Please help me with (i)(j)(k)(l) based on the previous settings posted below
3. Dwight is an employee in Dunder Mifflin. Beside working as a salesman, he enjoys spending time in his beets farm as leisure. He has a utility function of the following : (70%) U(L. X) = min(51, 3X}, where L is the time spent in beets farm and X'is his consumption. If he works, he receives a real wage w. His endowment of time is T. And the price of goods, p, is also normalized to 1. (a) Consider the case where 7= 100, w = 0.5, please write down and draw the budget constraint, denote it with BC. with _ on the x-axis and X on the y-axis, and show the slope and intersections. 2 L A) BCO : Total Consumption Spending = total income P*X= W(T-L) X = .5*(100-L) X =.5*(100-L)(b) Please solve for Dwight's optimal labor supply and optimal consumption. At egm, 51 = 3X L = (3/5) *X =.6X From BC, X = .5(100-.6X) X= 50-.3X X*= 50/1.3 = 38.46 [*=.6*X= 23 Labor supply h = 100-L= 77 hours (c) Draw the solution {L+, X-} in the graph and denote it as e,and an indifference curve ICo that provides the optimal utility level. c) IC is L shaped, having Kink along line 51 = 3X 5L = 3X 400 X 50 20 BC IC 50 L 100(d) Now. Dwight realizes that he is eligible for a social benefit program that provides monetary benefit payment to beet farmers of $20 per period. Please write down the new budget constraint. d) with monetary benefit, non-labor income = 20 L new BC X= 0.5*(100-L)+20 (e) Please draw the new budget constraint, and denote it as BCi X = 0.5*(T-L) + 20 X= 0.5*(100-L) + 200 : BCI so new BC is kinked, at (L= 100, X= 20) (f) Please solve for the new optimal labor supply. at new Eqm, 5L = 3X L = 0.6X solving X" = 70/1.3= 53.85 ["= 0.6*X"= 32.3 hours Labor supply = 100-L"= 67.7 hours(g) Draw the new solution (Z: , X: } in the graph and denote it as er, and a new indifference curve IC: that provides the new optimal utility level. -100 X 70 -50 el IC1 (100,20) 20 50 L 100 (h) Please compare e.and ei. Explain why there is a difference or no difference. When non-labor income is available, then work hours fall and leisure hours increase with rise in consumption as well.(i) Please decompose the change into total effect, substitution effect and income effect on the graph. Which effect dominates? () What if alternatively, instead of giving subsidy of $20, the government subsidizes by increasing (10%) of the wage that beets farmers eams in the labor market. (That is, whatever 2 Dwight earns, he receive 10% increase in wage. ) What is the new optimal labor supply and comsumption? And please denotes the new solution as er. (k) Please decompose the change into total effect, substitution effect and income effect on the graph. Which effect dominates? (Compare e= and e:.) (1) Consider a new case relative to the original problem (part(d)). Now, instead of receiving $20 anyways, the $20 social benefit can only be obtain if Dwight does not work at all. If he decide to work any hour greater than zero, he can only obtain $5 benefit. Do you think Dwight would choose not to work at all and receive $20 or work and receive $5? Why
