2

Own price elasticity of demand : A unit free measure of demand response to a good’s ownprice change

Cross price elasticity of demand : A unit free measure of demand response to other good’s price change

Income elasticity of demand : A unit free measure of demand response to an income change

Other general properties of demand curves

How can we use these demand elasticities

3
Key Concepts Covered…

Own price elasticity
 Represented as η ii
= %
 in Q for a given %
 in P
 i.e., the effect of a change in the price for hamburger on hamburger demand: η
HH i
= %
 in Q
H for a given %
 in P i
H

Cross price elasticity
 Represented as η ij
= % hamburger demand: η
HC
 in Q i
= %
 in Q for a given
H for a given
%
 i.e., the effect of a change in the price of chicken on
%

 in P in P j
C

Income elasticity

Represented as η iY demand: η
HY
= %
= %

Q
H

Q i for a given %

Income
 i.e., the effect of a change in income on hamburger for a given %

P
Y
Pages 70-76

4
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

%
 in P i for a given %
 in Q i
Pages 70-76

5

Own Price Elasticity of Demand
6
Own price elasticity of demand
η ii
=
Percentage change in quantity demanded (Q)
Percentage change in its own price (P)
$
Point Elasticity Approach:
Own price elasticity of
 demand

Q

P
Q a
P a


Q P a

P Q a
% Δ in Q

Q = (Q a
– Q b
)

P = (P a
– P b
)
% Δ in P
P a
P b
Single point on curve
Q
Q a
Q b

The subscript
• a stands for after price change
• b stands for before price change
Pages 70-72

Own Price Elasticity of Demand
7
Own price elasticity of demand
η ii
Percentage change in quantity
=
Percentage change in own price $
Arc Elasticity Approach:
Own price elasticity of
 demand

Q

P
Q P



Q P
P Q
P
P a
P b where:
Avg Price
Avg Quantity
P = (P
Q = (Q a a

Q = (Q

P = (P a
+ P b
+ Q a
)

2 b
)

2
– Q
– P b
) b
)

•
•
The subscript a b
Equation 5.3
stands for stands for
Specific range on curve
Q a
Q b
Q after price change before price change
Q
Page 72

8
If Elasticity
Measure is:
Demand is said to be:
%
 in
Quantity is:
Less than
–1.0
Equal to
–1.0
Greater than
–1.0
Elastic
Unitary
Elastic
Inelastic
Greater than
%
 in Price
Same as %
 in
Price
Less than % in Price
Note: The %Δ in Q is in terms of the absolute value of the change

Page 72

9
Own Price Elasticity of Demand
Snow Leopard was a previous version of Apple’s OS

10
Own Price Elasticity of Demand

What does a own-price elasticity of -2.25 mean?

For a 10% increase in price we get a
22.5% decrease in quantity purchase

Example of an elastic demand with respect to own-price changes

11
Own Price Elasticity of Demand
η ii
= -0.2 to -0.3

Own Price Elasticity of Demand
12

Why is η ii a unit free measure?

Why do we get the same value regardless if the quantity is measured in tons versus pounds?
 Example of Soybean Meal
Q b
= 2.25 tons P b
= $350/ton Q a
= 2.50 tons P a
= $300/ton
η tons
SS


2.50tons – 2.25tons
 
$300 / ton $350 / ton

2.50 tons $300 / ton

0.25 tons

$50 ton


0.25
2.50 tons $300 ton 2.50


 
50
300


 


0.10
0.167


 
0.60

13
Own Price Elasticity of Demand

Lets recalculate the above elasticity but this time in terms of lbs.
Q b
= 4,500 lbs P b
= $0.175/lb
Q a
η lbs
SS
= 5,000 lbs P a


= $0.150/lb
5000 lbs – 4, 500 lbs
5, 000 lbs
 
$0.150 / lb $0.175 / lb
$0.150 / lb


500 lbs

$0.025 lb



500
5, 000 lbs $0.150 lb 5, 000
 


0.10
0.167


 
0.60



0.025
0.150
←Same as previous value


14
Demand Curves Come in a
Variety of Shapes
$
Q

Demand Curves Come in a
Variety of Shapes
The two extremes
15
Perfectly Inelastic :
A price change does not change quantity purchased

Can you think of a good that would have this characteristic?
∆P
$
Perfectly Inelastic
Q
Perfectly Elastic
Page 72

16
Demand Curves Come in a
Variety of Shapes
$
Inelastic Demand
∆P
∆P
Elastic Demand
∆Q
∆Q
Q
Page 73

Demand Curves Come in a
Variety of Shapes
$
Elastic where (–%

Q ) > %

P
17
A single demand curve can exhibit various types of own-price elasticity
Unitary Elastic where (–%

Q) = %

P
Inelastic where (–%

Q )< %

P
Q
Page 73

Example of Arc Own-Price Elasticity of Demand
18

Unitary elasticity
 –% Change in Q = % Change in P
 η ii
= –1.0
Page 73

Elastic demand
19
Inelastic demand
Page 73

Elastic Demand Curve
P b
P a
$

With the price decrease from P b to P

What happens to producer revenue (or a consumer expenditures)?
20
0
Q b
Q a
Q

21
Cut in price
Elastic Demand Curve
$
An elastic demand curve → a larger % ↑in quantity demanded than the absolute value of the % price change (a price decrease)
P b
P a
0
Q b
Q a
Q

P b
C
P a
$
Elastic Demand Curve
A

Producer revenue (TR) = price x quantity
Revenue before the change (TR b
) is P b x Q b

Represented by the area 0P b
Revenue after the change is (TR
AQ b a
) is P a

Represented by the area 0P a
BQ a x Q a
B
22
0
Q b
Q a
Q

23
P b
C
P a
0
$
Elastic Demand Curve
A

Change in revenue (∆TR) is TR
 → ∆TR = 0P a
 → ∆TR = Q b
BQ a
DBQ a
– 0P b
AQ b
– P a
P b
AD a
– TR b
Red Box Purple Box
 →TR ↑

%Q ↑ is greater than %P ↓
D B
Q

When you have elastic demand
 ↑ in price → ↓ total revenue (expenditures)
 ↓ in price → ↑ total revenue (expenditures)
Q b
Q a

24
Inelastic Demand Curve
$
Cut in price
P b
P a
Results in smaller % increase in quantity demanded
Q
Q b
Q a

P b
P a
$
Inelastic Demand Curve

With price decrease from P b to P a

What happens to producer revenue or consumer expenditures)?
Q
25
Q b
Q a

P b
P a
$
Inelastic Demand Curve

Producer revenue (TR) = price x quantity
A

Revenue before the change (TR b

Represented by the area 0P b
AQ b

Revenue after the change is (TR

Represented by the area 0P a
BQ a
) is P a
) P a b x Q x Q a b
B
Q
26
0
Q b
Q a

27
P b
P a
0
$
Inelastic Demand Curve

Change in revenue (∆TR) is TR a
– TR b
 ∆TR = 0P a
BQ a
 ∆TR = Q b
DBQ a
– 0P b
AQ b
– P a
P b
AD
A
Red Box Purple Box
 →TR ↓
 % Q increase is less than %P decrease
B
D
Q

When you have inelastic demand
 ↑ in price → ↑ total revenue
 ↓ in price → ↓ total revenue
Q b
Q a

28
Own-price
Elasticity is:
Cutting the
Price Will:
Increasing the
Price Will:
Elastic
(η ii
< -1)
Unitary Elastic
(η ii
= -1)
Inelastic
(-1< η ii
< 0)
Increase Total
Revenue
Not Change
Revenue
Decrease Total
Revenue
Decrease Total
Revenue
Not Change
Revenue
Increase Total
Revenue
Typical of Agricultural Commodities
Page 81

C
P b
P a
$
Elastic Demand Curve
A

Consumer surplus (CS)

Before price cut CS is area P b
CA

After the price cut CS is area P a
CB
B
29
0
Q b
Q a
Q

30
Elastic Demand Curve
$
C
P b
A

The gain in consumer surplus after the price cut is area
P a
P b
AB = P a
CB – P b
CA
B
P a
0
Q b
Q a
Q

P b
P a
Inelastic Demand Curve
$
A
B

Inelastic demand and price decrease

Consumer surplus increases by area P a
P b
AB
Q
31
0
Q b
Q a

32
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) Page 79

33

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%
$ Demand
Curve
10% drop
1.5% increase
P b
P a
0
A
B

With a price drop

What is the impact on rice producer revenues?

What is the impact on consumer surplus from rice consumption?
Q
Q
B
Q a

34
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
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?_________

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¢ :
35 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
-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

36
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

37
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?

38
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

39
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.

40

41
Income Elasticity of Demand
Income elasticity of demand
η y
Percentage change in quantity demanded (Q)
η
Y
=

Percentage change in income (I)

Q

I
Q I


Q I

I Q where:
I = (I a
Q = (Q a

Q = (Q

I = (I a
+ I b
)  2
)  2 a
+ Q
– I
– Q b
) b b
)
 η
Y
: A quantitative measure of changes or shifts in quantity demanded (ΔQ) resulting from changes in consumer income (I)
Page 74-75

42
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

44

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?

45
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 = %

Q
Chicken
→ 0.3645 = % 
Q
→% 
Q
Chicken

%

I

.05
Chicken
= .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

46

Cross Price Elasticity of Demand
47
Cross Price elasticity of demand where:
η ij
η ij
Percentage change in quantity demanded
=

Percentage change in another good’s price

Q i

P j 

Q i
Q i
P j
P

P Q i j i and j are goods
(i.e., apples, oranges, peaches)
P j
= (P
Q i

Q i
= (Q ia
= (Q

P j
= (P ja ia ja
+ P jb
+ Q ib
)

2
)

2
– Q
– P ib jb
)
)
 η ij provides a quantitative measure of the impacts of changes or shifts in the demand curve as the price of other goods change
Page 75

48
Cross Price Elasticity of Demand

If commodities
↑ →Q i
↓ , Q j
↑ i & j are substitutes (η ij
> 0):

P i
 i.e., strawberries vs. blueberries, peaches vs.
 oranges
If commodities
↑ →Q i
↓
, Q j
↓ i & j are complements (η ij
< 0):

P i
 i.e., peanut butter and jelly, ground beef and hamburger buns

If commodities i & j are independent (η i j
= 0):

P i
↑ →Q i
↓
, Q j is not impacted
 i.e., peanut butter and Miller Lite
Page 75

49
If the Cross-Price
Elasticity is:
Positive
The Good is
Classified as a:
Substitute
Negative
Zero
Complement
Independent
Page 76

Quantity
Changing
Prego -2.550
Ragu
Price That is Changing
Prego Ragu
Hunt’s
0.510
Hunt’s
1.029
0.810
-2.061
0.535
0.392
0.138
-2.754
50
Values in red along
the diagonal are own price elasticities
Off diagonal values are all positive
→ These products are substitutes
Page 80

51
Spaghetti
Sauce Prego
Prego -2.550
Ragu 0.510
Hunt’s 1.029
Price Change
Ragu
Hunt’s
0.810
-2.061
0.392
0.138
0.535
-2.754
Note: An increase in Ragu spaghetti sauce price has a bigger impact on Hunt’s spaghetti sauce demand (η
RH
= 0.535) than an increase in Hunt’s spaghetti sauce price on Ragu demand (η
HR
= 0.138)
Page 80

52
Spaghetti
Sauce Prego
Prego -2.550
Ragu 0.510
Hunt’s 1.029
Price Change
Ragu
Hunt’s
0.810
-2.061
0.392
0.138
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

53
Spaghetti
Sauce Prego
Prego -2.550
Ragu 0.510
Hunt’s 1.029
Price Change
Ragu
Hunt’s
0.810
-2.061
0.392
0.138
0.535
-2.754
A 10% increase in Hunt’s spaghetti sauce price increases Ragu spaghetti sauce demand by 1.38%
Page 80

54
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?

55
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 = %

Q
-0.60 = %

Q
H
%

Q
H

%

P
HB
H

.05
= .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

56
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?

57
a. If the price of Coca Cola rises by 5%, what impact will that have on Pepsi consumption?
Solution:
.70 = %
.70 = %


Q
Q
Pepsi

%

P
Coke
Pepsi

.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

58

59

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: %∆P ÷ %∆Q

60

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.

61
Own-Price
Elasticity
Resulting
Price
Flexibility
Increase in
Supply Will
Elastic
Unitary elastic
Inelastic
< -1.0
Increase
Revenue
Decrease in
Supply Will
Decrease
Revenue
= -1.0
Between 0 and -1.0
Not Change
Revenue
Not Change
Rrevenue
Decrease
Revenue
Increase
Revenue
Characteristic of a large number of agricultural commodities
Page 81

Changing Price Response Over Time
Short run effects Long run effects
62

Over time consumers respond in greater 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
$
P b
P a
A
63
Increase in supply
0
Q b
Q a

Small
↑ in supply will cause agricultural product prices to
↓ sharply
 Explains why major program crops receive
Federal government subsidies
Q

64
Inelastic Demand Curve
Price
A
B
While this ↑ the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs.
Quantity

65

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?

66
Price
What causes movement along a demand curve?
Quantity

67
Price
What causes the demand curve to shift?
Quantity

68

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 shifts the demand curve

69
Chapter 6 starts a series of chapters that culminates in a market
for food and fiber products….