C......Suppose all people in RiverCity own identical cars worth $80,000 each. RiverCity cars are prone to complete loss by flooding. WaterCrop Insurance Company offers policies against flood damage. The chance of a major flood for a particular car is p. The value of p is known to the car owners but not to WaterCorp. The values of p run from 0 to as high as 0.4. Owners have no control over p. For example, Karen lives at the bottom of a hill and parks her car on the street. For her car p = 0.3. Wen lives on top of a hill and parks her car in a garage; for her car p = 0.09.

WaterCorp is risk neutral and offers two policies. The first is a full insurance policy, which pays the car owner back $80,000 in the event of a flood. The premium for this insurance policy is $11,600. The second policy offers partial insurance. It has a payback in the event of flood of $58,400, and a premium of $5900.

All the residents in RiverCity are expected utility maximizers and have the same utility function:

() = + 10,000

where x is the net of this situation, including the value of the car, if there is no flood.

For example, a consumer who buys the partial insurance policy and has no flood has utility of

(80,000 5,900) = 80,000 5,900 + 10,000 = 290, while with a flood, the utility is

(58,400 5,900) = 58,400 5,900 + 10,000 = 250

a)Of the three options available, no insurance, full insurance, partial insurance, what would Karen choose? What would Wu choose?

b)For which values of p would consumers with that value choose

i. no insurance

ii. partial insurance

iii. full insurance

c) Briefly discuss how the values you find in b) would change if the risk preferences of citizens in RiverCity were characterized by Prospect Theory rather than Expected Utility Theory.