1 Problem Let v denote the expected healthcare costs of a given individual. Suppose that v is distributed uniformly over the interval [10, 40] among the population of a given country. Suppose further that because of risk aversion, a person with expected healthcare cost v is willing to pay up to v + 4 to purchase (complete) health insurance. Each person knows their expected healthcare costs, but insurance companies don't know each in- dividual's cost. Assume that the insurance industry is perfectly competitive, so insurance companies earn zero expected profits. 1. Suppose all insurance companies set premium p. Identify the set of individuals who pur- chase health insurance at that premium, and find the expected insurance-company profits as a function of p. Find the equilibrium premium p*. 2. Suppose that, in a different country, expected healthcare costs v are distributed uniformly over the interval [10, 20]. As above, a person with expected healthcare cost v is willing to pay up to v + 4 to purchase (complete) health insurance. Find the equilibrium premium q* that insurance companies will charge in this market. Is the fraction of uninsured in this market larger or smaller than in the market in part (i)