Question

A city is considering purchasing automated license plate reader software dedicated to detecting a particular type of crime. This change would increase the fraction of offenders who get caught from 15% to 20%. The social cost of each crime is $10,000. The cost of trial and punishment for each convicted criminal is $100,000. Suppose the increase in detection results in a decrease in the number of crimes committed from 1,000 per year to 700 per year.

Calculate the effect that hiring the new software would have on the cost of trial and punishment: Before: 1,000 * 15% * $100,000 = $15,000,000 After: 700 * 20% * $100,000 = $14,000,000 Net Effect: $1,000,000 reduction in cost of trials and punishment

Answer 1

The effect that hiring the new software would have on the social cost of crimes committed per year:

Before: 1,000 X $10,000 = $10,000,000

After: 700 X $10,000 = $7,000,000

Effect: $3,000,000 reduction in social cost of crime

The effect it would have on the cost of trying and punishing offenders.

Before: 1,000 X 15% X $100,000 = $15,000,000

After: 700 X 20% $100,000 = $14,000,000

Effect: $1,000,000 reduction in cost of trials and punishment

From an efficiency point of view, the most that the city should be willing to pay for the new software is $4,000,000, since this is how much social costs are reduced by having higher detection.