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. $\begin{array}{ccc}
\begin{array}{c}
\text { Number of } \
\underline { \text { Detectives Assigned }}
\end{array} & \begin{array}{c}
\text { Number of } \
\underline { \text { Murders }}
\end{array} & \begin{array}{c}
\text { Number of } \
\underline { \text { Burglaries }}
\end{array} \
0 & 20 & 100 \
1 & 16 & 60 \
2 & 13 & 30 \
3 & 11 & 10 \
4 & 10 & 0
\end{array}$
Suppose the police department has $160,000 to spend on detectives.The allocation of detectives which results in the greatest social benefit is to assign

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. $\begin{array}{ccc}
\begin{array}{c}
\text { Number of } \
\underline { \text { Detectives Assigned }}
\end{array} & \begin{array}{c}
\text { Number of } \
\underline { \text { Murders }}
\end{array} & \begin{array}{c}
\text { Number of } \
\underline { \text { Burglaries }}
\end{array} \
 0 & 20 & 100 \
1 & 16 & 60 \
2 & 13 & 30 \
3 & 11 & 10 \
4 & 10 & 0
\end{array}$
Suppose the police department has $160,000 to spend on detectives.The allocation of detectives which results in the greatest social benefit is to assign

Quizplus · Accepted Answer

To maximize social benefit, we need to allocate detectives in a way that the marginal benefit of the last detective is equal to the marginal cost:
For murder prevention:

- MB = $20,000
- MC = $40,000

For burglary prevention:

- MB = $1,000
- MC = $40,000

Therefore, we should allocate detectives in a way that the marginal benefit of one less murder prevention detective is equal to the marginal benefit of one less burglary prevention detective:

$20,000 = $1,000
40 - x = y

Solving for x and y:

x = 3.6
y = 36.4

We need to allocate 3 detectives to murder prevention and 1 detective to burglary prevention to maximize social benefit. The total cost of this allocation is $160,000, which is exactly how much the police department has to spend on detectives.

A Police Department Is Trying to Allocate Crime Control Resources