Exercise 11.6 A Fiery State (Kahneman and Tversky 1979). Sonny owns a home in fire-prone California, where there 1s a 50% chance of wildfires 1gniting and damaging his home and property this year. He has a utility function over wealth, u(w) = /w, and an initial wealth of $160,000. Suppose that in the event of fire, the damage done will cost Sonny $120,000 to repair. o What 1s Sonny's expected wealth? What 1s Sonny's expected utility? Sonny has the option to buy a full insurance policy for the year that, in the case of fire, will reimburse him for all of the fire damage repair costs. What 1s the maximum amount that he would pay for a such an insurance policy? Hint: Compare his expected utility without insurance from part (b) to the utility of buying the full insurance policy. Now suppose a sprinkler salesperson offers to sell Sonny industrial strength sprinklers to install around his property to help mitigate the damage of a possible wildfire. The sprinkler system costs $7,000. Unfortunately, the sprinklers cannot stop the fire, but only limit the damage. In particular if there is a fire, then there will be a 10% chance that the damage will now only cost $63,000 to repair, but a 90% chance that the damage will cost $113,000 to repair. Note that these repair costs do not include the price of the sprinkler system. Does Sonny prefer the sprinkler insurance policy or the full insurance policy at the maximum price in part (c)? Explain whether or not Sonny's decision is surprising to you