Assume that the insurance company cannot distinguish between R-types and S-types, so they can only charge a single premium, T. Furthermore, suppose that 25 of the consumers are R-types and 75 of the consumers are S-types.

a) (1 point) Suppose all 100 consumers agree to sign up for insurance. Explain why the total profit in this industry is given by:

π = 100⋅T - 75⋅0.25⋅64+25⋅0.5⋅64

b) (1 point) Still assuming all 100 consumers agree to sign up for insurance, what will T be if industry profit is zero?

c) (2 points) Given your answer above, would S-types agree to buy insurance? Why or why not?

d) (3 points) Given your answer in part i, if the insurance companies charged the premium of T that you found in part h, would they make zero profit, negative profit, or positive profit?

e) (4 points) Describe how your results relate to concept of “adverse selection.”

f) (3 points) Suppose now that there are 10 R-types and 90 S-types. How do your answers to part g and h change? In other words, what premium would be charged, and would S-types accept it?

g) (4 points) Discuss how the market outcomes changed when R-types share fell from 25% to 10%. Does the market function “better” in one scenario than another? Are S-types offered an actuarially fair premium in either case? Do S-types accept the policy in either case? Explain why.