In the first part of this article, (hypothetical) contracts providing for all possible uncertain contingencies are considered. In the next part, contracts providing for only some contingencies are examined and are shown to be advantageous, due both to difficulties that could arise in making and enforcing contingent terms and to the presence of implicit substitutes for them. In the following, major part of the article, two of these substitutes for contingent terms are analyzed: remedies for breach, and the opportunity for renegotiation; the existence of both is demonstrated to induce parties to behave approximately as they would under detailed contracts.

I. Introduction, 541.—II. The model, 542.—III. Moral hazard when care is not observed by the insurer, 544.—IV. Moral hazard when care is observed by the insurer, 550.—Appendix, 561.

One of the functions of the criminal sanctions of imprisonment and the death sentence is to prevent individuals from doing harm by removing them from the population.' This incapacitative function of sanctions is considered below in a model in which the amount of harm individuals cause each period that they are free is not influenced by the threat of sanctions (so as to abstract from the role of sanctions as a deterrent).2 The model is initially examined assuming that an individual's dangerousness (i.e., the harm he will do if free) remains the same each period of his life, and that the sanction is imprisonment. In this case, it is optimal to imprison an individual if his dangerousness exceeds a threshold equal to the per period social cost of imprisonment. Moreover, if it is optimal to imprison an individual at all, it will be best to do so for life. The optimal probability of apprehension is also determined. The model is then extended in several ways. It is first supposed that the dangerousness of individuals declines with age. In this case, it is again optimal to imprison individuals if their dangerousness exceeds the per period cost of imprisonment, but it is optimal to release them if their dangerousness later falls below the threshold. It is next supposed that the dangerousness of individuals declines with time spent in prison due to a rehabilitative effect. In this case, it is optimal to imprison individuals beginning at a lower threshold of dangerousness than the per period cost of imprisonment (imprisonment is now socially more valuable) and to release them if their dangerousness becomes sufficiently low. Finally, it is supposed that a choice can be made between imprisonment and the death penalty, and the optimal choice is discussed.

Taxation and liability are compared as means of controlling harmful externalities, with a view toward explaining why the use of liability predominates over taxation. Taxation suffers from a disadvantage in the analysis: because taxes do not reflect all the variables affecting expected harm, inefficiency results, whereas efficiency under liability requires only assessment of actual harm. However, liability also suffers from a disadvantage: incentives are diluted because injurers escape suit. Joint use of taxation and liability is examined, and it is shown that liability should be employed fully, with taxation taking up the slack due to escape from suit.

A theoretical model of deterrence is studied in which the imposition of nonmonetary (as opposed to monetary) sanctions is socially costly. It is therefore desirable that the system of sanctions be designed so that sanctions are imposed infrequently. If courts possess perfect information, the optimal system is such that sanctions are never imposed-all who can be deterred will be--but, realistically, courts' information will be imperfect and sanctions will be imposed.

It is often true that a manager's opinions about events relevant to production are valued but are not fully known by others. This note suggests that in such circumstances there may be a problem with production. Consider a competitive equilibrium in a standard Arrow-Debreu model of an economy. In such an equilibrium production decisions are guided by prices and, in particular, by contingent commodity prices (which in fact may be implicit in stock market prices). Moreover, in such an equilibrium the managers of production processes play a strictly passive role since complete instructions for production are implicit in the criterion of profit maximization.' However, if the probabilistic beliefs of the managers are valued but are not fully known by the other agents in the economy, then it seems that these agents might well prefer to have the managers play an active role in making production decisions. In other words, it seems that profit maximization with respect to contingent commodity prices may encourage managers to act contrary to what would be the best wish of others, and consequently that the absence of markets in certain contingent commodities might not be undesirable.2 Our discussion of this issue will make reference to a simple example. An economy with many identical individuals and few identical managers uses seed to produce wheat which may be grown in two regions, A and B. Managers decide where to plant the seed. The wheat harvest is uncertainit is either positive or zero-depending on which of the two possible states of nature, a and ,B, occurs. This is described in Table 1, where si is the amount of seed planted in region i and f is the usual type of production function (f' > 0, f < 0). Let us suppose for simplicity that consumers alone determine prices in competitive equilibrium, that is, the few managers have only a negligible impact on the prices. Assume initially that consumers have fixed beliefs, independent of those which the managers might have. Specifically, assume that consumers believe the state a will occur with probability a. Then, since a competitive equilibrium in which there are markets for contingent wheat is Pareto efficient, it must in this case maximize expected utility of consumers. Consequently, if each consumer's endowment consists of one unit of seed and his von Neumann-Morgenstern concave utility function U(.) depends only on consumption of wheat, the problem solved by the market is to maximize expected utility:

Optimal enforcement of law is examined in a model with specific enforcement effort--effort devoted toward apprehending individuals who have committed a single type of harmful act--and general enforcement effort--effort devoted toward apprehending individuals who have committed any of a range of harmful acts (a police officer on patrol, for instance, is able to apprehend many types of violators of law). If enforcement effort is specific, optimal sanctions are extreme for all acts. If enforcement effort is general, however, optimal sanctions rise with the harmfulness of acts and reach the extreme only for the most harmful acts.

Because uncertainty often enters into economic transactions when payment is deferred, it may be advantageous to make the amount of payment depend on the occurrence of uncertain events. This general method of accomplishing risk-sharing is studied and its relevance is discussed in two cases: (1) uncertainty over the rate of inflation and cost-of-living escalators; (2) uncertainty over the exchange rate and foreign currency payment plans.

This article surveys the theory of the public enforcement of law—the use of public agents (inspectors, tax auditors, police, prosecutors) to detect and to sanction violators of legal rules. We first present the basic elements of the theory, focusing on the probability of imposition of sanctions, the magnitude and form of sanctions, and the rule of liability. We then examine a variety of extensions of the central theory, concerning accidental harms, costs of imposing fines, errors, general enforcement, marginal deterrence, the principal-agent relationship, settlements, self-reporting, repeat offenders, imperfect knowledge about the probability and magnitude of fines, and incapacitation.