All insurance companies set premium p for the young. Find the set of young people who purchase health insurance at that premium, and Identify expected insurance-company profits as a function of p. Then calculate the same for the old, when all companies set premium q for them.

Let v denote the expected healthcare costs of a given individual. Suppose that v is distributed uniformly over the interval [0,10] in the young population, and uniformly over the interval [10,30] in the old population. Suppose further that because of risk aversion, a person with expected healthcare costv is willing to pay up to v+4 to purchase (complete) health insurance. Assume that 21 of the total population are young and that 21 are old. Each person knows his or her expected healthcare costs, but insurance companies can observe only whether a person is young or old. Assume that the insurance industry is perfectly competitive. Let v denote the expected healthcare costs of a given individual. Suppose that v is distributed uniformly over the interval [0,10] in the young population, and uniformly over the interval [10,30] in the old population. Suppose further that because of risk aversion, a person with expected healthcare costv is willing to pay up to v+4 to purchase (complete) health insurance. Assume that 21 of the total population are young and that 21 are old. Each person knows his or her expected healthcare costs, but insurance companies can observe only whether a person is young or old. Assume that the insurance industry is perfectly competitive