3. This exercise explores the nature of insurance contracts. We examine a pervasive feature of actual insurance contractsa requirement that the purchaser bear part- of the cost of any claim. For example1 health insurance policies typically require the policy holder to pay some of the costs of medical care, and accident policies typically incorporate a deductible, requiring an agent to pay some of the cost. ISonsidecr' a case in which there are there are two possible states. [11 state one, the agent has income (or, equivalently in this case, wealth} of l. In state two, the agent suers an accident that imposes a loss L = T5, and hence has a net income [or wealth} of 25. The agents utility for money is given by u{c] = V\"? H: ' u I ..- 3.4 Now suppose that before accepting the insurance policy, the agent can decide whether to spend the 15 to reduce the probability of a loss. The insurance com pany cannot observe whether the lossprevention has been undertaken or not. [The insurance company may not be able to tell whether the agent has really stopped smoking, for example} Suppose that whatever the agent does, the insur ance company believes the risk has been reduced, and hence offers the contract described in 33. Will the agent reduce the risk in this case'iI Answer this by cal culating the agenth expected utility, given that she does pay the cost to reduce the risk and then assuming that she does not, in each case having available the insurance contract from 3.3. If the agent does not reduce the risk, what will the company expected pmt be? 3.5 Insurance companies often write policies with a deductible provision. A deductible essentially caps the amount of the claim the insurance company will pay, forcing the agent to bear some of the loss. For example, the insurance company might pay at most '55 of a loss. Suppose the insurance company modies the insurance contract described in 3.3 {i.e., a contract appropriate when the probability of a loss is lfril} by imposing an upper bound E {not necessarily 55) on the payment to the agent in the event of a loss. The corresponding premium is set so that the insurance company just breaks even, given probability 1K4 of a loss. Now will the agent he better off paying the 16 to reduce the probability of a loss, or not doing so?I Explain how your answer depends on the value of E. Notice that if the amount of insurance that maximizes the utility of the consumer is larger than "if, the optimal feasible choice is buying an amount of insurance E. BE in light ni' m'IIT' nrevious answers. emlain whv insurance mmnanies might nd it