Consider a population of 1,000,000 people that consists of two groups with varying need for mental health coverage:

(1) Ten percent of the population are individuals who have a mental health disorder that needs immediate treatment. Treatment costs $18,000, and thus these people are willing to pay up to $18,000 for insurance that covers the treatment.

(2) The other 90 percent of the population are people who understand that they are at risk of needing mental health treatment that will cost $18,000. These people understand that there is a 1 in 9 chance that they will require mental health treatment. They are each willing to pay up to $3500 for insurance to cover the treatment.

(a) Assume that individuals know what group they are in,but insurance companies cannot tell this. Assume that the market structure in the insurance industry is competitive. Even if the cost of selling insurance policies in negligible, will the insurance industry provide coverage for mental health? Give a careful proof for your answer, and explain the economic logic.

(b) Now suppose that insurance companies can screen for mental health status at the cost of $1000 per patient. Describe the competitive equilibrium. Is this outcome better or worse for the population than the one you describe in (a)? Support your answer with specific economic logic.

(c) Continue to assume (as in (b)) that companies can screen for mental health status at a cost of $1000. A proposal has been made for the government to provide universal coverage for mental health treatment (i.e., treatment for everyone who needs it), financed by charging each individual a fee just sufficient to fund the program. Write a short (one paragraph) statement that either favors or opposes the program. Provide economic arguments, e.g., dollar figures for the costs and benefits of your favored solution, compared to the alternative.