Dougie's car is worth $10,000. Dougie is a careless fellow who leaves the top down, the keys in the ignition, and his fanny pack in the front seat. As a result, the probability of his car being stolen is 0.3. If his car is stolen, he will never get it back (the fanny pack is a knockoff, assume that it has a value of zero). Dougie has $20,000 in other wealth and his utility function for wealth is () = 20.5. Suppose that Dougie can buy $K worth of insurance at a price of $.35K. a) Write down Dougie's von Neuman-Morgenstern utility function. b) Is Dougie risk-loving? Show your calculations. c) How much insurance will he buy? d) Does Dougie choose to fully insure? Explain why or why not.