ECO 464/564 Problem Set 5 Due Tuesday, November 28, 2:00pm Problem 1: Consider the market for car insurance. There are two types of drivers, reckless drivers and cautious drivers. Reckless drivers and cautious drivers each have an income (consumption) of $30,000 per year. The probability of getting into a car crash each year is 0.2 for a reckless driver and 0.05 for a cautious driver. If a crash occurs, it will cost $10,000. There are two types of car insurance policies: High deductible: $5000 deductible Low deductible: $500 deductible. Lastly, assume the utility function is U = C 1a. Assume car insurance companies know who is a reckless driver and who is a cautious driver. Calculate the actuarially fair premium for each policy for each type of driver. A premium is actuarially fair if the premium is equal to the expected insurance payout if a crash occurs. 1b. Show each type of driver prefers a low deductible plan if premiums are actuarially fair. 1c. Assume car insurance companies DO NOT know whether a driver is cautious or reckless. Calculate the actuarially fair premium for each plan, assuming there are an equal number of reckless drivers and cautious drivers. 1d. Show that it is not possible for both reckless and cautious drivers to buy the low deductible plan when the type is not observed, but the premium is actuarially fair. Which type of driver does not prefer the low deductible plan in this setting? 1e. Does an equilibrium exist where reckless drivers buy the low deductible plan and cautious drivers buy the high deductible plan, even if car insurance companies do not know the type of driver? An equilibrium exists if no type wants to switch insurance plans.