You run a private income-insurance plan, and are pricing risk for an individual who in a given week might have an income of $225 (60% probability), or $400 (40% probability). Assume that this individual has utility for income:U(x)=x

A. What is the expected value of this individuals' income?

B. Calculate the consumer's certainty equivalent and risk premium.

C. You would like to write an insurance policy that guarantees the individual $400 (before premiums) even in weeks when their earnings are $225. What would an actuarially fair premium be (per week) for individuals with this risk profile? What is the maximum amount the individual would pay for such a plan?

D. Now assume that the individual can increase the likelihood that they earn $400 be exerting effort. Do we think that the probabilities will remain the same (p($225)=0.6 and p($400)=0.4) if they are insured? Why or why not. If not, what might this do to the insurers' expected costs?

E. Now consider that the labor market is made up of lots of different individuals with different risks, risk preferences, earnings profiles, and effort costs and that many of these dimensions are difficult for the insurer observe. Discuss adverse selection in the context of this market, and whether we expect it to function efficiently.