Question 2 - Consumption under uncertainty (20 Points) Geico offers automobile insurance against various risks. Assume that Geico offers two contracts to all their customers Contract 1: consumers pay a premium Pi and the company pays 100% of the damages Contract 2: consumers pay a premium P2 and the company pays 50% of the damages if the value of the losses are above $350. Assume that P1 = 300 and P2 = 150 Nico and Paula live in the same area, where there is a 20% change their car will get damaged. If this happens, the value of the car is 15% of its original value. Nico's car is valued in $2,500 and Paula's car is valued in $2,000. Assume their utility functions are: Un - Vw Up = In(w) where w represents final wealth. 1. (5 points) For this question only: assume that only Nico would buy insurance. What is the premium P1 that would make contract 1 a fair gamble from the perspective of the insurance company? 2. (5 points) Which insurance contract, if any, would Nico buy? 3. (5 points) Which insurance contract, if any, would Paula buy? 4. (5 points) What is Paula willingness to pay for Contract 1