Commuters from the West Bank, across from New Orleans, are identical. They have

Question

Commuters from the West Bank, across from New Orleans, are identical. They have two routes from the West Bank to Uptown, either over the Crescent City Connection (C) or over the Huey P. Long Bridge (H). The average trip length of a commuter depends on how many people choose that route:
ACC (n) = 10 + n/100 and ACH(n) = 20 + n/300;
where time is measured in minutes. Suppose 5000 cars make this trip daily. Each driver ignores his or her own effect on the average trip time of commuters choosing the same route.
a. Calculate the equilibrium number of cars commuting by each route.
b. Suppose you are hired as a traffic consultant to improve traffic patterns among commuters. How should these 5000 cars be allocated over the two routes in order to minimize the total amount of time cars are commuting?
c. Devise a toll on just one bridge (the tolls are given in “minutes equivalents” -- e.g., you could impose a toll worth two minutes of travel time) to implement the efficient allocation of traffic (assume no costs of collecting tolls).

Explanation / Answer

a. For the equilibrium, equate ACC (n) to ACH (n); i.e: 10 + n/100 = 20 + n/300 and solve for n. b. If the 'n' you get from 'a' is smaller than 5000 then subtract it from 5000 and divide your answer by ACC to get how many cars to send there. After that, divide that same number by ACH to get how many cars to send there. c. Assuming you impose a toll of 4 mins, you divide ACC or ACH by 4 to get how many cars you would want going through whichever route.

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