Teams (from Eric Rasmusen's textbook) 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=w20 if his effort is high, and U=w if it is low, with a reservation utility of U=0. Nature chooses business conditions to be excellent, good, or bad, with probabilities 1,2, and 3. The principal observes output but not business conditions, as shown in the table: ' a. Suppose 1=2=3. Why is {(w(100)=30,w( not 100)=0),( High, High )} not an equilibrium? b. Suppose 1=2=3. Is it optimal to induce high effort? What is an optimal contract with nonnegative wages? c. Suppose 1=0.5,2=0.5, and 3=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?