Question

Suppose that the inverse demand for San Francisco cable car rides is: p=15-(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 revenues. What is the? revenue-maximizing price?

The? revenue-maximizing price is p=$7.50

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 ?$5 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?

Answer 1

Here we need to optimal price which increases total revenue

So, we need to express the inverse function in terms of Q

Q = (15-P)*1000

Now using the solver in excel we can set TR to be maximum by changing P

P	Q	TR
7.5	75000	562500

or

By substituting value of price, we can finnd that TR gets maximum at price = 7.5

P	Q	TR
0	150000	0
0.5	145000	72500
1	140000	140000
1.5	135000	202500
2	130000	260000
2.5	125000	312500
3	120000	360000
3.5	115000	402500
4	110000	440000
4.5	105000	472500
5	100000	500000
5.5	95000	522500
6	90000	540000
6.5	85000	552500
7	80000	560000
7.5	75000	562500
8	70000	560000