Answer Happy

Suppose that individual’s 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* 0.6V 0.4T W> W W T W < w* 0.6V 0.6T + W W V W < w* 0.4V +0.4wT W> W = W* * C* (w) = * =