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Assume that worker's utility function is given by UH}, L] = name + asmL. In class {Topic 22] we showed that with this utity function, the reservation wage is , esv ill _ ear' and optimal choice of leisure, labor and consumption are if [is] = is g or\" = 114T g as } w\" L' (is) = T to -:_: w" = {LET + g ts } w\" {3" [is] = V w 5 w' = .4V+.4wT res-11f\" Euppese that individual's time endowment is T = IE hours and has nen-laher income V = 32. There is a new government program designed to provide transfers to individuals with low consumption. All individuals with a total income (Le. non-labor and labor income} no more than $62 are given a transfer of $2ll. In class, we considered a worker with as = B and analysed 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 max- imum hours worked with which the worker qualies for the program, ii} nd the optimal hours worked without the program, iii} nd 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 solu- tion is not feasible, then there are two options either the worker chooses the maximum hours that make him eligihle 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},U" {as} provided above. If you evaluate it for the case with the transfer, then the non-labor income is V9 = 32 + 2D = 52 where I used superscript p to indicate that this is nen-laher 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.) Question 2.3 Suppose the wage is w = 6. Question 2.4 Suppose the wage is w = 15. (HINT: There is a corner solution.) Question 2.5 Suppose the wage is w = 25