1. (Adverse Selection) Consider a labor market model with many identical OĢrms hiring workers. The OĢrms produce a homogeneous product with a constant-returns-to-scale technology and act as price takers (we normalize the price of the product to $1). A worker, if hired by a OĢrm, can produce units of output per day, where diĀ§ers across workers. There are three possible values of : 1 = 10, 2 = 20 and 3 = 30. A worker with daily output i is called a type i 2 f1;2;3g worker. The fraction of each type of worker is 1=3. A worker can choose to work either at a OĢrm or at home. If a type i worker chooses to work at home, he earns $ (0:7 i) per day. Assume that a type i worker chooses to work for a OĢrm if and only if he can obtain a wage no less than $ (0:7 i) per day.
(a) Suppose that is publicly observable. Specify the competitive equilibrium of the labor market with complete information. Who will be employed in the equilib- rium? Is the equilibrium outcome Pareto eĀ¢ cient?
(b) Suppose that is each workeriĢs private information, and the OĢrms only know its distribution. Specify the competitive equilibrium of the labor market with asym- metric information. Who will be employed in the equilibrium? Is this equilibrium outcome Pareto eĀ¢ cient?
(c) Now suppose that every worker earns $15 per day if he chooses to work at home, regardless of his type. Hence, a worker chooses to work for a OĢrm if and only if he can obtain a wage no less than $15 per day. Everything else in the model remains the same as above. As in part b, specify the competitive equilibrium of the labor market with asymmetric information. Who will be employed in the equilibrium? Is this equilibrium outcome Pareto eĀ¢ cient?