Assume there is one insurance plan. Consumers decide whether to enroll in this insurance plan or remain uninsured. Consumers are heterogeneous in how much they value insurance and how costly they are to insure. Assume that a consumer of type θ gets utility equal to VI (θ) = θ from insurance.

The costs of providing this consumer with insurance are CI(θ)= α + 2βθ where -0.5 < β < 0.5 and -β < α < 1-2β . The utility and costs of remaining uninsured are VU (θ) = CU (θ) = 0. θ is distributed uniformly between zero and one.

a) If an insurer charges a price P, what are his total costs? What are his average costs? Briefly explain why average costs are increasing in P if there is adverse selection and decreasing in P if there is advantageous selection.

b) In a competive equilibrium, insurers must earn zero profits, or P = AC. What will be the price in equilibrium as a function of α and β ? Who will enroll in insurance?