A sales person has the following utility function: u(w, ?) = sqrt(w, ?), w is the hourly wage and ? is the number of hours worked in a typical day. This person is choosing between 2 jobs. The first job promises a constant work day of 8 hours and an hourly wage of $50 per hour. The second offers a random workday, with some days requiring 4 hours of work, and other days requiring 12 hours of work.
a. Assume the probability of a 4-hour workday in the 2nd job is 0.5 (and the probability of 12-hour workday is also 0.5). How high must the hourly wage be on the risky job to get the person to take it?
b. Assuming that the wage for the risky job is the one you found in part a, will a proportional tax on daily earnings affect this person’s choice of job?
c. How would your answer to part b change if daily earnings were subject to a progressive tax in which the first $300 of daily earnings are not taxed and daily earnings over $300 are taxed at a rate of 50%?
d. What proportional tax rate would yield the same tax revenue as the progressive tax, but not affect the person’s choice among jobs?