Moral Hazard. There is a risk neutral principal and a risk averse agent. The agent exerts effort a that results in output x = a + , where ∼ N(0; 1). The principal observes x but not a. The agent’s utility is u(w; a) = − 1/2e^2(w−c(a)) if he works for the principal and U= − 1/2e^2 if he does not; his costs of exerting effort a > 0 are c(a) = (a^2)/2 + 1/2 .
(a) Find the first best level of effort. Calculate the profit of the principal.
(b) Solve for the second-best linear contract w(x, a) = αx + β. Calculate the Principal’s profit. Compare your results to the FB and provide the intuition.