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Let B(g, P) represent the net benefit function of extramarital affairs, which is the difference between the benefits from affairs and the costs of effort devoted to the affairs. The benefit from affairs is assumed to be strictly concave in the level of affairs. The cost associated with the effort devoted to affairs reduces the net benefit. Thus B(g, P) increases with P but decreases with g.

This model setup is very similar to that in Tsur and Zemel (1998) except that I address completely different issues and the net benefit function has different properties. Tsur and Zemel analyze how the threat of occurrence of environmental catastrophes affects optimal pollution control. Their analysis is carried out via a method they call “the hδ-method”, which characterizes the dynamic behavior of the optimal state process without actually solving for it. The idea behind the method is as follows. Since the dynamic optimization problem is autonomous, the optimal state process associated with V(P) must evolve monotonically in time, and the optimal pre-event state process associated with V(P) must approach a steady state. The method identifies whether a state level P can be an optimal steady state by comparing steady state policies with small variations from them.

Tsur and Zemel discuss three types of tragic events with different post-event value functions. For the first type, catastrophes reduce social welfare to zero. For the second type, the tragic event can occur only once, and the economic activity will continue after a penalty is paid. For the third type, the tragic event can repeat over and over again, and the economic activity will continue after a penalty is paid each time after the event occurs. They show that for the last two types, risk induces less pollution under the conditions that both the hazard-rate and penalty are non-decreasing functions of the pollution level.

For the extramarital affairs problem I address in this paper, the agent would be punished if caught. Thus, getting caught is a tragic event for the agent. Except extreme cases, the agent’s life will continue after he or she is punished for affairs. Adultery may be committed only once, but may be committed many times. Therefore, the extramarital affairs problem is similar to the last two types of tragic events in Tsur and Zemel’s model.

Since my dynamic optimization model is very close to Tsur and Zemel, and I use the same notations on purpose, I can apply Tsur and Zemel’s analytical results to the extramarital affairs problem. However, since the value function in Tsur and Zemel’s model is a decreasing function with the state variable, and the value function in my model is an increasing function with the state variable, the conclusions are different. The difference is demonstrated with the recurrent case as follows.

In my model, B(g, P) increases with P, thus L(P) is a strictly increasing function and L(P) > 0 for any value of P. Both the punishment and risk functions are non-decreasing with P, which implies [ψ(P)λ(P)]′ ≥ 0. Then the sign of L e (P) depends on the relative magnitudes of L(P) and [ψ(P)λ(P)]′. The level of affairs plays three roles here. It increases the value function, but in the meantime it also increases the risk of getting caught and the punishment if caught, and thus increases the expected loss ψ(P)λ(P). Then facing the risk of getting caught, the agent would make decisions by comparing the marginal net benefit and marginal expected loss.

If L(P) > [ψ(P)λ(P)]′, then L e (P) > 0 and it is impossible that P is lower than P^$\stackrel{}{\mathrm{<span\; style="font-size:14px;">P</span>}}$$\stackrel{<span\; style="font-size:14px;">^</span>}{}$. In this case, even though the agent knows that he or she would be punished if caught, as long as the marginal net benefit from affairs is bigger than the marginal expected loss, the agent would not reduce his or her effort in affairs because of the risk. If L(P) > [ψ(P)λ(P)]′, then L e (P) < 0 and it is impossible that P is higher than P^$\stackrel{}{\mathrm{<span\; style="font-size:14px;">P</span>}}$$\stackrel{<span\; style="font-size:14px;">^</span>}{}$. That is, if the marginal expected loss is larger than the marginal net benefit from affairs, then the agent will induce effort in affairs.

The efficient level of P should be determined based on the marginal social benefits and marginal social costs of adultery reduction. It is unlikely to be zero for the same reason that it is inefficient to keep pollution level at zero. This topic is beyond the scope of the present paper because I study a private optimization problem. This private optimization can hardly lead to a socially efficient outcome because the market under study is far from being perfect.

I try to explore how to reduce adultery and achieve the efficient level of adultery reduction. I assume that society has determined the optimal amount of adultery reduction outside the model. Suppose the efficient amount of adultery is P S , as shown in Fig. 1. In order to achieve this efficient level, according to my theoretical analysis, the marginal expected loss at this level must be higher than the marginal net benefit from affairs at this level. Therefore, there is a need to make the marginal expected loss (MEL) significantly higher than zero, and make it either increasing with the level of adultery as shown by MEL1 or constant as shown by MEL2. A downward sloping MEL curve might intersect with the MB curve at P S , but the equilibrium, for obvious reason, is not stable. There are two ways to make the marginal expected loss positive and either increasing or constant with the level of adultery. One is through changing the probability function and the other is through changing the punishment function. Since these two functions can be controlled by policies and laws, then a well-designed legal punishment scheme can effectively reduce the effort devoted to adultery.

If punishment for adultery is fixed regardless of the level of adultery, then the marginal expected loss is zero. Given a zero marginal expected loss, the private optimal level of adultery is P p . Thus a fixed punishment will lead to two possible outcomes: if the fixed punishment is prohibitly high for the agent, he or she will not commit adultery at all; if the fixed punishment is not high enough to completely deter him or her to commit adultery, he or she will do it all the way up to the level of P p . That is, he or she will devote more effort than the social optimal amount to commit adultery at a level that is higher than the socially efficient level.

Although adultery has been treated as a crime in many societies, the enforcement of the adultery laws is difficult and the prosecution of offenders is rare. In the absence of legal punishment, the punishment from spouses in the form of losing trust and love or divorce is the major means to prevent affairs. This kind of punishment, however, will not effectively reduce extramarital affairs because it tends to be fixed regardless of the level of adultery. This may help to explain why extramarital affairs are a common phenomenon in most societies even though punishment exists.

Extramarital affairs should be punished for a number of reasons. First, the marriage contract explicitly pronounces that the husband and wife will be faithful to each other, thus the individuals who breach the marriage contract should be penalized. Second, the innocent spouses who are damaged by adultery should be compensated. Third, extramarital affairs have negative externalities not only on the spouses and children, but also on other people who dislike extramarital affairs for variety of reasons, thus punishment is needed to force adulterers to internalize the negative externalities (Rasmusen 2002).

I have explained that the punishment from the family, which tends to be fixed regardless of the level of adultery, will not effectively reduce extramarital affairs. Then legal punishment is needed to achieve social efficiency. Legal punishment can take many forms. No matter which form it takes, my model suggests that the punishment scheme should be designed in the way that makes the adulterer’s expected loss increase with the level of adultery at an increasing or constant rate. Adultery laws used to be an important means to punish adultery, but they are no longer enforced in most societies. I now discuss another form of punishment—the use of fault (breach) as a consideration in award of alimony.

As argued by Posner (1992), a fault ground may have a substantive purpose in penalizing inefficient behavior. Because the cost for the innocent spouse to monitor an adulterer at all times is high, an adulterer imposes an externality on the innocent spouse. In this case, legal punishment in the form of paying larger alimony or divorce settlement can elicit the efficient amount of adultery. In addition, Landes (1978) and Brinig and Crafton (1994) both stress that alimony, as a compensation for the wife for the opportunity cost she incurs by entering and investing in the marriage, is a means of promoting efficient resource allocation by encouraging wives to make marital-specific investment. Landes provides empirical evidence that the exclusion of alimony in the event of divorce and exclusion of fault as a relevant consideration in the determination of property settlements both substantially reduce the incentive to marry and marital-specific investments. Brinig and Crafton also provide empirical evidence that no-fault has caused a fewer marriages, less marital-specific investment and more opportunistic behavior. They suggest that one way to discourage adultery is to “place the burden of dissolution squarely on the shoulders of the responsible party.”

Currently in practice, the amount of alimony awarded is determined based on a number of factors, including the duration of marriage, number of children and the husband and wife’s relative earning power. Adultery is also an important judicial factor that is used to determine alimony awards in half the states of the US. However, judicial determination of alimony awards does not differentiate with the level of adultery. It basically treats a prolonged affair the same as being unfaithful only once; that is, the part of alimony associated with adultery is fixed regardless of the level of adultery.

Since alimony awards can be used to compensate a wife for the opportunity cost she incurs by entering and investing in the marriage, and can also be used to punish an adulterer and compensate the innocent spouse for the damages caused by the adultery, I would suggest to divide alimony into two parts: one part is determined according to the wife’s opportunity cost, and the other part is determined based on the level of adultery. My model implies that the part of alimony associated with adultery should be designed in the way that makes the adulterer’s expected loss increase with the level of adultery at an increasing or constant rate. Under such a scheme, an adulterer who is involved in a prolonged affair would pay a higher price than if he or she is unfaithful once. The total alimony awarded should be equal to the sum of the two parts. In cases where a husband commits adultery, the wife would be awarded more alimony than if he has not done so, and would receive more alimony if he commits a higher-level adultery than if he commits a lower-level one. In cases where a wife commits adultery, the wife would be awarded less alimony than if she has not done so, and might receive none or even negative amount of alimony if she commits a high-level adultery. A negative alimony means that she would have to transfer payment to the husband to compensate for the damages.

The expected loss depends on two functions: the probability of getting caught and punishment. By changing either function, the expected loss will change. I have discussed how to change the punishment function by holding the probability function constant. The other way to reduce adultery is through changing the probability function, which can be done by increasing the effort of monitoring with the level of adultery. This way would be more difficult to implement, and it will not work if adultery is not a determinant of alimony awards and property division, or if the adulterer has no property to distribute on divorce.

My theoretical analysis shows that the existence of punishment does not necessarily deter extramarital affairs unless the marginal expected loss is larger than the marginal net benefit from affairs. Punishment from the family, which tends to be fixed, cannot effectively reduce extramarital affairs. This may help to explain why extramarital affairs are a common phenomenon in most societies even though punishment exists. However, the fact that extramarital affairs have not been effectively reduced does not mean that there is no way to reduce adultery. In order to reduce adultery, legal punishment is needed. Such a legal punishment can take many forms. No matter which form it takes, an effective punishment scheme should have differentiated punishment for different levels of adultery. Since adultery laws are rarely enforced, I focus on another form of punishment—alimony. Alimony awards can be used as a means to compensate for a wife’s opportunity cost, it can also be used to punish adulterer for breaching the marriage contract and to compensate the innocent spouse for damages caused by the adultery. I suggest that the part of alimony associated with adultery be designed in the way that makes the adulterer’s expected loss increase with the level of adultery at an increasing or constant rate.