Consider a Rothschild and Stiglitz model of adverse selection in which there are two types of people (robust and frail) and a single insurance firm. Both types of people are risk averse in income and have utility function of wealth:

U (W) = W

where = 0.2. During any given year, frail individuals face a probability p L frail = 0.4 for minor medical conditions and a probability p H frail = 0.2 for catastrophic medical conditions. The corresponding probabilities for a robust individual are p L robust = 0.2 and p h robust = 0.1. Minor and catastrophic medical conditions have a fixed cost of $100 and $500 respectively. The initial wealth for both robust and frail is W = $1000.

1. (5%) Find the fair premium for a contract offered to frail individuals that offers (a) full coverage, (b) only minor conditions coverage and (c) only catastrophic coverage.

2. (5%) Find the fair premium for a contract offered to robust individuals that offers (a) full coverage, (b) only minor conditions coverage and (c) only catastrophic coverage.

3. (10%) Which contracts are attractive to frail individuals?

4. (10%) Which contracts are attractive to robust individuals?

5. (20%) Assume that catastrophic medical events now cost "only" $300. What happens to the attractiveness of the contracts for robust and frail individuals?