Suppose that all workers, male and female, have identical labor supply functions, which happen to be linear:
L = 100w(1-t)-700 for w(1-t) \geq 7
L = 0 for w(1-t)< 7
in which L is the number of hours a worker chooses to work (we assume that the worker is able to choose his or her own hours of work), w is the worker’s before-tax wage, and t is the (linear) tax rate.
Question:
a) Suppose that there are 100 workers in the country (50 women and 50 men), they are each paid $10 an hour, and the tax rate is 25%. What tax revenue is collected? What is the deadweight loss associated with the 25% tax on labor incomes?
b) As part of an initiative to encourage “family values,” the government decides to lower the tax rate on men to 20% while raising the tax rate on women to 30%. Please calculate the revenue raised by this new gender-differentiated system of taxing labor income. What deadweight loss is associated with the new tax system?