Measurement
and
Interpretation
of Elasticities
Chapter 5
Discussion Topics
Own price elasticity of demand
Income elasticity of demand
Cross price elasticity of demand
Other general properties
How can we use these demand elasticities
2
Key Concepts Covered…
Own price elasticity = %Qi
for a given %Pi, ηii
i.e., the effect of a change in the price for hamburger on
hamburger demand: ηHH = %QH for a given
%PH
Cross price elasticity = %Qi for a given %Pj, ηij
i.e., the effect of a change in the price of chicken on
hamburger demand: ηHC = %QH for a given %PC
Income elasticity = %Qi for a given %Income, ηiY
3
i.e., the effect of a change in income on hamburger
demand: ηHY = %QH for a given %PY
Pages 70-76
Key Concepts Covered…
Arc elasticity = elasticity estimated over a range of
prices and quantities along a demand curve
Point elasticity = elasticity estimated at a point on
the demand curve
Price flexibility = reciprocal (the inverse) of the
own price elasticity
 %Pi for a given %Qi
4
Pages 70-76
Own Price Elasticity
of Demand
5
Own Price Elasticity of Demand
Own price
elasticity of
demand
Percentage change in quantity demanded (Q)
ηii =
Percentage change in own price (P)
Point Elasticity Approach:
Own price
Q
elasticity of 
Qa
demand
Q = (Qa – Qb)
P = (Pa – Pb)
6
P Q Pa

Pa
P Qa
$
Single point
on curve
Pa
Pb
Qa Qb
Q
 The subscript
• a stands for after price change
• b stands for before price change
Pages 70-72
Own Price Elasticity of Demand
Own price
Percentage change in quantity
elasticity of ηii =Percentage change in own price
demand
Arc Elasticity Approach:
Own price
elasticity of
demand
Q

Q
P
P Q P

P
P Q
where:
Avg Price
P = (Pa + Pb) 2
Q = (Qa + Qb) 2
Avg Quantity
Q = (Qa – Qb)
P = (Pa – Pb)
$
Specific range
on curve
Pa
Pb
Equation 5.3
Qa Qb
Q
 The subscript
• a stands for after price change
• b stands for before price change
Page 72
7
Q
Interpreting the Own Price
Elasticity of Demand
If Elasticity
Measure is:
Demand is said
to be:
% in
Quantity is:
Less than
–1.0
Elastic
Greater than
% in Price
Equal to
–1.0
Unitary
Elastic
Same as % in
Price
Inelastic
Less than %
in Price
Greater than
–1.0
8
Note: The %Δ in Q is in terms of the absolute value
of the change
Page 72
Demand Curves Come in a
Variety of Shapes
$
Q
9
Demand Curves Come in a
Variety of Shapes
$
Perfectly Inelastic
∆P
Perfectly Inelastic:
A price change does
not change quantity
purchased
Perfectly Elastic
Q
10
Page 72
Demand Curves Come in a
Variety of Shapes
$
Inelastic Demand
∆P
∆P
Elastic Demand
Q
∆Q
11
∆Q
Page 73
Demand Curves Come in a
Variety of Shapes
$
Elastic where –%Q > % P
Unitary Elastic where –%Q = % P
Inelastic where –%Q < % P
Q
12
Page 73
Example of Arc Own-Price Elasticity of Demand
Unitary elasticity
13
–% Change in Q = % Change in P
ηii= –1.0
Page 73
Elastic demand
Inelastic demand
Page 73
14
Elastic Demand Curve
$
With the price decrease from Pb to Pa
What happens to producer revenue?
Pb
Pa
0
15
Qb
Qa
Q
Elastic Demand Curve
$
Cut in
price
Pb
Pa
0
16
Results in a larger %
increase in quantity
demanded
Q
Qb
Qa
Elastic Demand Curve
Producer revenue (TR) = price x quantity
• Revenue before the change (TRb) is Pb x Qb
$
C
Pb
A
B
Pa
0
17
Represented by the area 0PbAQb
• Revenue after the change is (TRa) is Pa x Qa
Represented by the area 0PaBQa
Qb
Qa
Q
Elastic Demand Curve
Change in revenue (∆TR) is TRa – TRb
→ ∆TR = 0PaBQa – 0PbAQb
→ ∆TR = QbDBQa – PaPbAD
$
Red Box
C
Pb
Pa
0
18
A
D
Qb
Purple Box
 →TR ↑
 %Q ↑ is greater than %P ↓
B
Qa
 When you have elastic
Q
demand
 ↑ in price → ↓ total
revenue
 ↓ in price → ↑ total
revenue
Inelastic Demand Curve
$
Pb
Cut in
price
Pa
Results in smaller %
increase in quantity
demanded
Q
Qb Qa
19
Inelastic Demand Curve
$
With price decrease from Pb to Pa
What happens to producer revenue?
Pb
Pa
Q
20
Qb Qa
Inelastic Demand Curve
$
Producer revenue (TR) = price x quantity
Revenue before the change (TRb) is Pb x Qb
 Represented by the area 0PbAQb
Revenue after the change is (TRa) Pa x Qa
Pb
Pa
0
21
A  Represented by the area 0PaBQa
B
Q
Qb Qa
Inelastic Demand Curve
Change in revenue (∆TR) is TRa – TRb
$
∆TR = 0PaBQa – 0PbAQb
∆TR = QbDBQa – PaPbAD
Purple Box
Red Box
Pa
0
22
 →TR ↓
 % Q increase is less than %P decrease
A
Pb
B
D
 When you have
Q
Qb Qa
inelastic demand
 ↑ in price → ↑ total
revenue
 ↓ in price → ↓ total
revenue
Revenue Implications
Own-price
Elasticity is:
Cutting the
Price Will:
Increasing the
Price Will:
Elastic
(ηii< -1)
Unitary Elastic
(ηii= -1)
Inelastic
(-1< ηii < 0)
Increase Total
Revenue
Decrease Total
Revenue
Not Change
Revenue
Not Change
Revenue
Decrease Total Increase Total
Revenue
Revenue
Typical of Agricultural Commodities
23
Page 81
Elastic Demand Curve
Consumer surplus (CS)
$
C
Pb
A
B
Pa
0
24
Before price cut CS is area PbCA
After the price cut CS is area PaCB
Qb
Qa
Q
Elastic Demand Curve
$
C
Pb
The gain in consumer surplus
A
B
Pa
0
25
after the price cut is area
PaPbAB = PaCB – PbCA
Q
Qb
Qa
Inelastic Demand Curve
$
Inelastic demand and
price decrease
Pb
Pa
0
26
Consumer surplus increases
by area PaPbAB
A
B
Q
Qb Q a
Retail Own Price Elasticities
•
•
•
•
•
•
•
Beef and veal= -0.62
Pork = -0.73
Fluid Milk = -0.26
Wheat = -0.11
Rice = -0.15
Carrots = -0.04
Non food = -0.99
Source: Huang, (1985)
27
Page 79
Interpretation
Let’s use rice as an example
Previous Table: own price elasticity of –0.15
→ If the price of rice drops by 10%, the quantity
of rice demanded will increase by 1.5%
$
Pb
10% drop
1.5% increase
28
Demand
Curve
With a price drop
 What is the impact on rice
producer revenues?
 What is the impact on
consumer surplus from rice
consumption?
A
Pa
B
0
QB Qa
Q
Own Price Elasticity Example
1. The local Kentucky Fried Chicken outlet typically
sells 1,500 Crunchy Chicken platters per month at
$3.50 each
2. The own price elasticity for the platter is estimated
to be –0.30
Inelastic demand
29
3. If the KFC outlet increases the price of the platter
to $4.00:
a. How many platters will the KFC outlet sell
after the price change?__________
b. The KFC outlet’s revenue will change by
$__________
c. Will consumers be worse or better off as a
result of this price change?_________
The answer…
1. The local KFCsells 1,500 crunchy chicken platters per
month at $3.50 each. The own price elasticity for this
platter is estimated to be –0.30. If the local KFC outlet
increases the price of the platter by 50¢:
a. How many platters will the chicken sell? 1,440
Solution:
-0.30 = %Q%P
P
Avg. Price
-0.30= %Q[($4.00-$3.50) (($4.00+$3.50) 2)]
%P
30
-0.30= %Q[$0.50$3.75]
-0.30= %Q0.1333
→ %Q=(-0.30 × 0.1333) = -0.04 or –4%
→ New quantity = (1–0.04)×1,500 = 0.96×1,500 = 1,440
The answer…
b. The Chicken’s revenue will change by +$510
Solution:
Current revenue = 1,500 × $3.50 = $5,250/month
New revenue = 1,440 × $4.00 = $5,760/month
→revenue increases by $510/month =
$5,760 - $5,250
c. Consumers will be __worse___ off as a result of
this price change
Why? Because price has increased
31
Another Example
1. The local KFC outlet sells 1,500 crunchy chicken
platters/month when their price was $3.50. The own
price elasticity for this platter is estimated to be
–1.30. If the KFC increases the platter price by 50¢:
Elastic demand
a. How many platters will the chicken
sell?__________
b. The Chicken’s revenue will change by
$__________
c. Will the consumers be worse or better off as a
result of this price change?
32
The answer…
1. The local KFC outlet sells 1,500 crunchy chicken
platters/month when the price is $3.50 . The own price
elasticity for this platter is estimated to be
–1.30. If the KFC increases the platter price by 50¢:
a. How many platters will the KFC outlet sell? 1,240
Solution:
-1.30 = %Q%P
-1.30= %Q[($4.00-$3.50) (($4.00+$3.50) 2)]
-1.30= %Q[$0.50$3.75]
-1.30= %Q0.1333
%Q=(-1.30 × 0.1333) = -0.1733 or –17.33%
→ New quantity = (1 ̶ 0.1733)×1,500 = 0.8267 ×1,500
= 1,240
33
The answer…
1. b. The Chicken’s revenue will change by –$290
Solution:
Current revenue = 1,500 × $3.50 = $5,250/mo
New revenue = 1,240 × $4.00 = $4,960/mo
→Revenue decreases by $290/mo = ($4,960 –
$5,250)
c. Consumers will be worse off as a result of this
price change
Why? Because the price increased.
34
Income Elasticity
of Demand
35
Income Elasticity of Demand
Income
Percentage change in quantity demanded (Q)
elasticity of ηY =
Percentage change in income (I)
demand
where:
Q
ηy 
Q
I = (Ia + Ib) 2
Q = (Qa + Qb) 2
Q = (Qa – Qb)
I = (Ia – Ib)
I Q I

I
I Q
ηY :
A quantitative measure of
changes or shifts in quantity
demanded (ΔQ) resulting from
changes in consumer income (I)
Page 74-75
36
Interpreting the Income
Elasticity of Demand
When the income
elasticity is:
The good is classified as:
Greater than 0.0
A normal good
Greater than 1.0
A luxury (and a normal)
good
Less than 1.0 but
greater than 0.0
A necessity (and a
normal) good
Less than 0.0
An inferior good
Page 75
37
Example
Assume Federal income taxes are cut
and disposable income (i.e., income fter
taxes) is increased by 5%
Assume the chicken income elasticity of
demand is estimated to be 0.3645
What impact would this tax cut have
upon the demand for chicken?
 Is chicken a normal or an inferior good?
Why?
39
The Answer
1. Assume the government cuts taxes, thereby
increasing disposable income (I) by 5%. The income
elasticity for chicken is 0.3645.
a. What impact would this tax cut have upon the
demand for chicken?
Solution:
0.3645 = %QChicken  % I
→ 0.3645 = %QChicken  .05
→%QChicken = .3645 .05 = .018 or + 1.8%
b. Chicken is a normal but not a luxury good since the
income elasticity is > 0 and < 1.0
40
Cross Price Elasticity
of Demand
41
Cross Price Elasticity of Demand
Cross Price
Percentage change in quantity demanded
elasticity of ηij =
Percentage change in another good’s price
demand
Qi Pj Qi Pj i and j are goods
ηij 

(i.e., apples,
Q
P

P
Q
i
j
j
i
where:
oranges, peaches)
Pj = (Pja + Pjb) 2
Qi = (Qia + Qib) 2
Qi = (Qia – Qib)
Pj = (Pja – Pjb)
ηij provides a quantitative measure
of the impacts of changes or shifts in
the demand curve as the price of
other goods change
Page 75
42
Cross Price Elasticity of Demand
If commodities i & j are substitutes (ηij > 0):
Pi↑→Qi↓, Qj↑
i.e., strawberries vs. blueberries, peaches vs.
oranges
If commodities i & j are complements (ηij < 0):
Pi↑→Qi↓, Qj↓
i.e., peanut butter and jelly, ground beef and
hamburger buns
If commodities i & j are independent (ηi j= 0):
Pi↑→Qi↓, Qj is not impacted
i.e., peanut butter and Miller Lite
43
Page 75
Interpreting the Cross Price
Elasticity of Demand
If the Cross-Price
Elasticity is:
Positive
The Good is
Classified as a:
Substitute
Negative
Complement
Zero
Independent
Page 76
44
Some Examples
Quantity
Changing
Prego
Ragu
Hunt’s
Values in red along
the diagonal are own
price elasticities
45
Price That is Changing
Prego
Ragu
Hunt’s
-2.550
0.810
0.392
0.510
-2.061
0.138
1.029
0.535
-2.754
Off diagonal values are all positive
→ These products are substitutes
Page 80
Some Examples
Spaghetti
Sauce
Prego
Ragu
Hunt’s
Price Change
Prego
Ragu
Hunt’s
-2.550
0.810
0.392
0.510
-2.061
0.138
1.029
0.535
-2.754
Note: An increase in Ragu spaghetti sauce price
has a bigger impact on Hunt’s spaghetti
sauce demand (ηRH = 0.535) than an increase
in Hunt’s spaghetti sauce price on Ragu
demand (ηHR = 0.138)
46
Page 80
Some Examples
Spaghetti
Sauce
Prego
Ragu
Hunt’s
Price Change
Prego
Ragu
Hunt’s
-2.550
0.810
0.392
0.510
-2.061
0.138
1.029
0.535
-2.754
A 10% increase in Ragu spaghetti sauce
price increases the demand for Hunt’s
spaghetti sauce by 5.35%
Page 80
47
Some Examples
Spaghetti
Sauce
Prego
Ragu
Hunt’s
Price Change
Prego
Ragu
Hunt’s
-2.550
0.810
0.392
0.510
-2.061
0.138
1.029
0.535
-2.754
A 10% increase in Hunt’s spaghetti
sauce price increases Ragu spaghetti
sauce demand by 1.38%
Page 80
48
Example
1. The cross price elasticity for hamburger demand
with respect to the price of hamburger buns is
equal to –0.60
a. If the price of hamburger buns rises by 5%,
what impact will that have on hamburger
consumption?
b. What is the demand relationship between these
products?
49
The Answer
1. The cross price elasticity for hamburger demand
with respect to the price of hamburger buns is
equal to –0.60
a. If the price of hamburger buns rises by 5%,
what impact will that have on hamburger
consumption? -3.0%
Solution:
-0.60 = %QH  %PHB
-0.60 = %QH  .05
%QH = .05  (-.60) = -.03 or – 3.0%
b. What is the demand relationship between these
products?
These two products are complements as
evidenced by the negative sign on the associated
cross price elasticity
50
Another Example
2. Assume a retailer:
i) Sells 1,000 six-packs of Pepsi/day at a price of
$3.00 per six-pack
ii) The cross price elasticity for Pepsi with respect
to Coca Cola price is 0.70
a. If the price of Coca Cola rises by 5%, what impact
will that have on Pepsi sales?
b. What is the demand relationship between these
products?
51
The Answer
a. If the price of Coca Cola rises by 5%, what impact
will that have on Pepsi consumption?
Solution:
.70 = %QPepsi  %PCoke
.70 = %QPepsi  .05 = .035 or 3.5%
New quantity of Pepsi sold = 1,000  1.035 =
1,035 six-packs, 35 additional six packs
New value of sales = 1,035  $3.00 = $3,105 or
$105/day extra
b. What is the demand relationship between these
products?
The products are substitutes as evidenced by the
positive sign on this cross price elasticity
52
Price Flexibility
of Demand
53
Price Flexibility
 The price flexibility is the reciprocal (inverse) of the
own-price elasticity
• If the calculated elasticty is - 0.25, then the
flexibility = 1/(-0.25) = - 4.0
 Price Flexibility interpretation:
54
%∆P ÷ %∆Q
Price Flexibility
 This is a useful concept to producers when forming
expectations for the current year
• i.e., Assume USDA projects an additional 2% of
supply will likely come on the market
• Given above price flexibility then producers know
the price will likely drop by 8%, or:
%Price = - 4.0 x %Quantity
= - 4.0 x (+2%)
= - 8%
→If supply ↑ by 2%,
price would ↓ by 8%
Note: make sure you use the negative sign for both the
elasticity and the flexibility.
55
Revenue Implications
Own-Price Resulting Increase in Decrease in
Elasticity Price
Supply Will Supply Will
Flexibility
Elastic
Unitary
elastic
Inelastic
< -1.0
Increase
Revenue
Decrease
Revenue
Not Change Not Change
Revenue
Rrevenue
Increase
Between 0 Decrease
Revenue
Revenue
and -1.0
= -1.0
Characteristic of a large number
of agricultural commodities
56
Page 81
Changing Price Response Over Time
Short run effects
Long run effects
 Over time consumers respond in greater
57
numbers
 This is referred to as a recognition lag
 With increasing time, price elasticities tend
to increase → flatter demand curve
Page 77
Implications of Agriculture’s
Inelastic Demand Curve
$
Pb
A
agricultural product prices
to ↓ sharply
 Explains why major
program crops receive
Federal government
subsidies
Pa
Increase in
supply
0
58
 Small ↑ in supply will cause
Q
Qb Qa
Inelastic Demand Curve
Price
Pb
Pa
0
59
A
B
Qb Qa
While this ↑ the costs of
government programs
and hence budget deficits,
remember consumers
benefit from cheaper food
costs.
Quantity
Demand Characteristics
Which market is riskier for
producers…elastic or inelastic demand?
Which market would you start a business
in?
Which market is more apt to need
government subsidies to stabilize producer
incomes?
60
The Market Demand Curve
Price
What causes movement
along a demand curve?
Quantity
61
The Market Demand Curve
Price
What causes the demand
curve to shift?
Quantity
62
In Summary…
Know how to interpret all three elasticities
Know how to interpret a price flexibility
Understand revenue implications for
producers if prices are cut (raised)
Understand the welfare implications for
consumers if prices are cut (raised)
Know what causes movement along versus
63
shifts the demand curve
Chapter 6 starts a series of
chapters that culminates in a
market supply curve for food
and fiber products….
64