1.Let the Utility of Wealth = Square root of wealth

Say you have a 5% chance of losing $25,000 of your $30,000 in wealth.

a.What is the expected loss?

b.What is your expected wealth? Calculate it using two different methods.

c.What is the utility of your expected wealth?

d.What is your expected utility with the gamble? Why is this different from your answer in c?

e.Plug your expected utility back into the left -hand side of the equation above, as shown below, and solve for CEW. This stands for the certainty-equivalent of wealth. Why is this lower than the expected value of wealth?

f.The difference between the CEW and the expected wealth is the risk premium, the amount that consumers are willing to pay in addition to their expected loss to cover the costs of insurance business, simply because the consumer prefers certainty. What is the value of the risk premium?

g.The total price consumers are willing to pay equals the expected loss plus the risk premium. What is the total price consumers are willing to pay?

2.Now imagine that most people in society (we'll call them type one) have a 5% chance of losing $25,000, but others (we'll call them type two) are more likely to fall ill and they have a 40% chance of losing $25,000. Say that society is made up of 80% type one and 20% type two.

a.What is the expected loss for the group? Calculate for each group, then weight them by their share of the population.

b.The insurance company can't tell the difference between type one and two, and they cannot charge them different amounts due to the Affordable Care Act's pre-existing condition clause. Using the willingness to pay from 1g, will type one want to purchase this insurance? Why?

c.If all of the type ones decide to drop out, what is the new actuarial price?

d.Say the Affordable Care Act's individual mandate now takes effect, and that it works. How would it affect this society's insurance market in terms of the prices that consumers pay? Why?