You own a small farm near a large city, and you are about to decide whether to work on that small farm or take a job in the city. Your utility depends on your income per day (Y) and on hours of leisure (L). Your daily income from farm work is:
where hr is hours of work on the farm, and your daily income from the city job is:
where he is hours of work in the city.
a. If you can work either on the farm or in the city, but not both, which sector would you choose?
b. If you can work both on the farm and in the city, how would you allocate your time?