Dougie's car is worth $10,000. Dougie is a careless fellow who leaves the top down, the keys in the ignition, and his murse in the front seat. As a result, the probability of his car being stolen is 0.4. If his car is stolen, he will never get it back (the murse is actually a knockoff bag full of expired coupons, assume that it has a value of zero). Dougie has $200,000 in other wealth and his utility function for wealth is () = 20^0.5. Suppose that Dougie can buy $ worth of insurance at a price of $0.55. 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. e. Suppose instead that Dougie's utility function for wealth is () = ln(()). How would this impact the amount of insurance that he wants to buy?