3. (10 points) Jay pays $400 a year for auto insurance that covers her against liability if sued for damages in the event of an accident where she is at fault. She expects (correctly) that there is a 1/1000 chance that in any given year that she will be sued for $100,000. a. Explain/calculate whether it is rational to buy the insurance (first, find the expected loss.) b.Draw a graph illustrating Jay's utility as a function of income, assuming that her marginal utility of income is declining. Jay is, in fact, willing to pay up to $800 to avoid incurring the loss. Show on your graph (and explain) that this amount ($800 payment) yields the same level of utility as with Jay's expected income without insurance. c. Show graphically the level of utility if Jay insures at the $400 premium. d.Suppose there are a thousand Jay's in the market. There is one insurance company that, for simplicity, incurs zero administrative costs to supply insurance policies. Calculate the annual profit the insurance company expects. e.Suppose the company expects to attract these same annual profits into perpetuity (assume a discount rate is 5% ). What is the company's worth in present value terms? f. Suppose the insurance market is competitive. What would you expect the competitive equilibrium premium to be? Explain..