Consider a labor market model with many identical firms hiring workers. The firms 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 firm, can produce 0 units of output per day, where 0 differs across workers. More specifically, there are four possible values of 0: 01 = 10, 02 = 20, 03 = 30 and 04 = 40. A worker with daily output 0; is called a type i e {1,2,3, 4} worker. The fraction of each type of worker is 1/4. A worker can choose to work either at a firm or at home. If a type i worker chooses to work at home, he earns $ (0.8 x 0;) per day. Assume that a type i worker chooses to work for a firm if and only if he can obtain a wage no less than $ (0.8 x 0;) per day. %3D a. Suppose that 0 is publicly observable. Specify the competitive equilibrium of the labor market with complete information. Who will be employed in the equilibrium? Is the equilibrium outcome Pareto efficient? Why or why not? (Note that in this case, there should be an equilibrium wage for every type of worker15 points) 6094053e26bd9_16203134022 33.jpg b. Suppose that 0 is each worker's private information, and the firms only know its the competitive equilibrium of the labor market with asymmetric information. Who WII Ue tmpioyed in the equilibrium? Is this equilibrium outcome Pareto efficient? Why or why not? (In this case, since 0 is unobservable, there should be a single wage for all workers in the market.) (10 points) Size: 251 KB Dimension: 1626 x 872 pixels pecify c. Now suppose that every worker earns $24 per day if he chooses to work at home, regardless of his type. Hence, a worker chooses to work for a firm if and only if he can obtain a wage no less than $24 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 efficient? Why or why not? (10 points)