Given the demand function for commodity X Qd = 12 - 2P where Qd is the quantity demanded and P the price of the commodity.
P
6
5
4
3
2
1
0
Qd
Use the demand function to complete the table (b) Draw the individual's demand curve (use of graph paper is essential (c) What is the maximum quantity the individual can buy of commodity X per unit of time? (d) What is the relationship between quantity demanded and price in the function Qd = f(P)?
Explanation
With demand function Qd = 12 - 2p the table is completed as follows: (a)
P
6
5
4
3
2
1
0
Qd
0
2
4
6
8
10
12
Qd = 12 - 2p when p = 6 Qd = 12 - (2 x 6) = 12 - 12 = 0 Qd = 12 - 2p when p = 5 Qd = 12 - (2 x 5) = 12 - 10 = 2 Qd = 12 - 2p when p = 4 Qd = 12 - (2 x 4) = 12 - 8 = 4 Qd = 12 - 2p when p = 3 Qd = 12 - (2 x 3) = 12 - 6 = 6 Qd = 12 - 2p when p = 2 Qd = 12 - (2 x 2) = 12 - 4 = 8 Qd= 12 - 2p when p = 1 Qd = 12 - (2 x 1) = 12 - 2 = 10
(b) The individual's demand curve (c) 12 (d) Inverse, i.e., the higher the price, the lower the quantity demanded Or the lower the price the higher the quantity demanded.
