2. Assume that two people have the same utility function, milar to the video: U(I)= sqrt(I). - Lena has a 90% chance of being healthy for the entire year. If that happens, then they would make $360,000. In the chance that they get sick, their income would only be $100,000 (other family members work). - Bree has a 20% chance of being healthy for the entire year. If that happens, then they would make $90,000. In the chance that they get sick, their income would only be $10,000 (government benefit programs). - Create 2 utility graphs for each of the people above. Show their income and utility levels with no uncertainty. Also show their income and utility levels adjusting for uncertainty. Finally, show both the utility of their expected income (find their expected income first, then plug that into the utility equation) and their expected utility (the probability-adjusted utility in a healthy or a sick state). Be careful here as the risk is different from the videos... there is not the same probability of being in a healthy vs. unhealthy state (not 50/50 ). 3. Calculate the premium and payoff for a full and fair insurance contract for each person. - What is the utility of each person when they are insured? - What is the utility increase over being uninsured? - Which person gains the most utility? - Which person pays the higher premium? 2. Assume that two people have the same utility function, milar to the video: U(I)= sqrt(I). - Lena has a 90% chance of being healthy for the entire year. If that happens, then they would make $360,000. In the chance that they get sick, their income would only be $100,000 (other family members work). - Bree has a 20% chance of being healthy for the entire year. If that happens, then they would make $90,000. In the chance that they get sick, their income would only be $10,000 (government benefit programs). - Create 2 utility graphs for each of the people above. Show their income and utility levels with no uncertainty. Also show their income and utility levels adjusting for uncertainty. Finally, show both the utility of their expected income (find their expected income first, then plug that into the utility equation) and their expected utility (the probability-adjusted utility in a healthy or a sick state). Be careful here as the risk is different from the videos... there is not the same probability of being in a healthy vs. unhealthy state (not 50/50 ). 3. Calculate the premium and payoff for a full and fair insurance contract for each person. - What is the utility of each person when they are insured? - What is the utility increase over being uninsured? - Which person gains the most utility? - Which person pays the higher premium