Suppose a treacherous stretch of road winds through Deadman's Canyon for 5 miles.A highway department study estimates that better lighting would reduce the traffic fatality rates as follows: $$\begin{array} { c c c }
\text { Number of lights } & \text { Estimated deaths per year } & \text { Total installation cost (in millions) } \
0 & 3 & \$ 0 \mathrm {~m} \
1 & 2 & \$ 3 \mathrm {~m} \
2 & 1.5 & \$ 7 \mathrm {~m} \
3 & 1.2 & \$ 12 \mathrm {~m} \
4 & 1 & \$ 18 \mathrm {~m} \
5 & 0.9 & \$ 25 \mathrm {~m}
\end{array}$$
According to the basic rule for allocating crime control resources,the optimal amount of crime control occurs when

Question

Suppose a treacherous stretch of road winds through Deadman's Canyon for 5 miles.A highway department study estimates that better lighting would reduce the traffic fatality rates as follows: $$\begin{array} { c c c } 
\text { Number of lights } & \text { Estimated deaths per year } & \text { Total installation cost (in millions) } \
0 & 3 & \$ 0 \mathrm {~m} \
1 & 2 & \$ 3 \mathrm {~m} \
2 & 1.5 & \$ 7 \mathrm {~m} \
3 & 1.2 & \$ 12 \mathrm {~m} \
4 & 1 & \$ 18 \mathrm {~m} \
5 & 0.9 & \$ 25 \mathrm {~m}
\end{array}$$
According to the basic rule for allocating crime control resources,the optimal amount of crime control occurs when

Quizplus · Accepted Answer

The basic rule for allocating crime control resources states that the optimal amount of crime control occurs when the marginal benefits of reduced crime equal the marginal cost of crime reduction. In this case, the estimated deaths per year decrease as the number of lights increases, but the cost of installing the lights also increases. The optimal amount of crime control would be when the marginal benefit of adding an additional light equals the marginal cost of installing the light. This occurs at two lights, where the estimated deaths per year decrease from 2 to 1.5 at a cost increase of $4 million. Adding a third light only decreases the estimated deaths per year from 1.5 to 1.2 at a cost increase of $5 million, which is not an equal marginal benefit and marginal cost. Therefore, the best choice would be to install two lights.

Suppose a Treacherous Stretch of Road Winds Through Deadman's Canyon