at a unit price of $700, the quantity demanded of a certain commodity is 90 pounds. if the unit price increases to $900, the quantity demanded decreases by 50 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? pounds

Answer and explanation:

Given : At a unit price of $700, the quantity demanded of a certain commodity is 90 pounds. If the unit price increases to $900, the quantity demanded decreases by 50 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 :

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

At a unit price of $700, the quantity demanded of a certain commodity is 90 pounds.

i.e. and

If the unit price increases to $900, the quantity demanded decreases by 50 pounds.

i.e. and

The relation between the price and demand is given by,

Substitute the values,

Cross multiply,

1) The demand equation is

2) No consumer will buy commodity i.e. x=0

Substitute in the demand function,

So, $1060 is the price where no consumers willing to buy this commodity.

3) If it is free means price became zero.

Substitute p=0 in the demand function,

So, 265 pounds of this commodity would consumers take if it was free.

true? is that what you're asking or do you mean something else?

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50