With price expressed as a function of quantity, the reserved seat demand curve can be
written:
P = $20 - $0.0025Q
Similarly, the number of tickets sold (quantity) can be expressed as a function of
price:
P = $20 - $0.0025Q
0.0025Q = $20 - P
Q = 8,000 – 400P
This simple linear characterization of the firm’s demand curve can be used to
profitably guide production, pricing and promotion decisions.
B.
The Portland Sea Dogs could use the estimated linear market demand curve to
estimate the quantity demanded during the same marketing period for ticket prices in
the range from $5 to $15 per ticket, using $1 increments:
Price
Quantity
TR=P×Q
$5
6,000
30,000
6
5,600
33,600
7
5,200
36,400
8
4,800
38,400
9
4,400
39,600
10
4,000
40,000
11
3,600
39,600
12
3,200
38,400
13
2,800
36,400
14
2,400
33,600
15
2,000
30,000
From the table, the revenue-maximizing ticket price is $10.
This is also the profit-
maximizing ticket price if variable costs and, hence, marginal costs are negligible.
The pricing promotion resulted in declining revenues, and the $7 price results in an
activity level that is above the revenue-maximizing output.
Because the marginal