Consider two people, Hap and Tootie. Both of them have the same utility function that

depends only on their income, U = . Each of them has a 50 percent chance of falling ill and

losing their entire income of $144. (Note: you will find that a diagram is extremely helpful to

visualise the concepts.)

a. (2 marks) Calculate Hap and Tootie's expected level of income and expected level of utility.

b. (2 marks) Briefly explain what is meant by actuarially fair insurance?

c. (2 marks) Calculate how much an insurer would charge Hap and Tootie if it were to offer a full

and actually fair insurance policy.

d. (2 marks) Calculate Hap and Tootie's certainty equivalent and risk premium.

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e. (2 marks) Based on parts (a), (c) and (d), briefly explain if Hap and/or Tootie would buy the

actually fair insurance offered to them.

Now assume that the probability of Hap falling ill is 75 percent and the probability of Tootie falling

ill is 25 percent. Hap and Tootie each know their probability of falling ill, but an insurer only knows

that one of them faces a 75 percent probability and one of them faces a 25 percent probability but

does not know which one faces which probability.

f. (2 marks) Calculate Hap and Tootie's expected level of income and expected level of utility now.

g. (2 marks) Given that the insurer does not know which one faces which probability, calculate

how much it would charge each of them if it were to offer a full and actually fair insurance policy

to Hap and Tootie.

h. (2 marks) Calculate Hap and Tootie's certainty equivalent and risk premium now.

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i. (2 marks) Based on your answers to parts (f), (g) and (h), briefly explain if Hap and/or Tootie

would buy the actually fair insurance offered to them.

j. (2 marks) Briefly explain what is adverse selection and how it applies in this example.

k. (2 marks) Briefly list two market-based solutions to eliminate the adverse selection problem in

this example.