How to find the values of p for which demand is elastic and the values for which demand in inelastic, with the price demand equation as f(p) = 455-35p ?

Mar 12, 2017

Demand will be relatively elastic for any price greater than $6.5$.
Demand will be relatively inelastic for any price less than $6.5$.!

Explanation:

Given -

$x = 455 - 35 p$

It is a linear function.
Let us the fix the demand curve.
Look at the graph

You know how to measure elasticity at any given point.

Elasticity of Demand = Lower segment of the demand curve / upper segment of the demand curve.

The two extreme points are -

At which price the demand vanishes?

$455 - 35 p = 0$
$p = \frac{- 455}{- 35} = 13$

At price 13 nothing will be demanded.
One of the point on the demand curve is ((0, 13)

At what quantity price will vanish?

$x = 455 - 35 p$
$x = 455 - 35 \left(0\right)$
$x = 420$

another extreme point is $\left(420 , 0\right)$
Plot these two points.
Join these two points.
You get a linear demand curve.

Exactly at the middle, the length of lower the segment of the demand curve is equal to the length of the upper segment.

Hence elasticity is unitary.

Find the mid point
Mid-point $\left(x , p\right) = \frac{0 + 420}{2} , \frac{13 + 0}{2} = \left(210 , 6.5\right)$

At price 6.5, the quantity demanded is 210.

Demand will be relatively elastic for any price greater than $6.5$.
Demand will be relatively inelastic for any price less than $6.5$.