Question

Jack gives each of his sister $600 in non-labor income per week. Each sister has 100 hours per week to spend on labor or leisure, and each can earn a wage of $30 per hour.

part a. (4 points) Allison utility is more accurately represented by the function U=CL2, which gives her a marginal rate of substitution (MUL/MUC) equal to 2C/L. where C is the amount of consumption (in $) and L is the hours of leisure she gets in a week.

i. Solve for the hours of work and leisure, and the amount of consumption for Allison.

ii. Sketch a graph that shows the change in her labor supply choice. (show before and after on the same graph)

(iii )Depict the optimal choice on the graph

1. part B (4 points) Solve for Allison’s utility if she can work her desired number of hours (as found in part a).
2. 1. 1. What would her utility be if she was forced to work 30 hours per week? How much extra consumption money would it take to make her as happy as she was before?
      2. iii What would her utility be if she was forced to work 40 hours per week? How much extra consumption money would it take to make her as happy as she was before?
   2. iii Comment on what this tells us about Allison’s feelings toward leisure and consumption

Answer 1

20 كما = C wl = 20 c=W(H-LOTA - WH-WLTA - WH-REAA 30. WHAA a {warta 1.3 3w [WHA Fod W-30, H 100 A: 600 c=1/3 [30x180+ Goo] = [2000 of Coo] - 3600 [wyta ) 3w 3430 2 అంది.
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[2000] 3430 2. Initial outlay utility [1200 Cs og c=moo (=80 Equilibrium 1200 utility a = [1200 + 6400 cepce 600 Budget O 80 100 in At gauilibrium : Ca Wwork of A W=30 i work-30, A. 600 (=30130 600 & Goot Goo Crisoo la resoot & Soot 4900 235.000 o onount to reach to .768000 = (1500 tx) (7072

2000. [(soo ty] (4000) 268000F 735000 + 4goox - 4goor & 735000 - 768000 = 4goor - 330000 49oor = 33oooo R = 3 30000 = 67.346 For to hours wookies 30x40 a 600 Mr = 180ox Cool - 1800 3600 = 480.000 To deach to let it takes y 268 goco = (1800 fy) (60) = 333.33 take in leisure the Consumer Consumption money to compensate need only 67.35 But for and to units he read 3333 unts to comperesate, then leisure in expensive to substitute for C to her.