1. Teams (from Eric Rasmusen's textbook) (40 points) A team of two workers produces and sells widgets for the principal. Each worker chooses high or low effort. An agent's utility is U = w 20 if his effort is high, and U = w if it is low, with a reservation utility of U = 0. Nature chooses business con- ditions to be excellent, good, or bad, with probabilities 91, 62, and 63. The principal observes output but not business conditions, as shown in the table: ' Excellent Good Bad (91) (92) (93) High, High 100 100 60 ' High, Low 100 50 20 Low, Low 50 20 0 a. Suppose 91 = 92 = 63. Why is {(w(100) = 30,w(not 100) = 0), (High, High)} not an equilibrium? (10 points) b. Suppose 61 = 92 = 93. Is it optimal to induce high effort? What is an optimal contract with nonnegative wages? (10 points) c. Suppose 91 = 0.5, 62 = 0.5, and 03 = 0. Is it optimal to induce high effort? What is an optimal contract (possibly with negative wages)? (10 points) d. Should the principal stop the agents from talking to each other? (10 points)