Section 14.3Further Business Application:

Elasticity of Demand

Questions P = R – C How do we increase profit? How do we increase revenue? The sensitivity of demand changes in price depends on

The types of the product or service The unit price set for a particular product or service

Ex: A gallon of milk ($2.00) vs. Sofa ($3000)

How does the demand change as a result of $1 decrease in price?

Elasticity of Demand

Elasticity of Demand is the negative ratio of percentage change in the quantity demanded to the percentage change in the unit price.

Percentage change in demandE

Percentage change in price

Elasticity of Demand

If f is a demand function defined by q= f(p), then the elasticity of demand at a price p is given by

If E < 1, the demand is inelastic. If E > 1, the demand is elastic. If E = 1, the demand is unitary (has unit elasticity)

'( )( )

( )

p dq p f pE p

q dp f p

E(p) and Revenue

If the demand is inelastic at p (when E<1), then an increase in the unit price will cause the revenue to increase, and vice versa.

If the demand is elastic at p (when E>1), then an increase in the unit price will cause the revenue to decrease, and vice versa.

E(p) and Revenue

If the demand is unitary at p (when E=1), then an increase or decrease in the unit price will cause the revenue to stay the same.

The Revenue is maximized when the demand is unitary; that is, when E = 1

Example

The demand function for a certain product is

a) Find the elasticity of demand function.

b) Find elasticity of demand for the indicated price

$10

$20

c) Interpret your results.

d) If the price is $20, would lowering the price cause the revenue to increase?

248000 10q p

Example

For the following demand function.

a) Find the elasticity of demand function.

b) Find elasticity of demand for the indicated price$100

$70

c) Interpret your results.

d) Is demand elastic or inelastic when the price is set at $ 50?

e) If the price is $50, to maximize the revenue, should we raise or lower the price?

300 2q p