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

1) The demand equation is
`x=-0.25p+300`

2) The price when no consumers willing to buy this commodity is $1200.

3) The quantity of the commodity would consumers take if it was free is 300 pounds.

Explanation:

Given : 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.

To find :

1) The demand equation ?

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

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

Solution :

1) According to question,

p is the unit price and x is the quantity demanded for this commodity in pounds.

Let,
`p_1=\$900` and
`x_1=75\text{ pounds}`

and
`p_2=\$956` and
`x_2=75-14=61\text{ pounds}`

To find the demand equation we apply two point slope form,

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

Substitute the values,

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

`(x - 75)=(-14)/(56)*(p-900)`

`(x - 75)=(-1)/(4)*(p-900)`

`x-75=-(1)/(4)p+225`

`x=-(1)/(4)p+300`

`x=-0.25p+300`

The demand equation is
`x=-0.25p+300`

2) For no consumers,

Substitute x=0 in demand equation,

`0=-0.25p+300`

`0.25p=300`

`p=(300)/(0.25)`

`p=1200`

The price when no consumers willing to buy this commodity is $1200.

3) For free,

Substitute p=0 in demand equation,

`x=-0.25(0)+300`

`x=300`

The quantity of the commodity would consumers take if it was free is 300 pounds.