CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE There is a fixed cost of financing a project which we normalize to zero and a finite number of projects a= 1,. A identified with the probabilit distributions p(a, s). The contract between the shareholder and the manager requires the shareholders to pay the cost of the investment and pay the manager w(s) contingent on the outcome R(s). The manager has a utility function U(c) and chooses the project a to maximize his expected utility Spla, sU(w(s)). Because the manager has limited liability and no personal resources,(s)≥0 We assume that the principal and agent both know all the parameters of the model, the cost function v(a), the possible outcomes R(s), the agent's utility function U(), etc. There is asymmetric information about the choice of project, which gives rise to an incentive problem. Both the principal and the agent observe the contract (a, w() that specifies the manager's remuneration and the project that should be chosen and they both observe the realization s. However, only the manager observes the actual choice of p roject Casting this in the form of a principal-agent problem, the principal is assumed to choose the contract (a, w()) to maximize his expected return SpLa, s)V(R(s-w(s), subject to an incentive constraint(IC) and an individual rationality or participation constraint (IR) pla, S (IC)∑。p(a,s)U((s)≥∑,P(b,s)U((s),b p(a,s)U((s)≥ Of course, there is a participation constraint for the principal as well. If the solution to this problem does not give the principal a return greater than his opportunity cost, it may not be optimal for him to invest in the project at Suppose that the principal is risk neutral and the agent strictly risk averse Then the obvious solution is to offer the agent a fixed wage w(s)=w such that u(w)=i. The agent will be indifferent between all projects so it will be optimal for him to choose the project that maximizes the principals payoff, namely, the project a that maximizes expected revenue. But note that it is also optimal for him to choose any other project so we have not found a very robust method of implementing the efficient project Suppose that the agent is risk neutral and the principal strictly risk averse Then optimal risk sharing would require that the agent bear all the risk assuming that this is consistent with the budget constraint. Recall that we6 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE There is a fixed cost of financing a project which we normalize to zero and a finite number of projects a = 1, ..., A identified with the probability distributions p(a, s). The contract between the shareholder and the manager requires the shareholders to pay the cost of the investment and pay the manager w(s) contingent on the outcome R(s). The manager has a utility P function U(c) and chooses the project a to maximize his expected utility s p(a, s)U(w(s)). Because the manager has limited liability and no personal resources, w(s) ≥ 0. We assume that the principal and agent both know all the parameters of the model, the cost function ψ(a), the possible outcomes R(s), the agent’s utility function U(·), etc. There is asymmetric information about the choice of project, which gives rise to an incentive problem. Both the principal and the agent observe the contract (a, w(·)) that specifies the manager’s remuneration and the project that should be chosen and they both observe the realization s. However, only the manager observes the actual choice of project. Casting this in the form of a principal-agent problem, the principal is assumed to choose the contract P (a, w(·)) to maximize his expected return s p(a, s)V (R(s) − w(s)), subject to an incentive constraint (IC) and an individual rationality or participation constraint (IR): max(a,w(·)) P s p(a, s)V (R(s) − w(s)) (IC) P s p(a, s)U(w(s)) ≥ P s p(b, s)U(w(s)), ∀b (IR) P s p(a, s)U(w(s)) ≥ u¯ Of course, there is a participation constraint for the principal as well. If the solution to this problem does not give the principal a return greater than his opportunity cost, it may not be optimal for him to invest in the project at all. Suppose that the principal is risk neutral and the agent strictly risk averse. Then the obvious solution is to offer the agent a fixed wage w(s)= ¯w such that u( ¯w)=¯u. The agent will be indifferent between all projects so it will be optimal for him to choose the project that maximizes the principal’s payoff, namely, the project a that maximizes expected revenue. But note that it is also optimal for him to choose any other project so we have not found a very robust method of implementing the efficient project. Suppose that the agent is risk neutral and the principal strictly risk averse. Then optimal risk sharing would require that the agent bear all the risk, assuming that this is consistent with the budget constraint. Recall that we