MONOTONE 2ND-BEST OPTIMAL-CONTRACTS

We review the two stage nonlinear programming approach to the principa l-agent problem proposed by Grossman and Hart (G-H) in 1983. The objec tive of the principal is to determine an optimal payment schedule to a n agent that depends only on observable outcomes when (random) outcome s are influenced by unobservable actions of the agent. We establish th at these 'second-best' optimal contracts are monotonically related to observable outputs under fairly mild conditions. Two methods of proof are employed to establish that the monotone likelihood ratio condition (MLRC) on the probabilities of outcomes is sufficient for monotonicit y of second-best optimal contracts in a three-state model. The first u ses ideas related to the variation-diminishing property of totally pos itive matrices. The second approach uses a theorem of the alternative from linear programming theory to establish a condition that must hold under MLRC. The paper concludes with a counter-example that is a pert urbed version of an example in G-H that shows that MLRC is not suffici ent for monotonicity of second-best optimal contracts when there are f our or more states.