The demand equation for crossing the G.W.Bridge in New York City is P = 50-0.000

Question

The demand equation for crossing the G.W.Bridge in New York City is P = 50-0.0001Q where P is the toll at the bridge and Q is the number of vehicles that cross the bridge every day.
a. Compute the toll that would maximize revenue for the state of New York. At this toll, how many cars would cross the bridge?
b. What is the price elasticity at this toll? Explain your answer.
c. Also illustrate this price/quantity combination in a graph with demand curve and marginal revenue curve.
d. Suppose the company in charge of the maintenance of the bridge successfully negotiates a 20% increase in its annual fee. The State of New York hires you to advise them how to cover this cost. Would you advise them to raise the toll you computed in part a)? (Yes, or No, explain your answer). Would you advise them to raise revenue some other way? Explain your answer.

Explanation / Answer

revenue =P*Q =50Q-0.0001Q^2 for max revenue d (revebue)/dQ =0 hence 50 -0.0002Q =0 hence Q =250000 q =10000p dq/dp =10000 at max revenue Q =250000 p =25 hence elasticity =(dq/dp)*(P/Q) = 10000*25/250000 ............. i will not advise them to raise the price as the price increases after equilibrium price revenue decreases.. they can take toll for some more years

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