1.Consider the labor market model that was described in class. 1)A worker is characterized by his type, which is commonly believed to be uniformly distributed on the interval [0,1]. A worker with abilityproduces $for the firm that employs her. A worker with abilityhas an outside option that gives her $r(). There is a competitive labor market in which a certain wage is paid, and all potential employers (firms) are risk neutral.

a)Suppose thatr() =+. Find an equilibrium in which firms pay a wagew >1/10.

Is the equilibrium efficient? Explain.

b) Suppose now thatr() =+. Find an equilibrium in which firms pay a wagew >1/10. Is the equilibrium efficient? Explain. Is the fraction of workers that take the job in this case larger or smaller than in (a)?

2.Letvdenote the expected healthcare costs of a given individual. Suppose thatvis 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 costvis willing to pay up tov+ 4 to purchase (complete) health insurance. Assume thatof the total population are young and thatare 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.

a)Suppose all insurance companies set premiumpfor the young. Identify the set of young people who purchase health insurance at that premium, and find expected insurance-company profits as a function ofp. Do the same for the old, when all companies set premiumqfor them.

b)Find equilibrium premiumspfor the young andqfor the old. Show that at these premiums, the proportion of the old people who purchase health insurance is smaller than that of the young. Hint: Note that the profits of the insurance company from young consumers are(p) =p E[v|insured young givenp] and the profits from old consumers are(q) =q E[v|insured old givenq]. Use the fact that there is perfect competition among insurance companies (so that they earn zero profits from both types of consumers) to derive the equilibrium prices.