1. The risk of being fired for cause from a job is an undesirable event that many people would like to insure against. However, private insurance companies generally do not offer such insurance. Identify and explain the problems that prevent private insurance companies from offering this insurance. Would a social insurance program be able to overcome these problems?
2. [Based on Gruber 12.1] The price of life insurance is substantially higher for men, relative to otherwise similar women. For example, in California 2018, the annual premium for a $1 million, 10-year term life insurance policy for a 50-year-old nonsmoker in exceptional health was around $950 for a man, but only $800 for a woman.

A. Explain the difference in pricing for men versus women.

B. Suppose the U.S. government were to pass a non-discrimination law requiring insurers to offer the same life insurance prices for men and women. What effect would you expect this law to have on prices and insurance coverage?

1. Suppose that you have a job paying $50,000 per year. With a 5% probability, next year your income will be reduced to $20,000 for the year.

A. What is your expected income next year?

B. Suppose that you could fully insure yourself against the risk of reduced income next year. What would the actuarially fair insurance premium be?

C. Suppose your utility function is U(x)=x . What is the maximum you would be willing to pay to fully insure yourself against the risk of reduced income next year? Given this, what is the risk premium you are willing to pay to fully insure?