1. Measurement and Interpretation of 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 Elasticity of Demand

7. Own Price Elasticity of Demand
We have the choice of focusing on the elasticity at a specific point on the demand curve or the elasticity over a relevant range on the demand curve
Point elasticity
Arc elasticity
Single point
on curve
Relevant range
on curve Pb Pa Pa Qb Qa Qa
Page 91

8. Own Price Elasticity of Demand
Our focus in this course will be on Arc Elasticity, or the response in quantity demanded as a result of a given change in the price of the product over a relevant range of the demand curve.
Arc elasticity
Relevant range
on curve Pb Pa Qb Qa
Page 91

9. Three approaches… Equation 5.1 = = Equation 5.2 = [QP] × [PQ]
Own price elasticity of demand
Percentage change in quantity
Equation 5.1 =
Percentage change in price
Own price elasticity of demand
(QA – QB) ([QA + QB] 2)
(PA – PB) ([PA + PB] 2) =
Equation 5.2
Own price elasticity of demand
= [QP] × [PQ]
Equation 5.3
Page 91

10. Three approaches… Given enough information, all three
Own price elasticity of demand
Percentage change in quantity
Equation 5.1 =
Percentage change in price
Own price elasticity of demand
Given enough information, all three
approaches give the same answer
[QA – QB  ([QA + QB] 2)
[PA – PB  ([PA + PB] 2) =
Equation 5.2
Own price elasticity of demand
= [QP] × [PQ]
Equation 5.3
Page 91

11. Own price elasticity of demand
First approach…
Own price elasticity of demand
Percentage change in quantity
Equation 5.1 =
Percentage change in price
If you know the percentage change in quantity over a range on the demand curve associated with a given percentage change in price, you can calculate the elasticity.
For example, if movie ticket sales drop by 40 percent as a result of a 22 percent increase in ticket prices, the elasticity would be -1.8, or
-1.8 = -.40 ÷ .22
Interpretation: A 1% increase (decrease) in price would cause quantity demanded to drop (rise) by 1.8 percent.
Page 91

12. Own price elasticity of demand
First approach…
Own price elasticity of demand
Percentage change in quantity
Equation 5.1 =
Percentage change in price
Alternatively, if you know the elasticity associated with ticket sales is and have been informed that the theater is planning to raise prices 22 percent, you can solve for the percentage change in the quantity of ticket sales, or:
-1.80 = %Q ÷ .22
%Q = × .22 = or - 40%
Thus ticket sales will drop by 40% if the theater raises ticket prices by 22%.
Page 91

13. Own price elasticity of demand
Second approach…
Own price elasticity of demand
[(QA – QB) ([QA + QB] 2)
[(PA – PB) ([PA + PB] 2) =
Equation 5.2
The subscript “a” here stands for “after” while “b” stands for “before”.
The numerator represents the percent change in quantity over the range of the demand curve associated with Qa and Qb. The denominator represents the percent change in price over the same range. Pb Pa Qb Qa
Page 91

14. Own price elasticity of demand
Second approach…
Own price elasticity of demand
[(QA – QB)  ([QA + QB] 2)
[(PA – PB)  ([PA + PB] 2) =
Equation 5.2
Suppose the quantity demanded fell from 3 to 2 when the price increased from $1.00 to $1.25, or:
PB = $1.00 QB = 3
PA = $1.25 QA = 2
Substituting these values into the equation above, we see the elasticity over this range would be:
-1.8 =
(2 – 3)  2.5
($1.25 – $1.00)  $1.125
Page 91

15. Own price elasticity of demand
Second approach…
Own price elasticity of demand
[(QA – QB)  ([QA + QB] 2)
[(PA – PB)  ([PA + PB] 2) =
Equation 5.2
(2 – 3)  2.5
($1.25 – $1.00)  $1.125
- 1.8 =
Thus if the quantity demanded fell from 3 to 2 when the price increased from $1.00 to $1.25, the elasticity over this range would be -1.8.
This suggests that a one percent increase in price would reduce the quantity demanded by 1.8 percent!!!
Page 91

16. Own price elasticity of demand
Second approach…
Own price elasticity of demand
[QA – QB  ([QA + QB] 2)
[PA – PB  ([PA + PB] 2) =
Equation 5.2
[2 – 3  ([3 + 2] 2)
[$1.25 – $1.00  $1.125])
- 1.8 =
Alternatively, if you were given the elasticity and told that the price increased from $1.00 to $1.25, you can calculate the percentage change in quantity demanded by:
- 1.8 = %∆Q ÷ [($1.25 – $1.00)  $1.125]
%∆Q = (-1.8) × [($1.25 – $1.00)  $1.125] = (-1.8) x .22 = -.40
%∆Q
($1.25 – $1.00)  $1.125
- 1.8 =
Page 91

17. Own price elasticity of demand
Third approach…
Own price elasticity of demand
Equation 5.3
= [Q  P] × [P  Q]
We can simplify the calculations in equation 5.2 by using equation 5.3 instead when given information on prices and corresponding quantities.
Page 91

18. Own price elasticity of demand
Third approach…
Own price elasticity of demand
= [QP] × [PQ]
Equation 5.3
Suppose the quantity demanded fell from 3 to 2 when the price increased from $1.00 to $1.25, or:
∆Q = (2 - 3) = -1;
∆P = ($ $1.00) = $0.25
Q = (2 + 3) ÷ 2= 2.5
P = ($ $1.00) ÷ 2 = $1.125
Page 91

19. Own price elasticity of demand
Third approach…
Substituting these values into equation 5.3, we see that the own price elasticity would once again be equal to -1.8, or:
Own price elasticity of demand
= [QP] × [PQ]
Equation 5.3
= [(-1)  $0.25] × [$1.125  2.5] = -1.8
This formula represents the easiest approach to calculating the elasticity for a given change in price and quantity.
Page 91

20. Hints for application…
If given the elasticity and the percentage change in price, and asked to determine the impact on quantity demanded, solve for %∆Q using equation 5.1.
Own price elasticity of demand
Percentage change in quantity
Equation 5.1 =
Percentage change in price
%∆Q =
%∆P Pb Pa Qb Qa
Page 91

21. Hints for application…
If given the elasticity and information on calculating the percentage change in price and asked to determine the impact on quantity demanded, solve for %∆Q using equation 5.2.
Own price elasticity of demand
[QA – QB  ([QA + QB] 2)
[PA – PB  ([PA + PB] 2) =
Equation 5.2
%∆Q
[PA – PB  ([PA + PB] 2) = Pb Pa Qb Qa
Page 91

22. Hints for application…
If given information on both price and quantity before and after the change and asked to calculate the elasticity, use equation 5.3.
Own price elasticity of demand
= [QP] x [PQ]
Equation 5.3
Q = Qa – Qb
P = Pa – Pb
P = (Pa + Pb) ÷ 2
Q = (Qa + Qb) ÷ 2 Pb Pa Qb Qa
Page 91

23. Interpreting the Own Price Elasticity of Demand
If elasticity coefficient is:
Demand is said to be:
% in quantity is:
Greater than 1.0
Elastic
Greater than % in price
Equal to 1.0
Unitary
elastic
Same as % in price
Less than 1.0
Inelastic
Less than % in price
Page 92

24. Demand Curves Come in a Variety of Shapes

25. Demand Curves Come in a Variety of Shapes
Perfectly inelastic
Perfectly elastic
Page 92

26. Demand Curves Come in a Variety of Shapes
Inelastic
Elastic

27. Demand Curves Come in a Variety of Shapes
Elastic where %Q > % P
Unitary Elastic where %Q = % P
Inelastic where %Q < % P
Page 93

28. Example of arc own-price elasticity of demand
Unitary elasticity…a one
for one exchange
Page 93

29. Elastic demand
Inelastic demand
Page 93

30. Elastic Demand Curve Price c Pb Cut in price Brings about a larger Pa
increase in the quantity
demanded Pa
Qb Qa
Quantity

31. Elastic Demand Curve Price What happened to producer revenue?
consumer surplus? c Pb Pa
Qb Qa
Quantity

32. 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
Qb Qa
Quantity

33. 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
Qb Qa
Quantity

34. 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
Qb Qa
Quantity

35. Revenue Implications Own-price elasticity is: Cutting the price will:
Increasing the price will:
Elastic
Increase revenue
Decrease revenue
Unitary elastic
Not change revenue
Inelastic
Page 101

36. Elastic Demand Curve Price Consumer surplus before the price cut
was area Pbca. c a Pb b Pa
Qb Qa
Quantity

37. Elastic Demand Curve Price Consumer surplus after the price cut is
Area Pacb. c a Pb b Pa
Qb Qa
Quantity

38. Elastic Demand Curve Price So the gain in consumer surplus
after the price cut is
area PaPbab. c a Pb b Pa
Qb Qa
Quantity

39. Inelastic Demand Curve
Price Pb
Cut in
price Pa
Brings about a smaller
increase in the quantity
demanded
Qb Qa
Quantity

40. Inelastic Demand Curve
Price Pb
What happened to
producer revenue?
consumer surplus? Pa
Qb Qa
Quantity

41. Inelastic Demand Curve
Price a Pb
Producer revenue
falls since %P is
greater than %Q.
Revenue before the
change was 0PbaQb.
Revenue after the
change was 0PabQa. Pa b
Qb Qa
Quantity

42. Inelastic Demand Curve
Price a Pb
Producer revenue
falls since %P is
greater than %Q.
Revenue before the
change was 0PbaQb.
Revenue after the
change was 0PabQa. Pa b
Qb Qa
Quantity

43. Inelastic Demand Curve
Price a Pb
Consumer surplus
increased by area
PaPbab Pa b
Qb Qa
Quantity

44. Revenue Implications Own-price elasticity is: Cutting the price will:
Increasing the price will:
Elastic
Increase revenue
Decrease revenue
Unitary elastic
Not change revenue
Inelastic
Characteristic of agriculture
Page 101

45. Retail Own Price Elasticities
Beef and veal= .6166
Milk = .2588
Wheat = .1092
Rice = .1467
Carrots = .0388
Non food = .9875
Page 99

46. Interpretation
Let’s take rice as an example, which has an own price elasticity of
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

47. Sample Problems from Old Exams

48. 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 – If the Chicken increases the price of the platter by 50 cents:
How many platters will the chicken sell?__________
b. The Chicken’s revenue will change by $__________
c. Consumers will be ____________ off as a result of this price change.

49. 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 – 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[(Pa-Pb)  ((Pa+Pb) 2)]
-0.30 = %Q[($4.00-$3.50)  (($4.00+$3.50) 2)]
-0.30 = %Q[$0.50$3.75]
-0.30 = %Q0.133
%Q =(-0.30 × 0.133) = or –4%
So new quantity is 1,440, or (1-.04) ×1,500, or .96 ×1,500
Equation 5.2

50. 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 – If the Chicken increases the price of the platter by 50 cents:
How many platters will the chicken sell?__1,440____
b. The Chicken’s 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

51. 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 – If the Chicken increases the price of the platter by 50 cents:
How many platters will the chicken sell?__1,440____
b. The Chicken’s revenue will change by $__+$510___
Consumers will be __worse___ off as a result of this price change.
Why? Because price increased.

52. If given %∆P….
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 – If the Chicken increases the price of the platter by 13.3 percent:
How many platters will the chicken sell?__________
b. The Chicken’s revenue will change by $__________
c. Consumers will be ____________ off as a result of this price change.

53. 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 – If the Chicken increases the price of the platter by 13.3 percent:
How many platters will the chicken sell?__1,440____
Solution:
-0.30 = %Q%P
-0.30 = %Q0.133
%Q = (-0.30 × 0.133) = or – 4%
So new quantity is 1,440, or (1-.04) ×1,500, or .96 ×1,500
Equation 5.1

54. Income Elasticity of Demand

55. Income Elasticity of Demand
Percentage change in quantity =
Equation 5.4
Percentage change in income
= [QI] x [IQ]
Equation 5.6
where:
I = (Ia + Ib) 2
Q = (Qa + Qb) 2
Q = (Qa – Qb)
I = (Ia – Ib)
Indicates potential changes in demand as the demand curve shifts as a result of a change in consumer disposable income…
Page 94-95

56. Interpreting the Income Elasticity of Demand
If the income elasticity is equal to:
The good is classified as:
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 95

57. Some Examples Commodity Own Price elasticity Income elasticity Elastic
Beef and veal
0.4549
Chicken
.3645
Cheese
0.5927
Rice
Lettuce
0.2344
Tomatoes
0.4619
Fruit juice
1.1254
Grapes
0.4407
Nonfood items
1.1773
Elastic
Page 99

58. Some Examples Commodity Own Price elasticity Income elasticity Elastic
Beef
0.4549
Chicken
.3645
Cheese
0.5927
Rice
Lettuce
0.2344
Tomatoes
0.4619
Fruit juice
1.1254
Grapes
0.4407
Nonfood items
1.1773
Elastic
Inferior good
Page 99

59. Some Examples Commodity Own Price elasticity Income elasticity Elastic
Beef
0.4549
Chicken
.3645
Cheese
0.5927
Rice
Lettuce
0.2344
Tomatoes
0.4619
Fruit juice
1.1254
Grapes
0.4407
Nonfood items
1.1773
Elastic
Inferior good
Luxury good
Page 99

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

61. The Answer
1. Assume the government cuts taxes, thereby increasing disposable income (I) by 5%. The income elasticity for chicken is
What impact would this tax cut have upon the demand for chicken?
Solution:
.3645 = %QChicken  % I
.3654 = %QChicken  .05
%QChicken = .05 = .018 or + 1.8%
Equation 5.4

62. The Answer
1. Assume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is
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 > 0 but < 1.0

63. Cross Price Elasticity of Demand

64. Cross Price Elasticity of Demand
Percentage change in quantity
Equation 5.7 =
Percentage change in another price
= [QHPT] × [PTQH]
Equation 5.9
where:
PT = (PTa + PTb) 2
QH = (QHa + QHb) 2
QH = (QHa – QHb)
PT = (PTa – PTb)
Indicates potential change in demand as the demand curve shifts as a result of a change in the price of another good…
Page 95

65. Interpreting the Cross Price Elasticity of Demand
If the cross price elasticity is equal to:
The good is classified as:
Positive
Substitutes
Negative
Complements
Zero
Independent
Page 96

66. Some Examples Item Prego Ragu Hunt’s -2.5502 .8103 .3918 .5100 -2.0610
.1381
1.0293
.5349
Values in red along
the diagonal are own
price elasticities…
Page 100

67. Some Examples Item Prego Ragu Hunt’s -2.5502 .8103 .3918 .5100 -2.0610
.1381
1.0293
.5349
Values off the diagonal are all positive, indicating these products are substitutes as prices change…
Page 100

68. Some Examples Item Prego Ragu Hunt’s -2.5502 .8103 .3918 .5100 -2.0610
.1381
1.0293
.5349
An increase in the price of
Ragu Spaghetti Sauce has a
bigger impact on Hunt’s
Spaghetti Sauce than vice
versa.
Page 100

69. Some Examples Item Prego Ragu Hunt’s -2.5502 .8103 .3918 .5100 -2.0610
.1381
1.0293
.5349
A 10% increase in the price of
Ragu Spaghetti Sauce increases
the demand for Hunt’s Spaghetti Sauce by 5.349%…..
Page 100

70. Some Examples Item Prego Ragu Hunt’s -2.5502 .8103 .3918 .5100 -2.0610
.1381
1.0293
.5349
But…a 10% increase in the price of
Hunt’s Spaghetti Sauce increases
the demand for Ragu Spaghetti Sauce by only 1.381%…..
Page 100

71. 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?

72. If Given %PHB…
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%
Equation 5.7

73. 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?

74. 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.

75. 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?

76. 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 this have on Pepsi consumption?
Solution:
.70 = %QPepsi  %PCoke
.70 = %QPepsi  .05 = .035 or 3.5%
New quantity of Pepsi sold = 1,000  = 1,035
New value of Pepsi sales = 1,035  $3.00 = $3,105
Equation 5.7

77. 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?

78. 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!

79. Elasticity Formulas For Exam
Own price elasticity of demand
Percentage change in quantity
Equation 5.1 =
Percentage change in price
Income elasticity of demand
Percentage change in quantity
Equation 5.4 =
Percentage change in income
Cross price elasticity of demand
Percentage change in quantity
Equation 5.7 =
Percentage change in another price
You will not have to calculate a percentage change in a
numerator or denominator…

80. Price Flexibility of Demand

81. Price Flexibility
We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is , then the flexibility would be

82. Price Flexibility
We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is , then the flexibility would be
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 = x %Quantity
= x (+2%)
= - 8%
If supply increases by 2%, price would fall by 8%!

83. Price Flexibility
We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is , then the flexibility would be
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 = x %Quantity
= 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.

84. Revenue Implications Own-price elasticity is: Increase in supply will:
Decrease in supply will:
Elastic
Increase revenue
Decrease revenue
Unitary elastic
Not change revenue
Inelastic
Characteristic of agriculture
Page 101

85. 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

86. Ag’s Inelastic Demand Curve
Price a Pb
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. Pa b
Increase in
supply
Qb Qa
Quantity

87. Inelastic Demand Curve
Price
Price a a Pb Pb
While this increases the
costs of government
programs and hence
budget deficits, remember
consumers benefit from
cheaper food costs. Pa Pa b b
Qb Qa
Qb Qa
Quantity

88. 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?

89. The Market Demand Curve
Price
What causes movement along a demand curve?
Quantity

90. The Market Demand Curve
Price
What causes the demand curve to shift?
Quantity

91. 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

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