Speedy Steve is a traveling salesman. His utility function is given by U = I0.5, where U is his utility and I is his income. Steve's income is $900 each week, but if Steve is caught speeding while making his rounds, he will receive a hefty fine. There is a 50% chance he will be caught speeding in any given week, and pay a fine of $500.
a. Calculate Steve's expected income and expected utility.
b. Suppose that Steve's boss offers him a position in online sales that eliminates the risk of being caught speeding.
What salary would provide Steve with the same utility he expected to receive as a traveling salesman?
c. Suppose instead that Steve was given the opportunity to purchase speeding ticket insurance that would pay all of his fines. What is the most Steve would be willing to pay to obtain this insurance? Explain how you arrived at this number.
d. If the company issuing the insurance referred to in (c) convinces Steve to pay the amount you indicated, will the insurer earn a profit? If so, how much profit will it earn?