Question

An album is downloaded 7000 times per week when its price is $12. it is downloaded 17000 times per week when the price drops to $9. find the demand equation, assuming it is linear. the equation should express price pp in terms of quantity qq.

Answer 1

Let the demand equation represent a line y = m*x + c where y is the demand, x is the price, m is the coefficient and c is the constant. Given 7000 = 12*m + c and 17000 = 9m + c, we can derive the value of m and c. Calculation of the two linear equations give m = -10000/3 and c = 13000. With these data, we can calculate the demand equation as qq + 10000*pp/3 = 13000 where qq represents quantity and pp represents price.

Answer 2

First we find the slope of the line:
m = (12-9) / (7000-17000) = - 0.0003
Then, the generic equation of the line is:
p-po = m (q-qo)
where
(po, qo): point that belongs to the line.
We have then:
p-12 = (- 0.0003) (q-7000)
Rewriting:
p = -0.0003 * q + 2.1 +12
p = -0.0003 * q + 14.1
answer:
the demand equation, assuming it is linear
p = -0.0003 * q + 14.1