Problem 19-13 There is a road between the suburbs and downtown. The road becomes
ID: 1122704 • Letter: P
Question
Problem 19-13
There is a road between the suburbs and downtown. The road becomes congested at rush hour. As long as fewer than 100 people use the road at rush hour, the trip takes 30 minutes. When the 101st person enters the road, everyone has to slow down and the trip now takes 31 minutes. People value their time at $6 per hour (i.e., $0.10 per minute) and so a 30 minute trip costs $3.
Instructions: Round your answers to two decimal places.
a. The private cost of one of the 100 individuals using the road is $ . The total private cost of 100 people using the road is $ . The total social cost of 100 people using the road is $ .
b. The total social cost of 101 people using the road is $ . The private cost of using the road for the 101st individual is $ . The external social cost of the 101st person using the road is $ .
Explanation / Answer
a). Private Cost of one individual if 100 individuals use the road = no. of min * cost per minute = 30 * 0.10 = $3
Total private cost of 100 people using the road = cost per person using the road * no. of people = 3 * 100 = $ 300
Total Social cost of 100 people using the road = 0 (since no one has to slow down and there is no extra cost involved)
b). The private cost for 101st individual is = 0.1 * 31 = $3.1
Total social cost of 101 people using the road = 3.1 * 101 = $313.1
External social cost = Extra cost incurred due to overcrowding = New Total Cost - Old Total Cost = 313.1 - 300 = $13.1