Question

At a unit price of $900, the quantity demanded of a certain commodity is 75 pounds. If the unit price increases to $956, the quantity demanded decreases by 14 pounds. Find the demand equation (assuming it is linear) where p is the unit price and x is the quantity demanded for this commodity in pounds.

p =

At what price are no consumers willing to buy this commodity?$

According to the above model, how many pounds of this commodity would consumers take if it was free?

Answer 1

a) 56x = 16800 - 14p

b) $1200

c) 300 pounds

Explanation:

Given:

At p₁ = $900 ; x₁ = 75 pounds

at p₂ = $956 ; x₂ = 75 - 14 = 61 pounds

Now,

from the standard equation of line, we have

`(x - x_1)=((x_2-x_1))/((p_2-p_1))*(p-p_1)`

on substituting the respective values, we get

`(x - 75)=((61-75))/((956-900))*(p-900)`

or

( x - 75 ) × 56 = -14p + 12600

or

56x - 4200 = -14p + 12600

or

56x = 16800 - 14p (relation between the unit price p and demand x)

b) For no consumers x = 0

thus, substituting in the relation we get

56 × 0 = 16800 - 14p

or

14p = 16800

or

p = $1200

c) For free , p = $0

on substituting in the above relation derived, we get

56x = 16800 - ( 14 × 0 )

or

x = 300 pounds