Question

A new software company wants to start selling DVDs with their
product. The manager notices that when the price for a DVD is 16
dollars, the company sells 134 units per week. When the price is
27 dollars, the number of DVDs sold decreases to 89 units per week.
Answer the following questions:


A. Assume that the demand curve is linear. Find the demand,
q

, as
a function of price,
p

.

Answer:
q
=

Answer 1

If q is a linear function of p, then

q = mp + b

We know from the given data

134 = 16m + b
89 = 27m + b

45 = -11m
m = -0.2444

b = 137.9111

q = -0.2444p + 137.9111

or, roughly,

q = -1/4 p + 138

Answer 2

That is incorrect. The linear function is (-13/6)p + 476/3.