Suppose that an individual has a total wealth of 100000. There is a 20% probability that their 20000 car will be stolen. The individual has a utility function of the form: U(W) = Wwhere W is wealth An insurance company offers the individual full insurance provided they purchase and install an alarm that reduces the probability of theft to 10%. The alarm costs 2000. a) How much is the individual willing to pay for full insurance provided they buy and install the alarm? Show your calculations. (60 marks) b) What if the insurance company cannot check if the individual has purchased this alarm? Describe the insurance offers that the insurance company should make to its potential customers given the informational uncertainty. Explain your answer. (40 marks)