In this volume, we have assumed that the judicial system is perfect and benevo- lent, and consequently can enforce any contract without cost. Implicit behind this enforcement is the use of penalties that prevent both partners from breaching the contract. We now briefly discuss a model of imperfect contractual enforcement.
Consider the model in section 2.11.1 with adverse selection, risk neutrality, and ex ante contracting, i.e., the principal offers a contract before the risk-neutral agent discovers its private information. We know that the first-best is then imple-mentable. However, the ex post utility level of the agent is negative when θ¯ realizes.
For example, for the contract that makes the efficient agent’s incentive constraint binding, the inefficient agent’s payoff is 
. The inef- ficient agent may be tempted to renege on the contract proposed by the principal to avoid this negative payoff.
Let us first assume that the judicial system is so inefficient that the principal can never enforce a contract with such a negative payoff. Anticipating this fact, the principal reverts to self-enforcing contracts, which are such that both ex post participation constraints 
are satisfied. In this case, we are in exactly the same situation as if the agent knew his private infor- mation at the time of signing the contract. The optimal self-enforcing contract is thus identical to the contract characterized in section 2.6.
The expected loss LSB incurred by the principal because of the complete absence of enforcement can be easily computed as
The expected loss associated with the complete absence of a judicial system that is enforcing contracts is thus composed of two terms: first, the information rent needed to elicit information when the agent’s ex post participation constraints must be satisfied; and second, the corresponding allocative inefficiency when θ¯ realizes.
Let us now analyze the case where the judicial system can enforce any con- tract stipulating a negative payoff with some probability p and at a cost c(p). We assume that the cost of enforcement is increasing and convex: c(0) = 0, c‘ ≥ 0 (with the Inada conditions c‘(0) = 0 and c‘(1) = +∞), and c“ > 0.
A mechanism is enforcement-proof if the inefficient agent always finds it opti-mal to comply and prefers taking the promised rent U¯ rather than refusing to produce. If he refuses to comply, the court nevertheless enforces the contract with probability p and imposes a penalty P on the agent. The enforcement-proofness constraint is thus written as
or, putting it differently, as
As in our analysis of auditing models made in section 3.6, the monetary punishment P can be either endogenous or exogenous. In the first case, P is bounded above by the value of the agent’s assets l plus the latter’s information rent
In the case of exogenous punishments, P is only bounded by the value of the agent’s assets,
We will focus on exogenous punishments in what follows. When the principal chooses to implement an enforcement-proof mechanism, he solves the following program:
First, note that the principal incurs the cost of the judicial system. Specifically, we assume that the principal pays an amount X1 − gccXpc to maintain a judicial system of quality p. Second, the principal’s objective function takes into account the fact that the contract is always enforced on the equilibrium path when it is enforcement-proof. Hence, the punishment P is only used as an out-of-equilibrium threat to force the inefficient agent’s compliance. Of course, the maximal pun- ishment principle already seen in section 3.6 still applies in this context, and the constraint (9.24) is binding at the optimum.
Remark 3: The reader will have noticed that the previous model is somewhat similar to the models of audit discussed in section 3.6. The only difference comes from the role played by the probability of enforcement p. Instead of being used to relax an incentive constraint as the probability of audit does, a greater probability of enforcement relaxes a participation constraint.
It is beyond the scope of this section to analyze all possible regimes that may arise at the optimum. However, note that (9.22) is binding when
In this case, the agent’s information rents in the states of nature b and b¯ are respectively given by 
. Inserting those expressions into the principal’s objective function and optimizing with respect to q and q¯ leads to the following expressions of the optimal outputs: 
, where the superscript EP means enforcement-proof. These outputs are thus exactly the same as in the case of self-enforcing contracts seen above.
Omitting terms that do not depend on p, the principal finds the optimal probability of enforcement as a solution to the following problem:
This objective function is strictly concave with respect to p when cX·c is suf- ficiently convex. Hence, its maximum is obtained for pEP such that 0 < pEP < 1, and the value of the maximand is strictly positive, i.e., 
The judicial system therefore commits to an optimal probability of enforce- ment pEP , which is the unique solution to
Note also that the probability of enforcement pEP increases with the liability of the agent l when c(·) is sufficiently convex.
Of course, the pair 
c is really the solution we are looking for when the condition (9.27) holds for pEP , as defined in (9.28). In particular, this condition holds when the marginal cost of enforcing contracts is large enough so that pEP is close enough to zero.
With the optimal enforcement-proof mechanism, the principal obtains an expected payoff:
Compared with the full enforcement outcome, the expected loss LEP incurred by the principal when the judicial system ensures a random enforcement of the contract is written as
The bracketed term is always strictly positive, and therefore LEP < LSB. Hence, the principal always finds it optimal to use an enforcement-proof mecha- nism involving the threat of some random intervention by the judge. Because pSB is strictly positive, the principal does strictly better with an enforcement-proof mech- anism than what he can get by writing a self-enforcing contract. Note in particular that the information rent obtained by the inefficient type remains negative, just as in the case of full enforcement.
We summarize this section in proposition 9.2.
Proposition 9.2: There is no loss of generality in using enforcement-proof contracts. The judicial system is not used on the equilibrium path, but the mere possibility that it could be used improves ex ante contracting.
Laffont and Meleu (2000) analyzed a model similar to the one that we have just presented, but they allowed for endogenous punish-ments and possibly fixed costs of enforcement. In particular, they observed that self-enforcing contracts may be optimal because of the fixed cost of using the judicial system. Fafchamps and Minten (1999) showed empirically that contracts used in less developed countries (LDC) are designed for low expo- sure to the breach of contracts. Indeed, low liabilities call for a reduction in the probability of using the judicial system. Krasa and Villamil (2000) ana- lyzed the issue of costly enforcement in the case of financial contracts.
Source: Laffont Jean-Jacques, Martimort David (2002), The Theory of Incentives: The Principal-Agent Model, Princeton University Press.