Question 1 {50%}: Rothcltild-Stiglitz Model. Consider a Rothschild and Stigliiz model of adverse selection in which there are two types of people (robust and trail] and a single insurance rm. Both types of people are risk averse in income and have utility function of wealth: ini = any: During any given year, frail individuals face a probability p'ym = {1.4 for minor medical con ditions and a probability FEE\" = Ill for catastrophic medical conditions. The corresponding probabilities for a robust individual are Fi-abate! = DJ and Films, = H.115. Minor and catas trophic medical conditions have a fixed cost of $101] and $500 respectively The initial wealth for both robust and frail is W = $1000. Assume that medical events are mutually exclusive, meaning that individuals can face either minor, catastrophic or no medical conditions. 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%} Asstune that catastrophic medical events nmv cost "only" $011]. 1i.r'|i.i'l'iat happens to the attractiveness of the contracts for robust and frail individuals? Explain your results