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 probabilityp^L frail=0.4 for

minor medical conditions and a probabilityp^H frail=0.2 for catastrophic medical conditions.

The corresponding probabilities for a robust individual arep^Lrobust=0.2 andp^hrobust=0.1.

Minor and catastrophic medical conditions have a fixed cost of $100 and $500 respectively. The initial wealth for both robust and frail isW=$1000.

1. 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. 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. Which contracts are attractive to frail individuals?

4. Which contracts are attractive to robust individuals?