A police department is trying to allocate crime control resources between murder and burglary.Detectives cost $40,000 each.Suppose that she marginal benefit of one less murder is $20,000 while the marginal benefit of one less burglary is $1,000.The number of murders and burglaries that occur at different levels of detective allocation is shown in the table. $\begin{array}{ccc}
\begin{array}{c}
\text { Number of } \
\underline { \text { Detectives Assigned }}
\end{array} & \begin{array}{c}
\text { Number of } \
\underline { \text { Murders }}
\end{array} & \begin{array}{c}
\text { Number of } \
\underline { \text { Burglaries }}
\end{array} \
0 & 20 & 100 \
1 & 16 & 60 \
2 & 13 & 30 \
3 & 11 & 10 \
4 & 10 & 0
\end{array}$
The marginal benefits of 1,2,3,and 4 detectives being assigned to burglary prevention are

Question

A police department is trying to allocate crime control resources between murder and burglary.Detectives cost $40,000 each.Suppose that she marginal benefit of one less murder is $20,000 while the marginal benefit of one less burglary is $1,000.The number of murders and burglaries that occur at different levels of detective allocation is shown in the table. $\begin{array}{ccc}
\begin{array}{c}
\text { Number of } \
\underline { \text { Detectives Assigned }}
\end{array} & \begin{array}{c}
\text { Number of } \
\underline { \text { Murders }}
\end{array} & \begin{array}{c}
\text { Number of } \
\underline { \text { Burglaries }}
\end{array} \
 0 & 20 & 100 \
1 & 16 & 60 \
2 & 13 & 30 \
3 & 11 & 10 \
4 & 10 & 0
\end{array}$
The marginal benefits of 1,2,3,and 4 detectives being assigned to burglary prevention are

Quizplus · Accepted Answer

The marginal benefit of assigning one more detective to burglary prevention is the difference in the total benefit from burglary prevention with one more detective and the total benefit from burglary prevention with one less detective. The total benefit from burglary prevention is the number of burglaries prevented multiplied by the marginal benefit of preventing one burglary, which is $1,000. So, the marginal benefit of assigning one more detective to burglary prevention is:MB = (Number of burglaries prevented with one more detective) * ($1,000)From the table, we can see that the number of burglaries prevented with one more detective is:1 detective: 100 - 60 = 40 burglaries2 detectives: 60 - 30 = 30 burglaries3 detectives: 30 - 10 = 20 burglaries4 detectives: 10 - 0 = 10 burglariesSo, the marginal benefit of assigning one more detective to burglary prevention is:1 detective: 40 * $1,000 = $40,0002 detectives: 30 * $1,000 = $30,0003 detectives: 20 * $1,000 = $20,0004 detectives: 10 * $1,000 = $10,000Therefore, the marginal benefits of 1, 2, 3, and 4 detectives being assigned to burglary prevention are $40,000, $30,000, $20,000, and $10,000, respectively.

A Police Department Is Trying to Allocate Crime Control Resources