earned income: the first $15,000 of
earnings are taxed at a 10% marginal rate, with earnings above $15,000 taxed at a
30% marginal rate. Unearned income is not taxed. Assume $1,000 of unearned
income and a gross wage of $20/hour.
a. (6 pts) Draw the annual budget constraint for an individual with these tax and
economic parameters. Carefully label all points and slopes.
b. (6 pts) Calculate and report the virtual income for each budget-set segment.
c. Calculate the utility-maximizing hours of labor supplied and indicate where on
the budget constraint you drew in part #a the person locates for each of the
following individuals:
i. (2 pts) An individual with and .
ii. (2 pts) An individual with and .
iii. (2 pts) An individual with and .
iv. (2 pts) An individual with and .
d. (6 pts) In an effort to cut taxes paid for lower-income individuals, the government
decides to increase the size of the bottom tax bracket from $15,000 to $25,000.
Draw the new annual budget constraint. Carefully label all points and slopes.
e. (8 pts) For each of the individuals in part #c, describe theoretically the impact of
the tax change in part #d on their labor supply.
f. (8 pts) For each of the individuals in part #c, calculate how increase in the bracket
in part #d changed their actual labor supply and indicate where on the budget
constraint you drew in part #d the person now locates.
2. (28 points) In 2017, President Trump and Congress cut the top federal marginal tax
rate from 40% to 25%. Recent estimates in the empirical literature in public
economics suggest an uncompensated elasticity of labor supply with respect to the net
wage of 1 and a compensated elasticity of 0.50 for married secondary earners.
Assume that the typical married secondary earner falling into the top federal tax
* H wy =aq b (1 ) – +
a = 50 b = -0.50
a = 50 b = -1
a =100 b = -0.10
a = 50 b = -0.10
2
bracket would earn $50 per hour and work 2,000 hours in the absence of the income
tax.
a. (4 pts) Briefly describe in words the substitution effect on labor supply for an
individual in the top bracket from the reduction in the marginal tax rate from 40%
to 25%.
b. (4 pts) Briefly describe in words the income effect on labor supply for an
individual in the top bracket from the reduction in the marginal tax rate from 40%
to 25%.
c. (4 pts) Calculate the deadweight loss for a typical married secondary earner
facing the top bracket rate under the pre-Trump tax law.
d. (6 pts) Based on the principles of deadweight weight loss, briefly explain how
you would expect the deadweight loss for a typical married secondary earner
facing the top bracket rate to change after vs. before the tax law was enacted.
e. (4 pts) In practice, calculate how much the deadweight loss changed for a typical
married secondary earner facing the top bracket rate under the post-Trump tax
law.
f. Based on the class lectures, what are the best estimates of the average deadweight
loss from the taxation of earned income in the United States for
i. (3 pts) Primary earners (traditionally, men)?
ii. (3 pts) Secondary earners (traditionally, women)?
