The Maxwell School
Syracuse University
Syracuse University
The market demand curve for a good originates from what individuals are willing to pay (W2P) for the good. Conceptually, it is constructed as follows: (1) start with a high price; (2) ask all potential buyers how many items they would be willing to buy at that price; (3) make a note of that price and quantity; (4) decrease the price slightly and repeat the process. The example below shows the steps in detail.
A person's willingness to pay for something shows the dollar value she attaches to it. Her willingness to pay for one more unit of a good is thus a dollar measure of the benefits the extra unit of the good gives her. As a result, the terms "willingness to pay" and "marginal benefit" are often used interchangably.
Suppose Alice and Bob are two buyers of downloadable songs and each has a monthly W2P that can be expressed in equation form as follows:
Alice: W2Pa = 5 - Qa/2
Bob: W2Pb = 10 - Qb/5
That is, Alice is willing to pay up to $4.50 for the first song (when Qa=1), $4.00 for the second song, and so on. Bob likes music more: he's willing to pay $9.80 for the first song (when Qb=1) and $9.60 for the second song.
Given this information, we can construct each person's demand curve--the number of songs they would be willing to buy at each price. If the price were very high, say $10 per song, neither person would buy any: Alice's maximum W2P is $4.50 and Bob's is $9.80. Qa and Qb would both be 0. If the price were $9, however, Bob would be willing to buy 5 songs. To see that, look at his W2P for the first few songs:
| Qb | W2P |
| 1 | 9.80 |
| 2 | 9.60 |
| 3 | 9.40 |
| 4 | 9.20 |
| 5 | 9.00 |
| 6 | 8.80 |
He's willing to pay more than $9 per song for songs 1-4, and is willing to pay $9 for song 5. He wouldn't want a 6th song at that price: song 6 is only worth $8.80 to him. Since he'll buy songs until his W2P for the last song is just equal to the price, we can use his W2P equation to find his demand curve:
W2Pb = 10 - Qb/5
W2Pb = P (for the last song he buys)
P = 10 - Qb/5 (substituting P for W2Pb)
Qb = (10-P)*5 (rearranging)
From this it's easy to calculate Bob's demand: when P=10, Qb=0; when P=9, Qb=5; etc. We can do the same thing to get Alice's demand curve:
W2Pa = 5 - Qa/2
W2Pa = P (for the last song she buys)
P = 5 - Qa/2
Qa = (5-P)*2
This reproduces the resuts we obtained above: when P=5, Qa=0; when P=4.50, Qa=1; when P=4, Qa=2.
| P | Qa | Qb | Market Q |
| 10.00 | 0 | 0 |
0 |
| 9.50 | 0 | 2.5 |
2.5 |
| 9.00 |
0 | 5 |
5 |
| 8.50 |
0 | 7.5 |
7.5 |
| 8.00 |
0 | 10 |
10 |
| 7.50 |
0 |
12.5 |
12.5 |
| 7.00 |
0 |
15 |
15 |
| 6.50 |
0 |
17.5 |
17.5 |
| 6.00 |
0 |
20 |
20 |
| 5.50 |
0 |
22.5 |
22.5 |
| 5.00 |
0 |
25 |
25 |
| 4.50 |
1 |
27.5 |
28.5 |
| 4.00 |
2 |
30 |
32 |
| 3.50 | 3 | 32.5 | 35.5 |
In algebra, what this says is the following, where Q is the total market demand:
P > 10:
Q = 0
P between 10 and 5:
Q = Qb
Q = (10-P)*5
P < 5:
Q = Qa + Qb
Q = (10-P)*5 + (5-P)*2
Q = 60 - 7*P