### Chapter 4 Notes

```CHAPTER
4
Elasticity
The Responsiveness of the
Quantity Demanded to Price
 When price rises, quantity demanded
decreases.
 The question is how much quantity
will decrease in response to a given
price increase.
 We want a measure that is units free
and can be compared across
different commodities.
The Responsiveness of
Quantity Demanded to Price
The measure we will study that
meets the criteria we want is
the price elasticity of
demand.
Price Elasticity of Demand
 Price elasticity of demand is a
measure of the responsiveness of
the quantity demanded of a good to a
change in its price (ceteris paribus).
 Elastic Demand - means demand is
sensitive to price
 Inelastic Demand - means demand is
insensitive to price
Elasticity: A Units-Free
Measure
Price elasticity of
=
demand
Percentage change
in quantity demanded
Percentage change in price
Calculating Elasticity
 Negative sign is ignored for
convenience.
 The changes in price and quantity
are expressed as percentages of the
average price and average quantity
between the two prices and
quantities being compared.
– Avoids having two values for the price
elasticity of demand
Calculating Elasticity
Percentage change in quantity demanded
Price elasticity of demand =
Percentage change in price
%Q

%P
Calculating Elasticity
Percentage change in quantity demanded
Price elasticity of demand =
Percentage change in price
%Q

%P
Q / Qave

P / Pave
Calculating Elasticity
Percentage change in quantity demanded
Price elasticity of demand =
Percentage change in price
%Q

%P
=
Q / Qave

P / Pave
(Q2 - Q1)/Qave
(P2 - P1)/Pave
Calculating the Elasticity of
Demand - Example
 P1 = 410
 P2 = 390
 Q1 = 36
 Q2 = 44
Price (dollars per chip)
Calculating the
Elasticity of Demand
Original
point (P1, Q1)
410
400
390
Da
36
40
44
Quantity (millions of chips per year)
Price (dollars per chip)
Calculating the
Elasticity of Demand
Original
point (P1, Q1)
410
400
New
point (P2, Q2)
390
Da
36
40
44
Quantity (millions of chips per year)
Price (dollars per chip)
Calculating the
Elasticity of Demand
Original
point (P1, Q1)
410
 P `=\$20
400
New
point (P2, Q2)
390
Da
36
Q = 8
40
44
Quantity (millions of chips per year)
Price (dollars per chip)
Calculating the
Elasticity of Demand
Original
point (P1, Q1)
410
 P=
\$20
400
Pave =
\$400
New
point (P2, Q2)
390
Da
36
Q = 8
40
44
Quantity (millions of chips per year)
Price (dollars per chip)
Calculating the
Elasticity of Demand
Original
point (P1, Q1)
410
 P=
\$20
400
Pave =
\$400
New
point (P1, Q1)
Qave = 40
390
Da
36
Q = 8
40
44
Quantity (millions of chips per year)
Calculating Elasticity
Percentage change in quantity demanded
Price elasticity of demand =
Percentage change in price
%Q

%P
=
Q / Qave

P / Pave
(Q2 - Q1)/Qave  8 / 40
(P2 - P1)/Pave
20 / 400
Calculating Elasticity
Percentage change in quantity demanded
Price elasticity of demand =
Percentage change in price
%Q

%P
=
Q / Qave

P / Pave
(Q2 - Q1)/Qave  8 / 40 = 4
(P2 - P1)/Pave
20 / 400
Elasticity Using Different Bases
 Use P1 and Q1 as base
– E = ((44 – 36)/36)/((390 – 410)/410)
–
= (8/36)/(-20/410) = .222/.0488 = 4.55
 Use P2 and Q2 as base
– E = ((44 – 36)/44)/((390 – 410)/390)
–
= (8/44)/(-20/390) = .182/.051 = 3.57
 Note that average of these two elasticities
is about 4, which is the elasticity obtained
using the average Ps and Qs
 P1 = 410, Q1 = 36; P2 = 390, Q2 = 44
Inelastic and Elastic
Demand
 Five demand curves that cover the
entire range of possible elasticities
of demand:
–
–
–
–
–
Perfectly inelastic (Elasticity=0)
Inelastic (0<Elasticity<1)
Unit elastic (Elasticity=1)
Elastic (1<Elasticity<
)
Perfectly elastic (Elasticity=
)


Price
Inelastic and Elastic
Demand
D
1
Elasticity = 0
12
Perfectly Inelastic
6
Quantity
Inelastic and Elastic
Demand
 Perfectly inelastic demand
– Implies that quantity demanded remains
constant when price changes occur.
– Price elasticity of demand = 0
Price
Inelastic and Elastic
Demand
D
2
0<Elasticity<1
12
Inelastic
6
Quantity
Inelastic and Elastic
Demand
 Inelastic demand
– Implies the percentage change in quantity
demanded is less than the percentage change in
price.
– Price elasticity of demand > 0 and < 1
Price
Inelastic and Elastic
Demand
D
3
Elasticity = 1
12
Unit Elasticity
6
1
2
3
Quantity
Inelastic and Elastic
Demand
 Unit elastic demand
– Implies that the percentage change in quantity
demanded equals the percentage change in
price.
– Price elasticity of demand = 1
Price
Inelastic and Elastic
Demand
12
1<Elasticity< ∞
D4
Elastic
6
Quantity
Inelastic and Elastic
Demand
 Elastic demand
– Implies the percentage change in quantity
demanded is greater than the percentage
change in price.
– Price elasticity of demand > 1 and <

Price
12
6
Inelastic and Elastic
Demand
Elasticity =

D5
Perfectly Elastic
Quantity
Inelastic and Elastic
Demand
 Perfectly elastic demand
– Implies that if price changes by any percentage
quantity demanded will fall to 0.
– Price elasticity of demand =

Examples of Elasticity
Calculation
(1)
 Q1 = 10, P1 = 50, Q2 = 8, P2 = 60
 Elasticity = ((8-10)/9)/(60-50)/55)
 = (-2/9)/(10/55)=-1.22
 Therefore demand over this range is
elastic
Examples of Elasticity
Calculation
(2)
 Q1 = 30, P1 = 20, Q2 = 28, P2 = 26
 Elasticity = ((28-30)/29)/(26-20)/23) =
 (-2/29)/(6/23)=-.264
 Therefore demand over this range is
inelastic
Examples of Elasticity
Calculation
(3)
 Q1 = 55, P1 = 9, Q2 = 45, P2 = 11
 Elasticity = ((45-55)/50)/(11-9)/10)
 = (-10/50)/(2/10)=-1.00
 Therefore demand over this range is
unitary elastic
The Factors that Influence
the Elasticity of Demand
 The closer the substitutes for a good,
the more elastic is demand.
 The higher the proportion of income
spent on a good, the more elastic is
demand.
 The greater the time elapsed since a
price change, the more elastic is
demand.
Total Revenue Test
 The total revenue test is a method of
estimating the price elasticity of
demand by observing the change in
total revenue that results from a
price change (all other things
remaining the same).
Unitary Elastic Demand
and Total Revenue
 If demand is unitary elastic, an
increase in price results in an equal
percentage decrease in the quantity
demanded and total revenue remains
constant.
Elastic Demand and
Total Revenue
 If demand is elastic, an increase in
price results in a larger percentage
decrease in the quantity demanded
and total revenue decreases.
Inelastic Demand and
Total Revenue
 If demand is inelastic, an increase in
price results in a smaller percentage
decrease in the quantity demanded
and total revenue increases.
Example
of Total Revenue Test
Elasticity Calculation (1)
 Q1 = 10, P1 = 50, Q2 = 8, P2 = 60
 Elasticity = ((8-10)/9)/(60-50)/55)
 = (-2/9)/(10/55)=-1.22 (elastic)
 TR1 = P1xQ1 = 50x10 = 500
 TR2 = P2xQ2 = 60x8 = 480
 TR falls as P increases
 Therefore demand is elastic
Example
of Total Revenue Test
Elasticity Calculation (2)
 Q1 = 30, P1 = 20, Q2 = 28, P2 = 26
 Elasticity = ((28-30)/29)/(26-20)/23)
 = (-2/29)/(6/23)=-.264 (inelastic)
 TR1 = P1xQ1 = 20x30 = 600
 TR2 = P2xQ2 = 26x28 = 728
 TR rises as P increases
 Therefore demand is inelastic
Example
of Total Revenue Test
Elasticity Calculation (3)
 Q1 = 55, P1 = 9, Q2 = 45, P2 = 11
 Elasticity = ((45-55)/50)/(11-9)/10)
 = (-10/50)/(2/10)=-1.00 (unitary elastic)
 TR1 = P1xQ1 = 9x55 = 495
 TR2 = P2xQ2 = 11x45 = 495
 TR doesn’t change as P increases
 Therefore demand is unitary elastic
Elasticity Along a StraightLine Demand Curve
 Elasticity is not the same as slope,
but the two are related.
 As the price increases, demand
becomes more elastic.
 Elasticity will equal 1.0 at the
midpoint of any linear demand curve.
Other Commonly Used
Elasticities
 Income Elasticity of Demand
 Cross Price Elasticity of Demand
 Price Elasticity of Supply
```