Suppose that individuals time endowment is T = 16 hours and has non-labor income V = 32. There is a new government program designed to provide transfers to individuals with low consumption. All individuals with a total income (i.e. non-labor and labor income) no more than $62 are given a transfer of $20. In class, we considered a worker with w = 8 and analyzed the response of his labor supply decision to this welfare program.

In this exercise, we will analyze four other cases. In each case, i) compute is the maximum hours worked with which the worker qualifies for the program, ii) find the optimal hours worked without the program, iii) find the optimal hours worked if the worker receives the transfer. Check if the solution from iii) is feasible given your answer to i). If the solution is not feasible, then there are two options either the worker chooses the maximum hours that make him eligible for the transfer (corner solution) or he chooses hours as if there was no welfare program. Which one he chooses depends on which option gives him higher utility. For all these answers you can use the formulas for h (w) , L (w) , C (w) provided above. If you evaluate it for the case with the transfer, then the non-labor income is V g = 32 + 20 = 52 where I used superscript g to indicate that this is non-labor income with the government program. In each case, comment on whether the program provided disincentives to work.

Question 2.1 What is the reservation wage with and without the government program?

Question 2.2 Suppose the wage is w = 4. (HINT: Think about the reservation wage when the worker is eligible for the transfer. There is a corner solution.)

Assume that worker's utility function is given by U(C,L) = 0.4 In C+0.6 In L. In class (Topic 02) we showed that with this utility function, the reservation wage is 0.6V w* = 0.4T ' and optimal choice of leisure, labor and consumption are * h* (w) = * = * L* (w) = 0 W W W T W W = W* * C* (w) = * = Assume that worker's utility function is given by U(C,L) = 0.4 In C+0.6 In L. In class (Topic 02) we showed that with this utility function, the reservation wage is 0.6V w* = 0.4T ' and optimal choice of leisure, labor and consumption are * h* (w) = * = * L* (w) = 0 W W W T W W = W* * C* (w) = * =