CRIMINAL LAW
Fighting Crime
Suppose a particular crime is always inefficient: it harms the rest of society $10,000 more than it benefits the criminal. Every time an offender is caught, he or she is tried, convicted, and imprisoned; the total (social) cost of trials and punishment is $100,000 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.
A city is considering hiring additional policemen dedicated to detecting this particular crime. This change would increase the fraction of offenders who get caught from 15% to 20%.
a. Suppose this increase in detection would result in a decrease in the number of crimes committed from 1,000 a year to 700 a year.
i. Calculate the effect that hiring the new policemen would have on the social cost of crimes committed.
ii. Calculate the effect it would have on the cost of trying and punishing offenders.
iii. From an efficiency point of view, what is the most that the city should be willing to pay for the new policemen?
b. Now suppose instead that the increase in detection would decrease the number of crimes committed from 1,000 a year to 900 a year.
i. Calculate the effect that hiring the new policemen would have on the social cost of crimes committed.
ii. Calculate the effect it would have on the cost of trying and punishing offenders.
ii. From an efficiency point of view, is there any positive amount that the city should be willing to pay for the new policemen?
c. Defend the following statement applied to this type of crime:
"Even when detection is cheap, more detection is only efficient if the supply of crimes is elastic."