Please show working out for all parts

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=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? (10 points) b. Suppose 1=2=3. Is it optimal to induce high effort? What is an optimal contract with nonnegative wages? (10 points) 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? (10 points) 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=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? (10 points) b. Suppose 1=2=3. Is it optimal to induce high effort? What is an optimal contract with nonnegative wages? (10 points) 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? (10 points)