Question 2 (7 points) The wealth of an agent consists in a house on the beach, which is evaluated at $500 000, and $60 000 that he keeps in a bank account (savings). The agent just saw on TV that a big hurricane might be heading towards the town in which his beach house is located, in which case there is a 20% probability that the hurricane will damage the house and that he will have to spend $200 000 in reparations. If the hurricane does not hit the house (with probability 80%), the house will retain its original value of $500 000. The agent preferences are represented by U(W) = In(W), and he ranks gambles using the expected utility criterion. The agent is therefore risk-averse, and is thinking about how he could insure his house from the hurricane. a) An insurance policy that will cover for all reparations in case a hurricane damages the house now sells for $50 000. Would the agent be interested in buying the insurance? b) Alternatively, he thinks that he could buy stocks of a local construction company that could see its business booming in case the hurricane hits town. If he spends $50 000 in buying the stocks, he believes the stocks could go up to $100 000 if the hurricane hits the town or down to $40 000 if it does not. Would the agent be interested in buying the stocks