Elasticity Elasticity measures consumer sensitivity to changes in price.

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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

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

)  

E

(

p

)(%

change pf f in

' (

p

) (

p

)

p

) 

approximat e

%

change in demand quantity

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?

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