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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

%

%

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

.

%

100 %

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

(

)

(

)(%

' (

) (

)

)

%

If 0 <

*E(p*

)<1 then demand is

**inelastic.**

If 1<

*E(p)*

then demand is elastic. Example: Find

*E(p)*

for

(

) 1 75

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

' (

) [ 1

(

)]

(

) 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

(

) 1 75

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

(

) 48

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?