Question

26. Consider an individual with preferences given by the formula U ₌ LY. Suppose the total time available per day is 16 hours, the wage rate is $5, and nonlabor income is zero.

26a. Calculate the optimal level of leisure and labor hours, and the resulting earnings and utility level.

26b. Suppose the person is injured on the job in such a way that he cannot work at all. Prove that a policy that compensates the worker for his lost income will increase his utility.

26c. Find the minimum percentage of income that could be replaced and just keep the worker at the same level of utility as before his injury. Do you see any problems with this analysis?

Answer 1

Sol: Given that, consider an individual with preferences given by the formula | 0 = Ly •0 The total time available per day = 16 hours. wage gate (W) = $5. Non labour income = 0 as Budget constraint (Bc): We know that the total labour income - Total consumpur e = Total consumption. > From the given data, Total laboud income - wx(16-) where, Lis leisure, then (16-L) will be wook hours. let y = Total consumption. Therefore, the equation will become as WX (16-1) = 4 -> ☺ so at equilibrium, We know that LOW Marginal utility at y Marginal Udility at L meðginal Rate of Substitution (MRS. 1=w All

, then the Substitute the equation in equation budget constraint (Bc) will become Wx/16 - L) - Y, 16W - WL = WL 16 W = WIL + WL 16W = Q WL We know that, from the given data wage tate (W) = 5. 16*5 = (2x5) 44 1: L=41) - 80 = 1041 L = 80 110 · 4 = 8 :: oplimal Work hours (12 = 8 Resulting earnings (4.)= WX(16-17) = 5x8 = 40 :: Resulting earnings (Y)= 40

vtility (y) - W* Earnings = 8 x 40 = 320 .utility level (Y) = 320 utility level before injury(u)= 320 in such a person is injured on the job Given that suppose the way that he cannot work atall. then Now labour hour s(): = 4y = 16. Hours of work = 0. So, if he is fully compensated with income, then 4, = 40. New utility level (U) = Ug = YL, = 40x16 = 640 a utility level after injusy (UA) = 640 c) Now, utility level before injudy (u) = 320 So, 320 = 16% 42

Y2 320 Y2 = = 16 Y2 = 20 comparing By both Y and Yg ( 40 and 20). Y2 is 50% less than the yn • Minimum percentage of income - 50% Yes, problem is there in this kind of analysis, because for consumption, income, the individual will surely suffet, with lower level of utility