Each morning during rush hour, 10,000 people want to travel from New Jersey to New York City. If a..

Each morning during rush hour, 10,000 people want to travel
from New Jersey to New York City. If a person takes the commuter train, the
trip lasts 40 minutes. If x thousand people per morning drive to New York, it
takes 20 + 5x minutes to make the trip. This problem illustrates a basic fact
of life: If people make their decisions individually, they will cause more
congestion than is actually necessary!

a. Show that if people make their decisions individually, an
average of 4000 people will travel by road from New Jersey to New York. Here
you should assume that people will divide up
»

Each morning during rush hour, 10,000 people want to travel
from New Jersey to New York City. If a person takes the commuter train, the
trip lasts 40 minutes. If x thousand people per morning drive to New York, it
takes 20 + 5x minutes to make the trip. This problem illustrates a basic fact
of life: If people make their decisions individually, they will cause more
congestion than is actually necessary!

a. Show that if people make their decisions individually, an
average of 4000 people will travel by road from New Jersey to New York. Here
you should assume that people will divide up between the trains and roads in a
way that makes the average travel time by road equal to the travel time by
train. When this “equilibrium” occurs, nobody has an incentive to switch from
the road to the train or vice versa.

b. Show that the average travel time per person is minimized
if 2000 people travel by road.

»