1. Measurement and Interpretation of Elasticities
Chapter 5

2. Discussion Topics
Own price elasticity of demand: A unit free measure of demand response to a good’s own-price 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 2

3. Key Concepts Covered…
Own price elasticity = % in Qi for a given % in Pi
Represented as ηii
i.e., the effect of a change in the price for hamburger on hamburger demand: ηHH = % in QH for a given % in PH
Cross price elasticity = % in Qi for a given % in Pj
Represented as ηij
i.e., the effect of a change in the price of chicken on hamburger demand: ηHC = % in QH for a given % in PC
Income elasticity = %Qi for a given %Income
Represented as ηiY
i.e., the effect of a change in income on hamburger demand: ηHY = %QH for a given %PY 3
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 Pi for a given % in Qi 4
Pages 70-76

5. Own Price Elasticity of Demand5

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

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

8. 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
Unitary
Same as % in Price
Greater than
Inelastic
Less than % in Price
Note: The %Δ in Q is in terms of the absolute value
of the change 8
Page 72

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

10. Own Price Elasticity of Demand
What does a own-price elasticity of 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 10

11. Own Price Elasticity of Demand
ηii = -0.2 to -0.3 11

12. Own Price Elasticity of Demand
Why is ηii 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
Qb = 2.25 tons Pb = $350/ton Qa = 2.50 tons Pa = $300/ton 12

13. Own Price Elasticity of Demand
Lets recalculate the above elasticity but this time in terms of lbs.
Qb = 4,500 lbs Pb = $0.175/lb
Qa = 5,000 lbs Pa = $0.150/lb
←Same as previous value 13

14. Demand Curves Come in a Variety of Shapes$ Q 14

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

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

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

18. Example of Arc Own-Price Elasticity of Demand
Unitary elasticity
–% Change in Q = % Change in P
ηii= –1.0 18
Page 73

19. Elastic demand
Inelastic demand 19
Page 73

20. Elastic Demand Curve With the price decrease from Pb to Pa$
With the price decrease from Pb to Pa
What happens to producer revenue (or consumer expenditures)? Pb Pa Q Qb Qa 20

21. Elastic Demand Curve $
An elastic demand curve → a larger % ↑in quantity demanded than the absolute value of the % price change (a price decrease) Pb
Cut in
price Pa Q
Qb Qa 21

22. Elastic 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) is Pa x Qa
Represented by the area 0PaBQa $ C A Pb B Pa Q Qa Qb 22

23. Elastic Demand Curve Change in revenue (∆TR) is TRa – TRb
→ ∆TR = 0PaBQa – 0PbAQb
→ ∆TR = QbDBQa – PaPbAD
→TR ↑
%Q ↑ is greater than %P ↓ $
Red Box
Purple Box C A Pb D B Pa
When you have elastic demand
↑ in price → ↓ total revenue (expenditures)
↓ in price → ↑ total revenue (expenditures) Q Qa Qb 23

24. Inelastic Demand Curve$ Pb
Cut in
price Pa
Results in smaller %
increase in quantity
demanded Q
Qb Qa 24

25. Inelastic Demand Curve$
With price decrease from Pb to Pa
What happens to producer revenue or consumer expenditures)? Pb Pa Q
Qb Qa 25

26. 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
Represented by the area 0PaBQa $ A Pb Pa B Q 26
Qb Qa

27. Inelastic Demand Curve
Change in revenue (∆TR) is TRa – TRb
∆TR = 0PaBQa – 0PbAQb
∆TR = QbDBQa – PaPbAD
→TR ↓
% Q increase is less than %P decrease $
Red Box
Purple Box A Pb Pa B
When you have inelastic demand
↑ in price → ↑ total revenue
↓ in price → ↓ total revenue D Q
Qb Qa 27

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

29. Elastic Demand Curve Consumer surplus (CS)$
Consumer surplus (CS)
Before price cut CS is area PbCA
After the price cut CS is area PaCB C A Pb B Pa Q Qb Qa 29

30. Elastic Demand Curve $
The gain in consumer surplus after the price cut is area PaPbAB = PaCB – PbCA C A Pb B Pa Q
Qb Qa 30

31. Inelastic Demand Curve$
Inelastic demand and price decrease
Consumer surplus increases by area PaPbAB A Pb Pa B Q
Qb Qa 31

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 32

33. 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% $
Demand
Curve
With a price drop
What is the impact on rice producer revenues?
What is the impact on consumer surplus from rice consumption? Pb A
10% drop B Pa
1.5% increase Q QB Qa 33

34. Own Price Elasticity Example
The local Kentucky Fried Chicken outlet typically sells 1,500 Crunchy Chicken platters per month at $3.50 each
The own price elasticity for the platter is estimated to be –0.30
If the KFC outlet increases the price of the platter to $4.00:
How many platters will the KFC outlet sell after the price change?__________
The KFC outlet’s revenue will change by $__________
Will consumers be worse or better off as a result of this price change?_________
Inelastic demand 34

35. The answer…
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 – If the local KFC outlet increases the price of the platter by 50¢:
How many platters will the chicken sell? 1,440
Solution:
-0.30 = %Q%P
-0.30= %Q[($4.00-$3.50) (($4.00+$3.50) 2)]
-0.30= %Q[$0.50$3.75]
-0.30= %Q0.1333
→ %Q=(-0.30 × ) = or –4%
→ New quantity = (1–0.04)×1,500 = 0.96×1,500 = 1,440 P
Avg. Price
%P 35

36. 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 36

37. Another Example
The local KFC outlet sells 1,500 crunchy chicken platters/month when their price was $ The own price elasticity for this platter is estimated to be
– If the KFC increases the platter price by 50¢:
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?
Elastic demand 37

38. The answer…
The local KFC outlet sells 1,500 crunchy chicken platters/month when the price is $ The own price elasticity for this platter is estimated to be
– If the KFC increases the platter price by 50¢:
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 × ) = or –17.33%
→ New quantity = (1 ̶ )×1,500 = ×1,500 = 1,240 38

39. The answer… 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)
Consumers will be worse off as a result of this price change
Why? Because the price increased. 39

40. Income Elasticity of Demand40

41. Income Elasticity of Demand
Percentage change in quantity demanded (Q)
ηY =
Percentage change in income (I)
where:
I = (Ia + Ib) 2
Q = (Qa + Qb) 2
Q = (Qa – Qb)
I = (Ia – Ib)
ηY : A quantitative measure of changes or shifts in quantity demanded (ΔQ) resulting from changes in consumer income (I)
Page 74-75 41

42. 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 42

43. Some Income Elasticity Examples
Commodity
Income
elasticity
Beef and veal
0.455
Chicken
0.365
Cheese
0.594
Rice
-0.366
Lettuce
0.234
Tomatoes
0.462
Fruit juice
1.125
Grapes
0.441
Nonfood items
1.177
Inferior good
Luxury goods
Source: Huang, 1985
Page 79 43

44. 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
What impact would this tax cut have upon the demand for chicken?
Is chicken a normal or an inferior good? Why? 44

45. 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:
= %QChicken  % I
→ = %QChicken  .05
→%QChicken = .05 = .018 or + 1.8%
b. Chicken is a normal but not a luxury good since the income elasticity is > 0 and < 1.0 45

46. Cross Price Elasticity of Demand46

47. Cross Price Elasticity of Demand
Percentage change in quantity demanded
ηij =
Percentage change in another good’s price
i and j are goods
(i.e., apples, oranges, peaches)
where:
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 47

48. 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
Page 75 48

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

50. Some Examples Quantity Changing 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
Values in red along
the diagonal are own
price elasticities
Page 80 50

51. Some Examples Spaghetti Sauce 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)
Page 80 51

52. Some Examples Spaghetti Sauce 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 52

53. Some Examples Spaghetti Sauce 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 53

54. Example
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?
What is the demand relationship between these products? 54

55. The Answer
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? -3.0%
Solution:
-0.60 = %QH  %PHB
-0.60 = %QH  .05
%QH = .05  (-.60) = -.03 or – 3.0%
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 55

56. Another Example Assume a retailer:
Sells 1,000 six-packs of Pepsi/day at a price of $3.00 per six-pack
The cross price elasticity for Pepsi with respect to Coca Cola price is 0.70
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? 56

57. The Answer
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 six-packs, 35 additional six packs
New value of sales = 1,035  $3.00 = $3,105 or $105/day extra
What is the demand relationship between these products?
The products are substitutes as evidenced by the positive sign on this cross price elasticity 57

58. Price Flexibility of Demand58

59. Price Flexibility
The price flexibility is the reciprocal (inverse) of the own-price elasticity
If the calculated elasticty is , then the flexibility = 1/(-0.25) = - 4.0
Price Flexibility interpretation: %∆P ÷ %∆Q 59

60. 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 = x %Quantity
= 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. 60

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

62. 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
With increasing time, price elasticities tend to increase → flatter demand curve
Page 77 62

63. Implications of Agriculture’s Inelastic Demand Curve$ Pb A
Small ↑ in supply will cause agricultural product prices to ↓ sharply
Explains why major program crops receive Federal government subsidies Pa
Increase in
supply Q
Qb Qa 63

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

65. 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? 65

66. The Market Demand Curve
Price
What causes movement along a demand curve?
Quantity 66

67. The Market Demand Curve
Price
What causes the demand curve to shift?
Quantity 67

68. 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 68

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