Question

3. Micheal has a utility function of the following: U(L, X) = Lº X1-a, where L is leisure and X is consumption. If he works, he receives real wage w. Outside of the labor market, he has non-labor market income V. And his endowment of time T is normalized to 1. And the price of goods p is also normalized to 1. (a) Please write down his budget constraint. (b) Assuming a = Į, V = 100, w = 200, what is his optimal supply of labor? (c) How much total income does he have? (d) How much consumption will he make? (e) Now, consider the case where Michael is subject to a 10% income tax on labor income only. What is his new optimal supply of labor? (f) Compare the result in (b) and (e). Elaborate on how income tax affect Micheals labor supply decision.

Answer 1

@ 9 U= LdXlx W, Vz, T=Y, PEY BC total consn spending total income X= W (T-1) tu. x= ((I-L) to b) x=1/2, 1=100, W=200, at eam MRS LX w. MRS = MOL/Mix= XL. --- XIL- 200 X=QooL from Brt X = 200(1-L)+100 ir 200L = 200 - 200L +100 400L= 300, L=314 =075 80 Labor ss = h = |-695= 25 fing 150 Ang d) C) Income 200x25 +100 - G= total Income = 150. C) [5.1, 80 BCI X= (1-T) W(1-1) + X = 69.60(1-1)+ V. at Eqm MRS LX = .qw. XIL = .9 X200 X = 180L from Be → 180L = 9x200 (1-1) +100 180L = 180-180L +100 360L = 280