Economics Exercise 1: A principal contracts an agent who must exert a contractible effort e in exchange of a wage w. The principal’s payoff is given by π(x,t) = 120e − w. The agent may be particularly competent or not. If he is competent, his profit function is given by U = w − 2e ଶ . If he is incompetent, his profit function is given by U ூ = w − 4e ଶ . The agent is competent with probability 1⁄2 . Finally, the agent will not accept the contract if he gets less than U = 100, whether he is competent or not. i. Find the optimal
