Moral Hazard: Risk Neutrality and First-Best Implementation

If the agent is risk-neutral, we can assume that (up to an affine transformation) u(t) = t for all t and h(u) = u for all u. The principal who wants to induce effort must thus choose the contract that solves the following problem:

With risk neutrality the principal can, for instance, choose incentive compat-ible transfers t¯ and t, which make the agent’s participation constraint binding and leave no rent to the agent. Indeed, solving (4.10) and (4.11) with equalities, we immediately obtain

and

The agent is rewarded if production is high. His net utility in this state of nature .  Conversely,  the  agent  is  punished  if production is low. His corresponding net utility .

The principal (who is risk-neutral with respect to transfers) makes an expected payment , which is equal to the disutility of effort he would incur if he could control the effort level perfectly or if he was carrying the agent’s task himself. The principal can costlessly structure the agent’s payment so that the latter has the right incentives to exert effort. Indeed, by increasing effort from e = 0 to  e = 1,  the  agent  receives  the  transfer  t¯*  more  often  than  the  transfer  t.  Using (4.12)  and  (4.13),  his  expected  gain  from  exerting  effort  is  thus , i.e., it exactly compensates the agent for the extra disutility of effort that he incurs when increasing his effort from e = 0 to e = 1.

Here delegation is costless to the principal. Therefore, if effort is socially valu- able in the first-best world, it will also be implemented by the principal with the incentive scheme  when effort is no longer observed by the principal and the agent is risk-neutral. Proposition 4.1 summarizes this result.

Proposition 4.1: Moral hazard is not an issue with a risk-neutral agent despite the nonobservability of effort. The first-best level of effort is still implemented.

Remark 1: The reader will have recognized the similarity of these results with those described in section 2.11. In both cases, when con- tracting takes place ex ante, i.e., before the realization of the state of nature, the incentive constraint, under either adverse selection or moral hazard, does not conflict with the ex ante participation con- straint with a risk-neutral agent, and the first-best outcome is still implemented.

Remark  2:  The  transfers   defined  in  (4.12)  and  (4.13)  yield only one possible implementation of the first-best outcome, an imple- mentation such that the incentive constraint (4.10) is exactly binding. Other pairs of transfers can be used, which may induce a strict pref- erence of the agent for exerting effort. Let us consider the following transfers ,  where  T is  an  up-front  pay- ment made by the agent before output realizes. These transfers satisfy the agent’s incentive constraint since:

where the inequality comes from the fact that effort is socially opti- mal in a first-best world. Moreover, the up-front payment T can be adjusted by the principal to have the agent’s participation constraint be  binding.  The  corresponding  value  of  this  transfer  is . With the transfers t¯*’  and t∗’  above, the agent becomes residual claimant for the profit of the firm. The up-front payment T is thus precisely equal to this expected profit. The principal chooses this ex ante payment to reap all gains from delegation.

Making the risk-neutral agent residual claimant for the hierarchy’s profit is an optimal response to the moral hazard problem. In other words, the principal then sells the property rights over the firm to the agent. Indeed, a proper allocation of property rights is sufficient to induce efficiency.

On the contrary, inefficiencies in effort provision due to moral hazard will arise when the agent is no longer risk-neutral. There are two alternative ways to model these transaction costs. One is to maintain risk neutrality for positive income levels but to impose a limited liability constraint, which requires transfers not to be too negative. The other is to let the agent be strictly risk-averse. In sections 4.3 and 4.4 we analyze these two contractual environments and the different trade-offs they imply.

Source: Laffont Jean-Jacques, Martimort David (2002), The Theory of Incentives: The Principal-Agent Model, Princeton University Press.