Question 2. (10 marks) Consider the principal agent model introduced in Lecture 9. The owner of a firm is attempting to design a contract that will minimize expected wage bill, E[we = 1] = 0.8w# + 0.2wl While also satisfying a pair of constraints reflecting the agent's preferences and beliefs, 0.8In(awh) + 0.2In(aw) 2 In(x') and, 0.8In(aw#) + 0.2In(awl) 2 0.4ln(wH) + 0.6In(wz) i) (4 marks) Graphically represent the principal's contract design problem and solution as was done in Lecture 9.2 for the numerical case where a = 0.9 and x' = 6 using the values provided on slide 7 of lecture 9.1. ii) (4 marks) Suppose that the principal believed that the probability of high and low revenue were equal when the agent worked hard, P(H|e = 1) = 0.5 = P(L|e = 1) Use a new graph to show how the principal would choose the pair (wl, wH) to reflect this difference in beliefs by the agent and principal. Note the change will alter the isocost lines representing the principal's objective, but not the constraints. (Assume the values a = 0.9 and x' = 6 still apply). iii) (2 marks) Would the difference of beliefs described in ii) be sustainable in a competitive labour market? Explain