Question

3. Suppose there are 3 buyers in the market. Buyer “A” has the demand function QA = 10 − 2P, “B” has the demand function QB = 6 − 0.5P, and “C” has the demand functionQC =12−3P.

(a) Derive the market demand. (3 points)

(b) Graph the demand curves for each consumer and the market demand when P is 1, 2, 4, 6, 8, and 10. (2 points)

Answer 1

Solution: 3

(a) The market demand curve = sum of individual demand curves

Q = Q1+Q2+Q3 = 10-2P+6-0.5P+12-3P = 28-5.5P

Thus market demand is Q = 28-5.5P

(b)

PA	QA	PB	QB	PC	QC	PM	QM
1	8	1	5.5	1	9	1	22.5
2	6	2	5	2	6	2	17
4	2	4	4	4	0	4	6
6	negative(0)	6	3	6	negative	6	negative
8	negative	8	2	8	negative	8	negative
10	negative	10	1	10	negative	10	negative

The green, blue, red and black lines show demand curves for A, B, C and market respectively.