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) Suppose Allison weekly utility function can be written as 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.

1. Solve to find her optimal labor supply decision. How much leisure will Allison take, how much will she work, and how much consumption spending will she have? Sketch a drawing of her optimal decision.

B (4 points) Solve for Allisons utility if she can work her desired number of hours (as found in part a).

i 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?

ii 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?

iii Comment on what this tells us about Allisons feelings toward leisure and consumption