Question

Suppose that the inverse demand for San Francisco cable car rides is p=10-(Q/1000), where p is the price per ride and Q is the number of rides per day. Suppose the objective of San​ Francisco's Municipal Authority​ (the cable car​ operator) is to maximize its revenuesL.

What is the​ revenue-maximizing price?

Answer 1

Step-by-step explanation:

Revenue is given by the number of rides per day (Q) multiplied by the price per ride (p):

`r=Q*p=Q*(10-(Q)/(1000)) \\R=10Q-(Q^2)/(1000)`

The number of rides 'Q' for which the derivate of the revenue function is zero is the revenue-maximizing number of rides:

`R(Q)=10Q-(Q^2)/(1000)\\R'(Q) = 0 = 10-(Q)/(500)\\Q=5000\ rides`

The price per ride at an activity of 5000 rides per day is:

`p(5,000) = 10 - (5,000)/(1,000)\\p=\$5`

Therefore, the revenue-maximizing price is $5