Chapter 24, Problem 5DQ

To determine

The minimum time saving in the toll lane to make it worthwhile for a motorist to pay the toll.

Concept introduction:

Congestion:

Congestion is defined as the slow movement of vehicles or traffic jams on the road due to large numbers of vehicles at the same time.

Toll:

The toll is defined as the tax or the fee collected from the vehicle’s driver for using the roads, in order to maintain them in better condition and control congestion.

Explanation:

• It is given that the suburb is connected through a single two-lane road. One lane has a toll of $5 for the trip while the other lane has no toll. Everyone’s time worth is $20 per hour.

• This means that the lane that has no toll will face congestion. However, it depends on the opportunity cost of congestion. If someone waits for 1 hour in the lane with no toll and his opportunity cost of that hour is $20 then he loses $15, if there is no waiting time in the other lane. This is because he might have used the other lane by paying $5 as toll and save his one-hour time. Thus, wage equals to $20.

Given,

Money earned in 1 hour is $20.

Money left after paying toll is $15.

Since, $20 can be earned in 1 hour. So, $15 can be earned in 45 minutes $\left(\frac{\$15}{\$20}\times 60\text{minutes}\right)$. Hence, the minimum time saving in the toll lane must be $\left(60-45\right)$ 15 minutes to make it worthwhile for a motorist to pay the toll.