Question

The quantity demanded for a certain brand of portable CD players is 200 units when the unit price is set at $90. The quantity demanded for 1,200 units when the unit price is set at $40. Find the demand question.

Answer 1

Given that the quantity demanded for a certain brand of portable CD players is 200 units when the unit price is set at $90.

If we set quantity=y and price=x then in point form, we can write above information as (90,200)

Similarly "The quantity demanded for 1,200 units when the unit price is set at $40. " can be written as (40,1200)

Now we can plug both points into two point formula to find the required equation:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

plug those points

$\frac{y-1200}{x-40}=\frac{200-1200}{90-40}$

$\frac{y-1200}{x-40}=\frac{-1000}{50}$

$\frac{y-1200}{x-40}=-20$

y-1200=-20(x-40)

y-1200=-20x+800

y=-20x+2000

Hence demand equation is y=-20x+2000

Answer 2

The demand equation is a linear equation with a slope equal to the rate

of change of price with demand.

Correct response:

• The demand equation is; Q = 2000 - 20·P

Method used to find the demand equation

The demand equation is can be used to predict the quantity demanded at a given price.

Given:

Quantity of CD players demanded at $90 = 200

The quantity demanded when the price is $40 = 1,200

Required:

The demand equation

Solution:

The demand equation is of the form; Q = C - m·P

Where;

Q = The quantity demanded

m = The slope of the demand line equation.

C = The constant term

$m = \dfrac{1,200 - 200}{40 - 90} = \mathbf{ -20}$

The equation is slope and intercept form is therefore;

(Q - 1200) = -20 × (P - 40)

Q = -20·P + 800 + 1200 = -20·P + 2000

The demand equation is therefore;

• Q = 2000 - 20·P

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