Question

A local retailer has decided to carry a well-known brand of shampoo. The marketing department tells them that the quarterly demand by an average man is:

qd = 3 - 0.25P
and the quarterly demand by an average woman is:

qd = 4 - 0.5P
Assume that the market consists of 10 men and 10 women.

1. Find the market demand for this shampoo, and graph it.

2. How may bottles of shampoo can they expect to sell if they charge $6 per bottle?

3. What would be the consumer surplus for this price (6$)?

4. By how much would the consumer surplus change if the price per bottle increased

   from $6 to $8?

Answer 1

(I)

Market demand for men (QM) = 10 x qd

QM = 10 x (3 - 0.25P) = 30 - 2.5P

Market demand for women (QW) = 10 x qd

QW = 10 x (4 - 0.5P) = 40 - 2P

Aggregate Market demand (Q) = QM + QW

Q = 30 - 2.5P + 40 - 2P

Q = 70 - 4.5P

[So, P = (70 - Q)/4.5]

Data table:

Q	P (Demand)
0	15.56
10	13.33
20	11.11
30	8.89
40	6.67
50	4.44
60	2.22
70	0.00

Graph:

(II)

When P = 6,

Q = 70 - 4.5 x 6 = 70 - 27 = 43

(III)

When Q = 0, P = 70/4.5 = 15.56

Consumer surplus (CS) = (1/2) x (15.56 - 6) x 43 = 21.5 x 9.56 = 205.54

(IV)

When P = 8, Q = 70 - 4.5 x 8 = 70 - 36 = 34

Decrease in CS = (1/2) x (8 - 6) x (43 + 34) = (1/2) x 2 x 77 = 77