A principal hires an agent to manage a firm.The firm's profit function is pi = 4e, where e denotes the agent's effort.The agent's utility function is u(w,x) = 2Sqrt(x) + (1/4)w, where x denotes leisure and w wage.The agent's time endowment is T = 24, and x +e = T.His reservation utility is 19.The principal offers the agent a wage contract w = F + (pi).

a. What are the values of F and in the optimal wage contract?What is the agent's effort level, his wage, the firm's gross profit, and the principal's net profit?

b. If the principal sets = 0.5, what should the value of F be? What would be the agent's level of effort, his wage, the firm's gross profit, and the principal's net profit?

c. Draw a graph to illustrate your answers for (a) and (b).