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: $$\begin{array} { c c c }
\text { Number of lights } & \text { Estimated deaths per year } & \text { Total installation cost (in millions) } \
0 & 3 & \$ 0 \mathrm {~m} \
1 & 2 & \$ 3 \mathrm {~m} \
2 & 1.5 & \$ 7 \mathrm {~m} \
3 & 1.2 & \$ 12 \mathrm {~m} \
4 & 1 & \$ 18 \mathrm {~m} \
5 & 0.9 & \$ 25 \mathrm {~m}
\end{array}$$
Suppose that experts have estimated the statistical value of a life saved to be $8m.The marginal benefit of the third light installed is ____ and the marginal cost is ____.Therefore the third light ____ be installed.

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: $$\begin{array} { c c c } 
\text { Number of lights } & \text { Estimated deaths per year } & \text { Total installation cost (in millions) } \
0 & 3 & \$ 0 \mathrm {~m} \
1 & 2 & \$ 3 \mathrm {~m} \
2 & 1.5 & \$ 7 \mathrm {~m} \
3 & 1.2 & \$ 12 \mathrm {~m} \
4 & 1 & \$ 18 \mathrm {~m} \
5 & 0.9 & \$ 25 \mathrm {~m}
\end{array}$$
Suppose that experts have estimated the statistical value of a life saved to be $8m.The marginal benefit of the third light installed is ____ and the marginal cost is ____.Therefore the third light ____ be installed.

Quizplus · Accepted Answer

The marginal benefit of the third light is the reduction in deaths from 2 lights to 3 lights, which is 0.3 lives saved, valued at $8m per life, totaling $2.4m. The marginal cost is the increase in cost from 2 lights to 3 lights, which is $5m. Since the marginal cost exceeds the marginal benefit, the third light should not be installed.

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