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 () = 200.5. Suppose that Dougie can buy $ worth of insurance at a price of $. 55. a. [2] Write down Dougie's von Neuman-Morgenstern utility function. b. [4] Is Dougie risk-loving? Show your calculations. c. [6] How much insurance will he buy? d. [4] Does Dougie choose to fully insure? Explain why or why not. e. [4] Suppose instead that Dougie's utility function for wealth is () = ln(()). How would this impact the amount of insurance that he wants to buy?