The visible hand in economics

Is policing some crimes optimal?

Posted on: January 15, 2008

When someone gets robbed there are some direct costs and benefits. Firstly, the perpetrator receives the goods and or services, and may also derive some pleasure from the activity itself. Secondly the victim suffers the loss of goods and services, and is hurt by the fact they have become a victim.

If this crime is reported to the police and solved successfully then there are a number of losers. Society has to pay the police to solve the crime, the criminal loses any goods and has to pay/go to jail, and the victim loses a significant amount of time making statements etc. In some cases, the time cost to the victim turns out to be greater than the benefit from having the crime solved (these are the people that regret having taken their case to the police).

In some cases, this type of outcome is quite common (eg for small traffic accidents), and the only reason people initially go to the police is because they don’t realise how large the effort and time cost will be (often as a result of mis-information). If this is the case, then everyone loses from a crime being reported and solved, implying that it would have been better if the crime was never reported.

However, this logic feels like it has something missing. Why would police be trained to under-sell the costs associated with reporting these crimes unless there was some good reason for it?

In fact I can think of two things that could make policing optimal in such a case:

  1. Social equity concerns. It is important to society that crimes are solved, implying that their is an additional social benefit from solving the crime
  2. The social benefit from the impact on criminal behaviour. If criminals realise that they are going to get caught, they are less likely to commit crimes. If the net social impact of the initial crime is negative (which I suspect it generally is) and the probability of being caught rises with the probability that the victim will report the crime, then this will be welfare enhancing.

Although this explains laws that are enforced even though it is not in the interest of any of the agents that are involved directly, there are other crimes that aren’t policed (e.g. obtaining some types of illegal substances). According to our little discussion the full social costs of enforcing these laws is greater than the social benefits. This raises two questions: Is the decision over what laws to enforce made efficiently? If the law is not going to be enforced, why does it exist?

9 Responses to "Is policing some crimes optimal?"

On the last question, it could be that changing the law itself is costly (all those pointless debates in parliament …) so the cheaper thing to do is just leave the law on the books but tell the police not to enforce it.

[…] prostitutes, police and pimps 15 01 2008 Matt observes that some crimes are not worth reporting, and it is probably sub-optimal for the police to do […]

Also some crimes are worth greater policing. The cost of 3,000 deaths on UK roads means punishing bad driving may have a high economic reward of less accidents and lower death rates.

Why is that whenever I report my bike is stolen, the only thing the police say is “why did you buy an expensive bike?” Why didn’t you spend £100 on a lock – they make it very clear they have no intention of pursuing it.


Hi aaron,

Old transaction costss, they should do the trick. Does that mean that the law was optimal when it was formed, but isn’t now? I guess so 😛

Hi Tejvan,

There are definitely crimes that are worth reporting, but the purpose of this blog piece was to talk about crimes where people end up finding them not worth reporting. As their is a postivite externality associated with them reporting the crime (in so far as its impact on society), if the police accurately portrayed the difficulties associated with reporting these types of crimes we would have a suboptimal level of reporting. As a result, police make it sound easier to report a crime than it is, to try to enduce a level of reporting closer to the social optimum.

Your post just popped up under my “related” tag so I came for a look.

The biggest mistake you are making is that you are confusing socially normalized costs with individualized costs. The macro and micro level analysis are separate. The fact that the cost/benefit calculus may result in a different conclusion depending on the unit is expected. The real issues is a value judgment. What good are your trying to promote? The social good? Or are your trying to increase the marginal utility of the individual victim or criminal.

I think it is best to abandon an abstract notion of the social good. What is socially optimal is precisely the option that increases the marginal utility of both the victim and the criminal. In plain terms, if both the victim and the criminal are “at peace” with the result, then society has nothing more to say on the matter.

“I think it is best to abandon an abstract notion of the social good. What is socially optimal is precisely the option that increases the marginal utility of both the victim and the criminal”

Not necessarily for two reasons:

1) You can have a socially optimal outcome when one of the parties is worse off – however it involves making value judgments (and assuming some type of cardinal utility as a result).

2) Even if both parties are better off, there could be an externality to the rest of society. The is what is discussed above.

One such externality stems from the prevention of crime – if it is optimal for both the victim and the criminal to ignore the crime, it may create a situation where the criminal has the incentive to victimise someone else. As a result, not dealing with the crime may not be socially optimal, even if it is for the victim and the criminal.

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