You run a small company with 100 employees. As a good employer, you offer life insurance to all your employees. This is insurance that pays out $1M to the family of an employee who dies. For simplicity, suppose that your employees divide into two equal groups: risky and safe.

• Risky employees face a 1% chance of dying in any given year.
• Safe employees face a 0.2% chance of dying in any given year.

Last year, the life insurance premium for all employees (regardless of type) was $5,000, and all risky employees purchased policies, while only one-third of safe employees did.

This year, your insurance company decided to change premiums, and charge different premiums based on the employees' risk level. (Which the insurance company can figure out through a doctor's physical exam.) Risky employees now face premiums of $10,000 while safe employees are charged only $3,000. With these premiums, all risky employees purchase insurance, and two-thirds of safe ones do.

You can assume that no one has been hired or fired, so your employees have been the same last year and this year.

What can we say about the risk preferences of your employees? Specifically, in your answer, state whether each of the statements below is true or false and provide a brief explanation.

• All risky employees are definitely risk neutral.
• All risky employees are definitely risk averse.
• Greater than or equal to one-third of safe employees are definitely risk neutral.
• Greater than or equal to one-third of safe employees are definitely risk averse.