Question

The quantity demanded x for a certain brand of MP3 players is 100 units when the unit price p is set at $100. The quantity demanded is 1100 units when the unit price is $50. Find the demand equation.

P=

Answer 1

x = 2100 - 20p

Explanation:

Let the quantity demanded be 'x'

unit price be 'p'

thus, from the given relation in the question, we have

p (100) = $100

and,

p (1100) = $50

now, from the standard equation for the line

`\frac{\textup{p - p(100)}}{\textup{x - 100}}` =
`\frac{\textup{p(1100) - p(100)}}{\textup{50 - 100}}`

or

`\frac{\textup{p - 100}}{\textup{x - 100}}` =
`\frac{\textup{50 - 100}}{\textup{1100 - 100}}`

or

1000 × (p - 100) = - 50 × ( x - 100 )

or

20p - 2000 = - x + 100

or

x = 2100 - 20p