This exercise explore the nature of insurance contracts. We examine a permis feature of actualitate contacts requirement that the purch bear part of the cost of any claim. For example, health insurance policies typically in the policy bolder to pay some of the costs of medical care, and accident policies typically incorporate a deductible, toquiring an agent to pay some of the cost. Considera in which there are there are two posible states. In state the agent has increme (or, quivalently in this case, wealth) of 100. In state two, the agent state an accident that imposakus L75, and bence has a net income (or wealth) of 25. The utility for money is given by we) 31 Calelate this agent’s expected utility, under the station that the two states are equally lily 1 3.2 Now ppose that at a cost of 16, the petit could reduce the probability of a los Le due the probability of state to 1/4. Hence, the income would be 81 in state 0 100 mints the 16 paid to reduce the risk of a ) and 9 in state two. For example, the agent may install smoke alarms that make a catastrophic fire les likely install anti-lock brakes on her car, install a scenity ystem in her house stop soking and so on. Would the spent pay the cotto reduce the risk of loss? Answer this question by calculating and comparing the relevant expected utilities 3.3 Supowe tow that after paying the 16 to reduce the risk of a low, and bence ensuring the
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