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: $$\begin{array} { c c c }
\text { Number of lights } & \text { Estimated deaths per year } & \text { Total installation cost (in millions) } \
0 & 3 & \$ 0 \mathrm {~m} \
1 & 2 & \$ 3 \mathrm {~m} \
2 & 1.5 & \$ 7 \mathrm {~m} \
3 & 1.2 & \$ 12 \mathrm {~m} \
4 & 1 & \$ 18 \mathrm {~m} \
5 & 0.9 & \$ 25 \mathrm {~m}
\end{array}$$
The fifth light is estimated to reduce the fatality rate by ___ at a marginal cost of $__ per life saved.

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: $$\begin{array} { c c c } 
\text { Number of lights } & \text { Estimated deaths per year } & \text { Total installation cost (in millions) } \
0 & 3 & \$ 0 \mathrm {~m} \
1 & 2 & \$ 3 \mathrm {~m} \
2 & 1.5 & \$ 7 \mathrm {~m} \
3 & 1.2 & \$ 12 \mathrm {~m} \
4 & 1 & \$ 18 \mathrm {~m} \
5 & 0.9 & \$ 25 \mathrm {~m}
\end{array}$$
The fifth light is estimated to reduce the fatality rate by ___ at a marginal cost of $__ per life saved.

Quizplus · Accepted Answer

The fifth light reduces the fatality rate from 1 to 0.9, which is a reduction of 0.1. The marginal cost is the difference in cost between 4 and 5 lights, which is $25m - $18m = $7m. The cost per life saved is $7m / 0.1 = $70m.

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