Question

Question #9eaa0

Answer 1

At `P=0` Elasticity is zero
At `P=150` Elasticity is infinity
At `P=75` Elasticity is equal to one.

Explanation:

Refer the picture ----

It is a linear function. The demand curve is a straight line.

On such demand curves, geometric method shall be used to find the elasticity at different points.
It is given in the picture.

At `p = 0 ; Q = 300 – 2(0) = 300`

When price is Zero, the length of the Lower segment is zero. The length of the upper segment is some positive value. Zero divided by any value is zero. Hence elasticity is Zero.

When `P = 0` the elasticity is equal to zero or demand is perfectly inelastic.

At `Q = 0 ; 300 – 2P = 0`
`-2p = - 300`
`P = (-300)/(-2)= 150.`

When price is 150, quantity is zero. Now length of lower segment is some positive value. But upper segment is zero. Any value divided by zero is infinity.

Hence, when `P = 150`, the elasticity is infinity or demand is perfectly elastic.

Exactly at the middle the price is 75 and quantity is 150. This is the co-ordinates of the mid point of the straight line demand curve. Its calculation is given in the picture.

Then the length of lower segment is equal to the length of upper segment. Any value divided by the same value is equal to 1.

Hence, when `P = 75`, elasticity is unitary or demand is unitary.

For your information

Elasticity in the price range `<150` and `>75` is greater than 1 i.e., demand is relatively elastic.

Elasticity in the price range `<75` and `>0` is less than 1 i.e., demand is relatively inelastic.

I have shown the calculation of how to find the co-ordinates of the mid point of the demand curve in the picture.