Each potential user of the Phoenix River Bridge is willing to pay up to $299 per crossing, provided there are no other cars to slow him down. When there are more cars, willingness to pay goes down. Specifically, when there are N cars per day on the bridge, each user is willing to pay up to ($300 − N2) to cross.
a. In terms of N, what is the social gain from the existence of the bridge?
b. If there is no bridge toll, how many people cross per day and what is the social gain?
c. What is the optimal number of bridge crossings per day? (To answer this question, you will need either some calculus or some patience with trial and error.)
d. If there is a bridge toll of $T, how many people cross per day? (Answer in terms of T.)
e. What is the optimal bridge toll? How much social gain results when this toll is set? Who gets the benefits?