Measurement and Interpretation of Elasticities

1
Measurementand Interpretationof Elasticities

• Chapter 5

2
Discussion Topics

• Own price elasticity of demand
• Income elasticity of demand
• Cross price elasticity of demand
• Other general properties
• Applicability of demand elasticities

3
Key Concepts Covered

• Own price elasticity ?Qbeef for a given
  ?Pbeef
• Income elasticity ?Qbeef for a given ?Income
• Cross price elasticity ?Qbeef for a given
  ?Pchicken

Pages 91-95
4
Key Concepts Covered

• Own price elasticity ?Qbeef for a given
  ?Pbeef
• Income elasticity ?Qbeef for a given ?Income
• Cross price elasticity ?Qbeef for a given
  ?Pchicken

• Arc elasticity range along the demand curve
• Point elasticity point on the demand curve

Pages 91-95
5
Key Concepts Covered

• Own price elasticity ?Qbeef for a given
  ?Pbeef
• Income elasticity ?Qbeef for a given ?Income
• Cross price elasticity ?Qbeef for a given
  ?Pchicken

• Arc elasticity range along the demand curve
• Point elasticity point on the demand curve

• Price flexibility reciprocal of own price
  elasticity

Pages 91-95
6
Own Price Elasticityof Demand
7
Own Price Elasticity of Demand
Own price elasticity of demand
Percentage change in quantity

Percentage change in price
Point Elasticity Approach
Page 91
8
Own Price Elasticity of Demand
Own price elasticity of demand
Percentage change in quantity

Percentage change in price
Point elasticity
Own price elasticity of demand
?Q??P Pa?Qa
The subscript a here stands for after while
b stands for before
?Q (Qa Qb) and ?P (Pa Pb)
Page 91
9
Own Price Elasticity of Demand
Own price elasticity of demand
Percentage change in quantity

Percentage change in price
Single point on curve
Point elasticity
Pa
Own price elasticity of demand
?Q??P Pa?Qa
Qa
The subscript a here stands for after while
b stands for before
?Q (Qa Qb) and ?P (Pa Pb)
Page 91
10
Own Price Elasticity of Demand
Own price elasticity of demand
Percentage change in quantity

Percentage change in price
Arc Elasticity Approach
Page 91
11
Own Price Elasticity of Demand
Own price elasticity of demand
Percentage change in quantity

Percentage change in price
Arc elasticity
Own price elasticity of demand
Equation 5.3
?Q??P x P?Q
where P (Pa Pb) ?2 Q (Qa Qb) ?2 ?Q
(Qa Qb) and ?P (Pa Pb)
The subscript a here again stands for after
while b stands for before
Page 91
12
Own Price Elasticity of Demand
Own price elasticity of demand
Percentage change in quantity

Percentage change in price
The bar over the P and Q variables indicates
an average or mean.
Arc elasticity
Own price elasticity of demand
?Q??P x P?Q
where P (Pa Pb) ?2 Q (Qa Qb) ?2 ?Q
(Qa Qb) and ?P (Pa Pb)
The subscript a here again stands for after
while b stands for before
Page 91
13
Own Price Elasticity of Demand
Own price elasticity of demand
Percentage change in quantity

Percentage change in price
Specific range on curve
Arc elasticity
Pb
Own price elasticity of demand
Pa
?Q??P x P?Q
Qb
Qa
where P (Pa Pb) ?2 Q (Qa Qb) ?2 ?Q
(Qa Qb) and ?P (Pa Pb)
The subscript a here again stands for after
while b stands for before
Page 91
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Interpreting the Own Price Elasticity of Demand
Page 92
15
Demand Curves Come in a Variety of Shapes
16
Demand Curves Come in a Variety of Shapes
Perfectly inelastic
Perfectly elastic
Page 92
17
Demand Curves Come in a Variety of Shapes
Inelastic
Elastic
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Demand Curves Come in a Variety of Shapes
Elastic where ?Q gt ?P
Unitary Elastic where ?Q ?P
Inelastic where ?Q lt ?P
Page 93
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Example of arc own-price elasticity of demand
Unitary elasticitya one for one exchange
Page 93
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Elastic demand
Inelastic demand
Page 93
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Elastic Demand Curve
Price
c
Pb
Cut in price
Brings about a larger increase in the quantity
demanded
Pa
0
Qb Qa
Quantity
22
Elastic Demand Curve
Price
What happened to producer revenue? What happened
to consumer surplus?
c
Pb
Pa
0
Qb Qa
Quantity
23
Elastic Demand Curve
Price
Producer revenue increases since ?P is less that
?Q. Revenue before the change was
0PbaQb. Revenue after the change was 0PabQa.
c
a
Pb
b
Pa
0
Qb Qa
Quantity
24
Elastic Demand Curve
Price
Producer revenue increases since ?P is less that
?Q. Revenue before the change was
0PbaQb. Revenue after the change was 0PabQa.
c
a
Pb
b
Pa
0
Qb Qa
Quantity
25
Elastic Demand Curve
Price
Producer revenue increases since ?P is less that
?Q. Revenue before the change was
0PbaQb. Revenue after the change was 0PabQa.
c
a
Pb
b
Pa
0
Qb Qa
Quantity
26
Revenue Implications
Page 101
27
Elastic Demand Curve
Price
Consumer surplus before the price cut was area
Pbca.
c
a
Pb
b
Pa
0
Qb Qa
Quantity
28
Elastic Demand Curve
Price
Consumer surplus after the price cut is Area Pacb.
c
a
Pb
b
Pa
0
Qb Qa
Quantity
29
Elastic Demand Curve
Price
So the gain in consumer surplus after the price
cut is area PaPbab.
c
a
Pb
b
Pa
0
Qb Qa
Quantity
30
Inelastic Demand Curve
Price
Pb
Cut in price
Pa
Brings about a smaller increase in the
quantity demanded
Qb Qa
Quantity
31
Inelastic Demand Curve
Price
What happened to producer revenue? What happened
to consumer surplus?
Pb
Pa
Qb Qa
Quantity
32
Inelastic Demand Curve
Price
a
Producer revenue falls since ?P is greater than
?Q. Revenue before the change was
0PbaQb. Revenue after the change was 0PabQa.
Pb
b
Pa
0
Qb Qa
Quantity
33
Inelastic Demand Curve
Price
a
Producer revenue falls since ?P is greater than
?Q. Revenue before the change was
0PbaQb. Revenue after the change was 0PabQa.
Pb
b
Pa
0
Qb Qa
Quantity
34
Inelastic Demand Curve
Price
a
Consumer surplus increased by area PaPbab
Pb
b
Pa
0
Qb Qa
Quantity
35
Revenue Implications
Page 101
Characteristic of agriculture
36
Retail Own Price Elasticities

• Beef and veal .6166
• Milk .2588
• Wheat .1092
• Rice .1467
• Carrots .0388
• Non food .9875

Page 99
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Interpretation
Lets take rice as an example, which has an own
price elasticity of - 0.1467. This suggests
that if the price of rice drops by 10, for
example, the quantity of rice demanded will only
increase by 1.467.
P
Rice producer Revenue? Consumer surplus?
10 drop
1.467 increase
Q
38
Example

• 1. The Dixie Chicken sells 1,500 Freddie Burger
  platters per month at 3.50 each. The own price
  elasticity for this platter is estimated to be
  0.30. If the Chicken increases the price of the
  platter by 50 cents
• How many platters will the chicken
  sell?__________
• b. The Chickens revenue will change by
  __________
• c. Consumers will be ____________ off as a
  result of this price change.

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The answer

• 1. The Dixie Chicken sells 1,500 Freddie Burger
  platters per month at 3.50 each. The own price
  elasticity for this platter is estimated to be
  0.30. If the Chicken increases the price of the
  platter by 50 cents
• How many platters will the chicken
  sell?__1,440____
• Solution
• -0.30 ?Q??P
• -0.30 ?Q?(4.00-3.50) ?((4.003.50) ?2)
• -0.30 ?Q?0.50?3.75
• -0.30 ?Q?0.1333
• ?Q(-0.30 0.1333) -0.04 or 4
• So new quantity is 1,440, or (1-.04) 1,500,
• or .96 1,500

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The answer

• 1. The Dixie Chicken sells 1,500 Freddie Burger
  platters per month at 3.50 each. The own price
  elasticity for this platter is estimated to be
  0.30. If the Chicken increases the price of the
  platter by 50 cents
• How many platters will the chicken
  sell?__1,440____
• b. The Chickens revenue will change by
  __510___
• Solution
• Current revenue 1,500 3.50 5,250 per
  month
• New revenue 1,440 4.00 5,760 per month
• So revenue increases by 510 per month, or 5,760
• minus 5,250

41
The answer

• 1. The Dixie Chicken sells 1,500 Freddie Burger
  platters per month at 3.50 each. The own price
  elasticity for this platter is estimated to be
  0.30. If the Chicken increases the price of the
  platter by 50 cents
• How many platters will the chicken
  sell?__1,440____
• b. The Chickens revenue will change by
  __510___
• Consumers will be __worse___ off as a result of
  this price change.
• Why? Because price increased.

42
Another Example

• 1. The Dixie Chicken sells 1,500 Freddie Burger
  platters per month at 3.50 each. The own price
  elasticity for this platter is estimated to be
  1.30. If the Chicken increases the price of the
  platter by 50 cents
• How many platters will the chicken
  sell?__________
• b. The Chickens revenue will change by
  __________
• c. Consumers will be ____________ off as a
  result of this price change.

43
The answer

• 1. The Dixie Chicken sells 1,500 Freddie Burger
  platters per month at 3.50 each. The own price
  elasticity for this platter is estimated to be
  1.30. If the Chicken increases the price of the
  platter by 50 cents
• How many platters will the chicken
  sell?__1,240____
• Solution
• -1.30 ?Q??P
• -1.30 ?Q?(4.00-3.50) ?((4.003.50) ?2)
• -1.30 ?Q?0.50?3.75
• -1.30 ?Q?0.1333
• ?Q(-1.30 0.1333) -0.1733 or 17.33
• So new quantity is 1,240, or (1-.1733) 1,500,
• or .8267 1,500

44
The answer

• 1. The Dixie Chicken sells 1,500 Freddie Burger
  platters per month at 3.50 each. The own price
  elasticity for this platter is estimated to be
  1.30. If the Chicken increases the price of the
  platter by 50 cents
• How many platters will the chicken
  sell?__1,240____
• b. The Chickens revenue will change by __-
  290___
• Solution
• Current revenue 1,500 3.50 5,250 per
  month
• New revenue 1,240 4.00 4,960 per month
• So revenue decreases by 290 per month,
• or 4,960 minus 5,250

45
The answer

• 1. The Dixie Chicken sells 1,500 Freddie Burger
  platters per month at 3.50 each. The own price
  elasticity for this platter is estimated to be
  1.30. If the Chicken increases the price of the
  platter by 50 cents
• How many platters will the chicken
  sell?__1,240____
• b. The Chickens revenue will change by __-
  290___
• Consumers will be __worse___ off as a result of
  this price change.
• Why? Because the price increased.

46
Income Elasticityof Demand
47
Income Elasticity of Demand
Income elasticity of demand
Percentage change in quantity

Percentage change in income
?Q??I x I?Q
where I (Ia Ib) ?2 Q (Qa Qb) ?2 ?Q
(Qa Qb) ?I (Ia Ib)
Indicates potential changes or shifts in the
demand curve as consumer income (I) changes.
Page 94
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Interpreting the Income Elasticity of Demand
Page 95
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Some Examples
Elastic
Page 99
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Some Examples
Inferior good
Elastic
Page 99
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Some Examples
Luxury good
Inferior good
Elastic
Page 99
52
Example

• Assume the government cuts taxes, thereby
  increasing disposable income by 5. The income
  elasticity for chicken is .3645.
• What impact would this tax cut have upon the
  demand for chicken?
• Is chicken a normal good or an inferior good?
  Why?

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The Answer

• 1. Assume the government cuts taxes, thereby
  increasing disposable income (I) by 5. The
  income elasticity for chicken is .3645.
• What impact would this tax cut have upon the
  demand for chicken?
• Solution
• .3645 ?QChicken ? ? I
• .3654 ?QChicken ? .05
• ?QChicken .3645 ?.05 .018 or 1.8

54
The Answer

• 1. Assume the government cuts taxes, thereby
  increasing disposable income by 5. The income
  elasticity for chicken is .3645.
• What impact would this tax cut have upon the
  demand for chicken? _____ 1.8___
• Is chicken a normal good or an inferior good?
  Why?
• Chicken is a normal good but not a luxury since
  the income elasticity is gt 0 but lt 1.0

55
Cross Price Elasticityof Demand
56
Cross Price Elasticity of Demand
Cross Price elasticity of demand
Percentage change in quantity

Percentage change in another price
?QH??PT PT?QH
where PT (PTa PTb) ?2 QH (QHa QHb)
?2 ?QH (QHa QHb) ?PT (PTa PTb)
Indicates potential changes or shifts in the
demand curve as the price of other goods change
Page 95
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Interpreting the Cross Price Elasticity of Demand
Page 96
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Some Examples
Values in red along the diagonal are own price
elasticities
Page 100
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Some Examples
Values off the diagonal are all positive,
indicating these products are substitutes as
prices change
Page 100
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Some Examples
An increase in the price of Ragu Spaghetti Sauce
has a bigger impact on Hunts Spaghetti Sauce
than vice versa.
Page 100
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Some Examples
A 10 increase in the price of Ragu Spaghetti
Sauce increases the demand for Hunts Spaghetti
Sauce by 5.349..
Page 100
62
Some Examples
Buta 10 increase in the price of Hunts
Spaghetti Sauce increases the demand for Ragu
Spaghetti Sauce by only 1.381..
Page 100
63
Example

• 1. The cross price elasticity for hamburger
  demand with respect to the price of hamburger
  buns is equal to 0.60.
• If the price of hamburger buns rises by 5
  percent, what impact will that have on hamburger
  consumption?
• What is the demand relationship between these
  products?

64
The Answer

• 1. The cross price elasticity for hamburger
  demand with respect to the price of hamburger
  buns is equal to 0.60.
• If the price of hamburger buns rises by 5, what
  impact will that have on hamburger consumption?
  ____ - 3 ______
• Solution
• -.60 ?QH ? ?PHB
• -.60 ?QH ? .05
• ?QH .05 ? (-.60) -.03 or 3

65
The Answer

• 1. The cross price elasticity for hamburger
  demand with respect to the price of hamburger
  buns is equal to 0.60.
• If the price of hamburger buns rises by 5, what
  impact will that have on hamburger consumption?
  ___ - 3 _____
• What is the demand relationship between these
  products?

66
The Answer

• 1. The cross price elasticity for hamburger
  demand with respect to the price of hamburger
  buns is equal to 0.60.
• If the price of hamburger buns rises by 5, what
  impact will that have on hamburger consumption?
  ___ - 3 _____
• What is the demand relationship between these
  products?
• These two products are complements as evidenced
  by the negative sign on this cross price
  elasticity.

67
Another Example

• 2. Assume that a retailer sells 1,000 six-packs
  of Pepsi per day at a price of 3.00 per
  six-pack. Also assume the cross price elasticity
  for Pepsi with respect to the price of Coca Cola
  is 0.70.
• If the price of Coca Cola rises by 5 percent,
  what impact will that have on Pepsi consumption?
• b. What is the demand relationship between
  these products?

68
The Answer

• 2. Assume that a retailer sells 1,000 six-packs
  of Pepsi per day at a price of 3.00 per
  six-pack. Also assume the cross price elasticity
  for Pepsi with respect to the price of Coca Cola
  is 0.70.
• If the price of Coca Cola rises by 5 percent,
  what impact will that have on Pepsi consumption?
• Solution
• .70 ?QPepsi ? ?PCoke
• .70 ?QPepsi ? .05 .035 or 3.5
• New quantity sold 1,000 ? 1.035 1,035
• New value of sales 1,035 ? 3.00 3,105

69
The Answer

• 2. Assume that a retailer sells 1,000 six-packs
  of Pepsi per day at a price of 3.00 per
  six-pack. Also assume the cross price elasticity
  for Pepsi with respect to the price of Coca Cola
  is 0.70.
• If the price of Coca Cola rises by 5 percent,
  what impact will that have on Pepsi consumption?
  __35 six-packs or 105 per day__
• What is the demand relationship between these
  products?

70
The Answer

• 2. Assume that a retailer sells 1,000 six-packs
  of Pepsi per day at a price of 3.00 per
  six-pack. Also assume the cross price elasticity
  for Pepsi with respect to the price of Coca Cola
  is 0.70.
• If the price of Coca Cola rises by 5 percent,
  what impact will that have on Pepsi consumption?
  __35 six-packs or 105 per day__
• What is the demand relationship between these
  products?
• The products are substitutes as evidenced by the
  positive sign on this cross price elasticity!

71
Price Flexibilityof Demand
72
Price Flexibility
We earlier said that the price flexibility is the
reciprocal of the own-price elasticity. If the
calculated elasticty is - 0.25, then the
flexibility would be - 4.0.
73
Price Flexibility
We earlier said that the price flexibility is the
reciprocal of the own-price elasticity. If the
calculated elasticty is - 0.25, then the
flexibility would be - 4.0. This is a useful
concept to producers when forming expectations
for the current year. If the USDA projects an
additional 2 of supply will likely come on the
market, then producers know the price will likely
drop by 8, or ?Price - 4.0 x ?Quantity
- 4.0 x (2)
- 8
If supply increases by 2, price would fall by 8!
74
Price Flexibility
We earlier said that the price flexibility is the
reciprocal of the own-price elasticity. If the
calculated elasticty is - 0.25, then the
flexibility would be - 4.0. This is a useful
concept to producers when forming expectations
for the current year. If the USDA projects an
additional 2 of supply will likely come on the
market, then producers know the price will likely
drop by 8, or ?Price - 4.0 x ?Quantity
- 4.0 x (2)
- 8
If supply increases by 2, price would fall by 8!
Note make sure you use the negative sign for
both the elasticity and the flexibility.
75
Revenue Implications
Page 101
Characteristic of agriculture
76
Changing Price Response Over Time
Short run effects
Long run effects
Over time, consumers respond in greater numbers.
This is referred to as a recognition lag
Page 97
77
Ags Inelastic Demand Curve
Price
a
A small increase in supply will cause the price
of Ag products to fall sharply. This explains
why major program crops receive Subsidies from
the federal government.
Pb
b
Pa
Increase in supply
0
Qb Qa
Quantity
78
Inelastic Demand Curve
Price
Price
a
a
While this increases the costs of
government programs and hence budget deficits,
remember consumers benefit from cheaper food
costs.
Pb
Pb
b
b
Pa
Pa
0
0
Qb Qa
Qb Qa
Quantity
79
Demand Characteristics

• Which market is riskier for producerselastic or
  inelastic demand?
• Which market would you start a business in?
• Which market is more apt to need government
  subsidies to stabilize producer incomes?

80
The Market Demand Curve
Price
What causes movement along a demand curve?
Quantity
81
The Market Demand Curve
Price
What causes the demand curve to shift?
Quantity
82
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 shifts the
  demand curve

83
Chapter 6 starts a series of chapters that
culminates in a market supply curve for food and
fiber products.