Lecture 4 Notes
Elasticity
These notes focus on the price elasticity of demand. You
should also be familiar with Income elasticity of demand
Cross-price elasticity of demand
Price elasticity of supply
These related concepts are covered in ch. 2 of the text.
Elastic Demand
P’
Inelastic Demand
P’
Q’
Q’
If demand is elastic then purchases are very responsive to a
price change; there is a large change in quantity demanded
when the price changes, so that the demand curve is
relatively flat.
If demand is inelastic then purchases are not very
responsive to a price change; there is a small change in
quantity demanded when the price changes, so that the
demand curve is relatively steep.
The price elasticity of demand is defined as, η =
%∆QD
%∆P
Classifying Elasticity:
Perfectly elastic
Elastic
Unit elastic
Inelastic
Perfectly inelastic
η =∞
η >1
η =1
η <1
η =0
Calculating Elasticity:
There are two primary methods for this: arc elasticity
and point elasticity. Both methods can be understood by
rewriting the definition of η as follows:
∆Q D
QDbase
η=
∆P
P base
Arc Elasticity
This method calculates elasticity by looking at the
change in quantity and the change in price between two
points on a demand curve. The base quantity demanded is
computed as the average of the two quantities; similarly for
the base price.
Point Elasticity
This method calculates elasticity at a single point on the
demand curve; the price and quantity at this point are used
as the base price and quantity. This method requires
knowledge of 4 D /∆P , the rate of change of quantity
demanded with respect to a price change. The fractions in
the elasticity formula above can be rearranged to yield the
P ∆QD
following expression for the point elasticity: η =
QD ∆P
Consumer Expenditure, Price Changes and Elasticity:
The price elasticity of demand reveals how consumer
expenditures on a good changes when the price of a good
changes. By the Law of Demand we already know that
quantity of demand is inversely related to price; for example,
when the price of a good rises, quantity demanded falls. But
when the price of a good rises, total consumer spending on
the good may either rise of fall.
Analysis:
Let E designate total consumer expenditures on a good
in a market. Then E = PD(P), where D(P) is the market
demand function.
Step 1 - Use the product rule to calculate the derivative of E
with respect to P:
dE
= 1D(P) + PD’(P) = D(P) + PD’(P)
dP
Step 2 - substitute quantity demanded for D(P) and
substitute 4 D /∆P for D’(P):
∆QD
dE
= QD + P
dP
∆P
Step 3 - multiply and divide the second term by quantity
demanded, then factor out quantity demanded:
dE
P ∆QD
P ∆QD
)
= QD + QD
= QD (1 +
dP
QD ∆P
QD ∆P
Step 4 - the product of fractions in the last term above is the
negative of the price elasticity. So, the final result is:
dE
= QD (1 − η )
dP
There is simple and intuitive relationship between price
change and expenditures that depends on elasticity.
Œ If demand is inelastic (η < 1 ) then dE/dP is positive; a price
increase yields higher consumer spending because
quantity demanded responds relatively little to the price
increase.
Œ If demand is elastic (η > 1) then dE/dP is negative; a price
increase yields lower consumer spending because
quantity demanded responds strongly to the price
increase.
Œ For the intermediate case of unit elasticity (η = 1), a price
increase has no effect on expenditures; the % drop in
quantity equals the % increase in price and spending is
unchanged.