Question

A city is considering hiring additional police dedicated to detecting a particular crime. This change would increase the fraction of offenders who get caught from 15% to 25%. Suppose this increase in detection would result in a decrease in the number of crimes committed from 800 per year to 600 per year. The social cost of each crime is $5,000. The cost of trial and punishment for each criminal is $150,000.

a. Calculate the effect that hiring more police would have on the social cost of crimes committed.

b. Calculate the effect this increase in detection would have on the cost of trying and punishing offenders.

Answer 1

A. Lets compare the total social cost in both of the cases.

Before the increase, there were 800 such crimes and the social cost of each was $5000. So,

Total cost before the increase=800*5000= $4000000

Post increase the number of crimes dropped to 600.

Social cost after the increase=600*5000= $3000000

So, the social cost decreased by 4000000-3000000=1000000 after the increase in police.

B. Before increase, there were 800 crimes and 15% were being caught, meaning 800*15%=120 were being caught.

So, total cost of trying and punishing the offenders=120*150000= 18000000

After the increase in police, there were 600 crimes and 25% got caught. Meaning 600*25%=150 got caught.

So, total cost of trying and punishing after the increase=150*150000= 22500000.

So, the total cost of trying and punishing increased by 22500000-18000000= $4500000 after the increase

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