CHAPTER 3. THE PRINCIPAL-AGENT PROBLEM Suppose, for example, that the principal is risk neutral and the agent strictly) risk averse, i. e, U(c)<0. The Borch conditions for an interior solution imply that w(s) is a constant for all s. In that case, the agent's income is independent of his action, so in the hidden action case he would choose the cost-minimizing action. Thus, the first best can be achieved with hidden actions only if the optimal action is cost-minimizing Risk neutral agent Suppose that the agent is risk neutral and the principal is(strictly)risk averse, i.e., V(c)<0. Then the Borch conditions for the first best impl that the principal's income R(s-w(s)is constant, as long as the solution is interior. This corresponds to the solution of "selling the firm to the agent but it works only as long as the agent's non-negative consumption constraint is not binding In general, there is some constant y such that R(s-w(s)=min, R(s) w(s)= maxR(s)-g,0J Both parties risk averse More generally, if we assume the first best is an interior solution and maintain the differentiability assumptions discussed above, the first-order condition for the first best is ∑P2(a,s)[(R()-m(s)-MU((s)+'(a)=0. and the first-order(necessary) condition for the incentive-compatibility con- straint is ∑ma(a,s)U((s)-v()=0 So the incentive-efficient and first-best contracts coincide only if ∑p(a,sV(F(s)-t(s)=0 s∈S6 CHAPTER 3. THE PRINCIPAL-AGENT PROBLEM Suppose, for example, that the principal is risk neutral and the agent is (strictly) risk averse, i.e., U00(c) < 0. The Borch conditions for an interior solution imply that w(s) is a constant for all s. In that case, the agent’s income is independent of his action, so in the hidden action case he would choose the cost-minimizing action. Thus, the first best can be achieved with hidden actions only if the optimal action is cost-minimizing. Risk neutral agent Suppose that the agent is risk neutral and the principal is (strictly) risk averse, i.e., V 00(c) < 0. Then the Borch conditions for the first best imply that the principal’s income R(s)−w(s) is constant, as long as the solution is interior. This corresponds to the solution of “selling the firm to the agent”, but it works only as long as the agent’s non-negative consumption constraint is not binding. In general, there is some constant y¯ such that R(s) − w(s) = min{y, R¯ (s)} and w(s) = max{R(s) − y, ¯ 0}. Both parties risk averse More generally, if we assume the first best is an interior solution and maintain the differentiability assumptions discussed above, the first-order condition for the first best is X s∈S pa(a, s) [V (R(s) − w(s)) − λU(w(s)] + λψ0 (a)=0. and the first-order (necessary) condition for the incentive-compatibility con￾straint is X s∈S pa(a, s) [U(w(s)] − ψ0 (a)=0. So the incentive-efficient and first-best contracts coincide only if X s∈S pa(a, s)V (R(s) − w(s)) = 0