Suppose that the inverse demand for San Francisco cable car rides is p= 10-1000

Question

Suppose that the inverse demand for San Francisco cable car rides is p= 10-1000 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 revenues. What is the revenue-maximizing price? The revenue-maximizing price is p(Enter a numeric response using a real number rounded to two decimal places) The city of San Francisco calculates that the city's businesses benefit from both tourists and residents alike riding on the city's cable cars by $4 per ride. Suppose the city's objective is to maximize the sum of the cable car revenues and the economic impact. What is the optimal price? The price that maximizes the sum of cable car revenues and the economic impact is p=$ . (Enter a numeric response using a real number rounded to two decimal places.)

Explanation / Answer

REVENUE = PQ

= (10-Q/1000)Q

= 10Q-Q^2/1000

MAX TR WRT Q:

DIFFERENTIATE TR WRT Q AND EQUATE TO 0:

dTR/dQ = 10-2Q/1000 = 0

10=2Q/1000

10000=2Q

Q = 5000

p= 10-5000/1000

P = 10-5 = 5

P = $5

TR = 4Q+(10-Q/1000)Q

dTR/dQ = 4+10-2q/1000 = 0

14=2Q/1000

14000 = 2Q

Q = 7000

p = 10-7000/1000

P = 10-7

P = $3

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