a man has a car accident and gets hurt. After the injury he finds it hard to work full time and his preferences for time spent on unpaid activities (L) and consumption (C) become U(C,L) = C1/3L2/3. he has no income from other sources and before the accident he could find work at an hourly wage of w = $40. The unit price of consumption is p = $1.

a. After the injury, how many hours does Stan want to work each week if he can still find jobs that pay $40 an hour?

b. In a diagram measuring leisure time along the horizontal axis, illustrate the man's optimal choice after the injury. Make sure you highlight his weekly number of hours worked.

Now suppose instead that after the injury, he can only find work at an hourly wage of w' = $20.

c. Given his preferences, does the lower wage push him to work shorter or longer hours? Why? Clearly explain.

Last, suppose that he was responsible for the car accident and that now he must pay $300 per week for the property damage he caused. d. Given his preferences, does the weekly payment of $300 push him to work shorter or longer hours? Why?