3. Assume that an insurance company is selling insurance to a client who can be of different types - healthy (H) and unhealthy (U). The probability of a client being healthy is 0.7, and the type is the client's private information. The insurance package is in terms of (q,p), where q is the amount of coverage and p is the price per unit of coverage. Given (qu, p), the payoffs of healthy and unhealthy clients are uH(q,p)=12qq2pquu(q,p)=18qq2pq Notice that the utility of an unhealthy client is higher because insurance is more helpful when someone is more likely to have medical conditions. In addition, assume that the cost of providing insurance is c=2 per unit of coverage, i.e. the cost of providing coverage q is 2q. (1) Suppose that the company can only offer one package (q, p). What package will maximize the company's expected profit? Now assume that the company can design two packages (q1,p1) and (q2,p2). A client can pick either one to purchase or reject both. (2) Suppose that the company wants a healthy client to pick (q1,p1) and an unhealthy client to pick (q2,p2). Write down the IRs and ICs. (3) What packages will maximize the company's expected profit now? Is the profit higher or lower than your answer to (1)? 3. Assume that an insurance company is selling insurance to a client who can be of different types - healthy (H) and unhealthy (U). The probability of a client being healthy is 0.7, and the type is the client's private information. The insurance package is in terms of (q,p), where q is the amount of coverage and p is the price per unit of coverage. Given (qu, p), the payoffs of healthy and unhealthy clients are uH(q,p)=12qq2pquu(q,p)=18qq2pq Notice that the utility of an unhealthy client is higher because insurance is more helpful when someone is more likely to have medical conditions. In addition, assume that the cost of providing insurance is c=2 per unit of coverage, i.e. the cost of providing coverage q is 2q. (1) Suppose that the company can only offer one package (q, p). What package will maximize the company's expected profit? Now assume that the company can design two packages (q1,p1) and (q2,p2). A client can pick either one to purchase or reject both. (2) Suppose that the company wants a healthy client to pick (q1,p1) and an unhealthy client to pick (q2,p2). Write down the IRs and ICs. (3) What packages will maximize the company's expected profit now? Is the profit higher or lower than your answer to (1)