Your bike is worth $200 and if you park it outside on campus there is a 10% chance that it will be stolen.
a. What is the expected value of your bike in the scenario described above?
b. Your utility function for wealth is U = (wealth)^2. The bike is your only possession. Campus security has a bike check in that will guard your bike for $20 so there will be no risk of loss. Do you take the campus security deal?
c. What is the maximum you would pay security to check in your bike?
d. Next suppose your utility function for wealth is U = 100x(wealth). What is the maximum you will pay the campus security for the safekeeping service now?
e. Now suppose your utility functioin is U= (square root)Wealth. What is the maximum you will pay for the bike check-in now?
f. Are you risk loving, risk neutral or risk averse in each scenario described above? Why?