1. Car Thieves

After a wild crime spree, stealing cars in Maryland, Adam and XiXi are brought to justice by the University of Maryland campus police. The judge goes easy on them, giving them just a warning if they agree to advise the State of Maryland on crime prevention and efficient legal systems.

Adam and Xixi collect information on car theft, their expertise. When it occurs in Maryland, it causes $40,000 in harm to its victims, even though the criminal only stands to gain $10,000 in benefit (by selling the stolen car for parts). 

Every time a car thief is caught, he or she is tried, convicted, and imprisoned; the total (social) cost of trials and punishment is $200,000 per criminal caught. Recall that the aim of criminal law is to minimize the sum of three things: (1) the social cost of the crimes that are committed, (2) the cost of detection, and (3) the cost of trying and punishing the offenders who get caught.

Adam and Xixi tell the state to consider hiring more police policemen who would specialize in detecting car theft. They estimate that doing so would increase the fraction of thieves who get caught from 15% to 20%.

a. Adam's Analysis. Car thieves hear about the extra police and they are scared. According to Adam, the increase in the police force would cause the number of car thefts to fall from 5,000 thefts to 200 thefts.

1.) Calculate the effect that hiring the new policemen would have on the social cost of crimes committed.

2.) Calculate the effect it would have on the cost of trying and punishing offenders.

3.) From an efficiency point of view, what is the most that the city should be willing to pay for the new policemen?