The existence of an optimal deterministic contract in moral hazard problems

This paper proposes a new method for investigating the existence of a deterministic solution to pure moral hazard problems under a general setting without imposing a priori topological restriction on the contract space. Our method avoids the detour to show the existence of a random contract before showing the existence of a deterministic contract. We show the existence of a solution in the classical moral hazard setting wherein the agent's utility is separable between money and effort, and the utilities of the principal and agent are concave in money. The proposed sufficient condition for the existence is comparable with the state-of-the-art results, and we use an easy-to-check approach. For example, we show the existence if the marginal incentive cost (per util given to the agent) is unbounded, or if the signal is finite. Also our approach can apply to multi-agent settings and the cases in which the agent utility is quasi-separable.