Mathematics, 20.09.2019 18:00 Anne4912

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?

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Answer from: xxxanitaxxx

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.

Step-by-step 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,

$(x - x_1)=\frac{(x_2-x_1)}{(p_2-p_1)}\times(p-p_1)$

Substitute the values,

$(x - 75)=\frac{61-75}{956-900}\times(p-900)$

$(x - 75)=\frac{-14}{56}\times(p-900)$

$(x - 75)=\frac{-1}{4}\times(p-900)$

$x-75=-\frac{1}{4}p+225$

$x=-\frac{1}{4}p+300$

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

$p=\frac{300}{0.25}$

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.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

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step-by-step explanation: