Since the early 1970’s, the U.S. government has had a program called the Earned Income Tax Credit (previously mentioned in end-of-chapter exercises in Chapter 3.) A simplified version of this program works as follows: The government subsidizes your wages by paying you 50% in addition to what your employer paid you but the subsidy applies only to the first $300 (per week) you receive from your employer. If you earn more than $300 per week, the government gives you only the subsidy for the first $300 you earned but nothing for anything additional you earn. For instance, if you earn $500 per week, the government would give you 50% of the first $300 you earned—or $150.
A. Suppose you consider workers 1 and 2. Both can work up to 60 hours per week at a wage of $10 per hour, and after the policy is put in place you observe that worker 1works 39 hours per week while worker 2 works 24 hours per week. Assume throughout that Leisure is a normal good.
(a) Illustrate these workers’ budget constraints with and without the program.
(b) Can you tell whether the program has increased the amount that worker 1 works? Explain.
(c) Can you tell whether worker 2 works more or less after the program than he did before? Explain.
(d) Now suppose the government expands the program by raising the cut-off from $300 to $400. In other words, now the government applies the subsidy to earnings up to $400 per week. Can you tell whether worker 1 will now work more or less? What about worker 2?
B. Suppose that workers have tastes over consumption c and leisure ℓ that can be represented by the function u(c,ℓ) = cαℓ(1−α).
(a) Given you know which portion of the budget constraint worker 2 ends up on, can you write down the optimization problem that solves for his optimal choice? Solve the problem and determine what value α must take for worker 2 in order for him to have chosen to work 24 hours under the EITC program.
(b) Repeat the same for worker 1 — but be sure you specify the budget constraint correctly given that you know the worker is on a different portion of the EITC budget. (Hint: If you extend the relevant portion of the budget constraint to the leisure axis, you should find that it intersects at 75 leisure hours.)
(c) Having identified the relevant α parameters for workers 1 and 2, determine whether either of them works more or less than he would have in the absence of the program.
(d) Determine how each worker would respond to an increase in the EITC cut-off from $300 to $400.
(e) For what ranges of α would a worker choose the kink-point in the original EITC budget you drew (i.e. the one with a $300 cutoff)?