Question

Please tutor walkthrough as to how the solution for part A was found. Also, part C.

(6) Geo's utility function is described as Ley, where Leis hours of leisure per day, and Y is disposable income per day. Geo is employed in a job with a wage of $20 per hour and has 10 hours per day that he can spend in either working or leisure. His income from working is his only source of disposable income. He does not receive any non-wage income. Geo can work as many hours as he chooses, up to the limit of 10 hours per day. (a) (2 points) How many hours will Geo choose to work with a wage of $20 per hour? MRS E- WY/LEW Y = WL Since Y =WL, = w(T - L.), then w(TL) = WL. → T-L.-L. → L.=T/2 Since T = 10, then L = 5. L. = 10 -5 = 5. (b) (2 points) How many hours will Geo choose to work with a wage of $5 per hour? Note that number of hours of work is independent of wage, so Geo will once again work 5 hours. (c) (3.5 points) The change in Geo's hours of work due to the decline in his wage can be decomposed into a substitution effect and an income effect. What is the change in his work hours through the substitution effect? Utility at 1, 5, Y = 100, is 500. For U500 and w=5, we need M' such that (0.5M) (0.5 * M'/5) = 500. (Note that half of potential income goes to each of Y and leisure, which is derived from L, -T/2 derived in part (a).) Then M'. 100. L'=(0.5 M'/5) = 10 →1=0 So the change in work hours due to the substitution effect is 0-5-5.

Answer 1

Solution

Geo's utility is allocated between leisure and his disposable income per day.

Optimal condition of geo will be

Slope of budget constraint= slope of utility function

solution Time Geo has 10 hours So Time = work & Leisure Time 10-W tle . The = 10-6 or w=110-le] Also Incon Income & wW, wswage rate y Hours of work 1 Y=20w. = Y = 20 (10-Le) = (y = 200 - 20let Budget constraint Optimal condition Slope of Budget constraint = Slope of Utility Funct Slope of B. c = 20 - © U= Ley mes moins 0

Equating ④ 4 ④ we get, =/7 = 2016 – Pulling 'Y' in B. Co y= 200-20le 2016 = 200 - 20le 2) 40le - 200 2) * - 200 = 5 hos) So, Geo has s has of Leisure and shas s: W= 10-le = 10.55 of work

c) Number of hours worked by Geo is independent of wage. Now

Optimal level of income is $ 20×le= $20×5= $100 and Utility U=le×Y=5×100=500

So the change in leisure is given by =0.5×M'/5 , as half of his potential income is devoted to leisure. Also leisure is 1/5th of half of new potential income.

So change in leisure= 0.5×100/5=10

He will devote 0 hrs to work now

So change in working hours due to substitution effect=0-5=-5