Question

1. Consumer 1’s demand function is q = 20 – p, while consumer 2’s demand function is q = 12 – 2p.

1) Draw the individual demand curves of each of two consumers.

2) Draw the aggregate demand function of the two consumers (bold the curve in your graphs). You can either use the method we discussed in class by dividing p into several intervals, or a more direct way by adding up the curves (see textbook). No matter which method you choose, show your detailed work to earn points (e.g. coordinates of points, slope, some horizontal dashed lines linking graphs).

Answer 1

Individual demand curves:

q = 20 – p

Coordinates would be as (q, p) form.

If (q = 0) is placed in the above function, 0 = 20 – p; therefore, p = 20; the coordinate is (0, 20).

If (p = 0) is placed in the above function, q = 20 – 0; therefore, q = 20; the coordinate is (20, 0).

The demand curve (D1) is as below:

q = 12 – 2p

Coordinates would be as (q, p) form.

If (q = 0) is placed in the above function, 0 = 12 – 2p; therefore, p = 6; the coordinate is (0, 6).

If (p = 0) is placed in the above function, q = 12 – 0; therefore, q = 12; the coordinate is (12, 0).

The demand curve (D2) is as below:

Aggregate demand function:

Q = 20 – p + 12 – 2p

Or, Q = 32 – 3p

Coordinates would be as (Q, p) form.

If (Q = 0) is placed in the above function, 0 = 32 – 3p; therefore, p = 10.67; the coordinate is (0, 10.67).

If (p = 0) is placed in the above function, Q = 32 – 0; therefore, Q = 32; the coordinate is (32, 0).

The demand curve (Da) is as below: