Consider a police department trying to decide how to allocate its crime prevention resources between motor vehicle thefts and burglaries. The marginal benefit of one less motor vehicle theft is $20,000, and the marginal benefit of one less burglary is $1,000. Suppose the annual number of motor vehicle thefts and the annual number of burglaries depends on the number of detectives assigned to each type of crime, as shown in the table below. Each detective costs $35,000 each per year, regardless of whether the detective is assigned to motor vehicle thefts or burglaries. Suppose the police department hires 4 detectives and assigns all of them to motor vehicle theft. The marginal benefit of the fourth detective assigned to motor vehicle theft is ______, and the marginal benefit that would have been gained had the detective instead been assigned to burglary is ______.
A)$20,000; $40,000
B)$40,000; $40,000
C)$20,000; $20,000
D)$40,000; $20,000

Question

Consider a police department trying to decide how to allocate its crime prevention resources between motor vehicle thefts and burglaries. The marginal benefit of one less motor vehicle theft is $20,000, and the marginal benefit of one less burglary is $1,000. Suppose the annual number of motor vehicle thefts and the annual number of burglaries depends on the number of detectives assigned to each type of crime, as shown in the table below. Each detective costs $35,000 each per year, regardless of whether the detective is assigned to motor vehicle thefts or burglaries.  Suppose the police department hires 4 detectives and assigns all of them to motor vehicle theft. The marginal benefit of the fourth detective assigned to motor vehicle theft is ______, and the marginal benefit that would have been gained had the detective instead been assigned to burglary is ______.
A)$20,000; $40,000 
B)$40,000; $40,000 
C)$20,000; $20,000 
D)$40,000; $20,000

Quizplus · Accepted Answer

The marginal benefit of the fourth detective assigned to motor vehicle theft is $20,000, as given in the question. 
If the detective had instead been assigned to burglary, the marginal benefit would have been the difference between the benefit of preventing one more burglary and the cost of hiring the detective, which is $1,000 - $35,000 = -$34,000 (negative). Therefore, the police department would have incurred a net loss by assigning the detective to burglary instead of motor vehicle theft. Hence, it is best to allocate all 4 detectives to motor vehicle theft.

Consider a Police Department Trying to Decide How to Allocate