3. 4. THE IMPACT OF INCENTIVE CONSTRAINTS Note that U( and V( are concave functions. A suitable transformation of this problem(see Section 3.10)is a convex programming problem for which the Kuhn-Tucker conditions are necessary and sufficient Once the function V* is determined, the optimal action is chosen to max nize the principals payoff a∈ arg max v(a) The advantage of the two-stage procedure is that it allows us to focus ol the problem of implementing a particular action. As we have seen, DP3 is (equivalent to)a convex programming problem and hence easier to"solve" and it turns out that many interesting properties can be derived from a study of DP3 without worrying about the optimal choice of action 3.3.1 Risk neutrality An interesting special case arises if the principal is risk neutral. In that case, maximization of the principals expected utility, taking a as given, is equivalent to minimizing the cost of the payments to the agent. Thus, DP3 can be re-written as nin∑p(a,s)(s) subject to p(a, s)U(w(s)-v(a)>>P(b, s)U(w(s))-v(b),Vb, ∑p(a,s)((s)-a)≥ 3.4 The impact of incentive constraint What is the impact of hidden actions? When does the imposition of incentive constraints affect the choice of contract? If one of the parties to the contract is risk neutral, it is particularly easy to check whether the first best can be achieved. that is. whether an incentive. efficient contract is also pareto-efficient Risk neutral principal3.4. THE IMPACT OF INCENTIVE CONSTRAINTS 5 Note that U(·) and V (·) are concave functions. A suitable transformation of this problem (see Section 3.10) is a convex programming problem for which the Kuhn-Tucker conditions are necessary and sufficient. Once the function V ∗ is determined, the optimal action is chosen to max￾imize the principal’s payoff: a∗ ∈ arg max V ∗ (a). The advantage of the two-stage procedure is that it allows us to focus on the problem of implementing a particular action. As we have seen, DP3 is (equivalent to) a convex programming problem and hence easier to “solve” and it turns out that many interesting properties can be derived from a study of DP3 without worrying about the optimal choice of action. 3.3.1 Risk neutrality An interesting special case arises if the principal is risk neutral. In that case, maximization of the principal’s expected utility, taking a as given, is equivalent to minimizing the cost of the payments to the agent. Thus, DP3 can be re-written as min w(·) X s∈S p(a, s)w(s)) subject to X s∈S p(a, s)U(w(s)) − ψ(a) ≥ X s∈S p(b, s)U(w(s)) − ψ(b), ∀b, X s∈S p(a, s)U(w(s)) − ψ(a) ≥ u. ¯ 3.4 The impact of incentive constraints What is the impact of hidden actions? When does the imposition of incentive constraints affect the choice of contract? If one of the parties to the contract is risk neutral, it is particularly easy to check whether the first best can be achieved, that is, whether an incentive￾efficient contract is also Pareto-efficient. Risk neutral principal