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 first 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 first light is estimated to reduce the fatality rate by ___ at a marginal cost of $__ per life saved.

Quizplus · Accepted Answer

To find the reduction in fatality rate and marginal cost per life saved, we need to calculate the difference in estimated deaths per year and total installation cost between two consecutive options.

For the first option, the reduction in fatality rate would be 3-2 = 1 and the marginal cost per life saved would be (7-3)/1 = 4 million dollars.

For the second option, the reduction in fatality rate would be 2-1.5 = 0.5 and the marginal cost per life saved would be (12-7)/0.5 = 10 million dollars.

For the third option, the reduction in fatality rate would be 1.5-1.2 = 0.3 and the marginal cost per life saved would be (18-12)/0.3 = 20 million dollars.

For the fourth option, the reduction in fatality rate would be 1.2-1 = 0.2 and the marginal cost per life saved would be (25-18)/0.2 = 35 million dollars.

Therefore, the best choice would be the one with the highest reduction in fatality rate per marginal cost per life saved, which is option C: 1 reduction in fatality rate for every 3 million dollars spent.

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