Question

Suppose consumers will demand 40 units of a product when the price is $12 per unit and 25 units when the price is $18 each. Find the demand equation assuming that it is linear. Find the price per unit when 30 units are demanded.

Answer 1

Answer: The price per unit is $48, when 30 units are demanded.

Step-by-step explanation:

Since we have given that

At price of $12 per unit, the number of units demanded = 40 units

At price of $18 per unit, the number of units demanded = 25 units.

So, the coordinates would be

(40,12) and (25,18)

As we know that x- axis denoted the quantity demanded.

y-axis denoted the price per unit.

So, the slope would be

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{18-12}{25-40}\\\\m=\dfrac{-6}{15}\\\\m=\dfrac{-2}{5}$

So, the equation would be

$y-y_1=m(x-x_1)\\\\y-12=\dfrac{-2}{5}(x-40)\\\\5(y-12)=-2(x-40)\\\\5y-60=-2x+80\\\\5y+2x=80+60\\\\5y+2x=140$

So, if 30 units are demanded, the price per unit would be

$5y=140+2x\\\\5y=140+2\times 30\\\\5y=140+60\\\\5y=240\\\\y=\dfrac{240}{5}\\\\y=\ 48$

Hence, the price per unit is $48, when 30 units are demanded.