The basic economic objection to crime is that a crime is a costly but sterile transaction. It redistributes wealth, which doesn't increase the size of the social pie; and therefore the costs involved in crime‚Äîthe time and other inputs of the criminal, and the defensive measures taken by potential victims‚Äîare a deadweight loss to society.
But notice that the economic definition of crime as a sterile transaction (or coerced transfer payment) does not correspond to the legal definition of crime; in law, a crime is anything that the government forbids on pain of criminal penalties. Victimless crimes tend to be productive transactions, which make the parties better off (at least by their own lights). Attempting to deter or prevent such transactions are likely therefore to reduce the overall social welfare, like other interferences with the operation of free markets. Of course there may be external costs, costs external to the parties to the drug transaction or other victimless crime, that in some cases justify punishment, but this is probably not true in general.
So the first question to consider in assessing the effects of crime on economic welfare is how much of what is criminalized should be. Bribery of officials is, as Becker points out, an interesting mixed case. It is a voluntary transaction with external costs, but sometimes the social benefits exceed those costs, as where the bribe results in circumvention of an inefficient restriction on commercial activity.
Robberies, kidnappings, and other coerced transfers involve a reallocation of resources from productive commercial activities to a zero-sum game of attack and defend. But I am not sure that we should expect this type of criminality to be a simple function of poor prospects for legal employment. If everyone has poor prospects, and is therefore poor, the gains from crime will be meager; both the benefits of crime and the opportunity costs of the criminal (mainly what he could earn in legal employment) will be depressed. Steeply unequal incomes would seem a better explanation for a high crime rate in a poor country, since despite the overall poverty there would be attractive targets for criminals. The high rate of kidnapping in Mexico City seems related to the fact that the city has many wealthy residents as well as many poor ones.
Another factor in high crime rates in poor countries is that it is difficult to finance an effective apparatus for fighting crime. It requires police and judges who are paid enough not to be readily bribable by criminal gangs; in addition, the police must be sufficiently numerous and well-armed to be capable of protecting judges, witnesses, and criminal investigators. So there is a chicken and egg problem: a poor country has difficulty affording the means of preventing crimes rates from skyrocketing, and the high crime rates help to keep the country poor.
It is true that the aggregate expense of even well-paid police and judges is likely to be only a small percentage of GDP even in a poor country. But it is difficult to set a wage scale for a class of workers that is grossly in excess of prevailing wages for work involving similar skills and education.
A possible response to resource limitations on crime fighting is very severe punishment of convicted criminals. The threat of punishment has a deterrent effect, provided the probability of punishment is not negligible; and as Becker long ago pointed out in his famous 1968 article on crime and punishment, making the threat is a lot cheaper than hiring a huge police force. In other words, resources on maintaining a high probability of apprehending and punishing criminals can be economized on, without lose of deterrence, by jacking up the punishment of those who are apprehended; the expected cost of punishment need be no higher. Moreover, the probability of apprehension and conviction can be cheaply enhanced, too, by reducing the procedural rights of criminal defendants. In addition, purging the statute books of victimless crimes, and eliminating foolish regulations that invite bribery to circumvent them, can reduce demands on the criminal justice system and permit refocusing it on the crimes that impose the greatest costs on the society.