Elasticity
Elasticity measures consumer sensitivity to changes in price.
Demand for a product such as a gallon of milk is fairly insensitive to price change.
People who buy milk buy it even if the price goes up. Demand for milk is inelastic.
Demand for a luxury item such as diamond jewelry is more price sensitive. when the price goes up, people buy less. Demand for luxury items is elastic .
Elasticity of demand is
E
 
% change
% in demand change in quantity price
Given the value of E at a certain price, the % change in demand is E times % change in price. We assume demand decreases if price increases so E is always positive . new price
 old
% change in price
 price
100 % old price
Example 1: For a certain product, E (25)=1.2. If price increases from $25 to $26, what is the % change in demand quantity? Will demand increase or decrease under this price change?
Example 2: For a certain product, E (50) = 0.6. If price increases from $50 to $52, what is the % change in demand quantity? Will demand increase or decrease?

The elasticity function for demand quantity given by x = f(p) is defined to be
E ( p )
 
(
)(%
pf f
' ( p )
( p )
)

%
If 0 < E(p )<1 then demand is inelastic.
If 1< E(p) then demand is elastic.
Example: Find E(p) for f ( p )

1
75
 p 2
. On what price interval is demand inelastic? elastic?
A question to be answered by the seller is given a certain elasticity, 'Should he increase or decrease the price to increase revenue?'. At what value of p is revenue a maximum?
It can be shown using the product rule and the definition of the elasticity function that
R ' ( p )

[ 1

E ( p )] f ( p )
From this, we can conclude that
R(p) is a max when E(p) = 1, R(p) is increasing if E<1 and decreasing if E>1.
Example: Given that f ( p )

1
75
 p 2
At what value of p is revenue a max? Graph R(p) and label the curve where E<1 and E>1.

Example: The demand quantity for a certain product is f ( p )

48
 p 2
.
Find E(p)
If the price is increased from $3.00 to $3.50, what is the approximate % change in demand quantity? Will demand increase or decrease? Will revenue increase or decrease?
If the price is decreased from $3.00 to $2.50, what is the approximate %change in demand? Will demand increase or decrease? Will revenue increase or decrease?
On what intervals is demand inelastic? elastic?
At what price is revenue a max?