Answer to Question #274119 in Microeconomics for Monten

Question

Suppose that the inverse demand for San Francisco cable car rides is p = 10 - Q/1,000, where p is the price per ride and Q is the number of rides per day. Suppose the objective of San Francisco's Municipal per day. Authority (the cable car operator) is to maximize its revenues. What is the revenue maximizing price? Suppose that San Francisco calculates that the city's businesses benefit from tourists and residents riding on the city's cable cars at $4 per ride. If the city's objective is to maximize the sum of the cable car revenues and the economic impact, what is the optimal price?

Answer 1

Solution:

Revenue maximizing price:

Derive TR:

TR = P x Q

TR = (10 – Q/1000) x Q = 10Q – Q²/1000

Profit maximizing price is where MR = MC

Derive MR:

TR = 10Q – Q²/1000

MR = $\frac{\partial TR} {\partial Q}$

= 10 – $\frac{Q} {500}$

MC = 0

Set MR = MC

10 – $\frac{Q} {500}$ = 0

Q = 5000 rides

 

Profit maximizing price = 10 – 5,000/1,000 = 10 – 5 = 5

Profit maximizing price = $5

 

The optimal price = 3