Measurement and Interpretation of Elasticities Chapter 5.
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Transcript of Measurement and Interpretation of Elasticities Chapter 5.
Measurementand
Interpretationof Elasticities
Chapter 5
Discussion TopicsOwn 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 elasticities2
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 %IncomeRepresented as ηiY
i.e., the effect of a change in income on hamburger demand: ηHY = %QH for a given %PY
Pages 70-763
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
Pages 70-764
Own Price Elasticityof Demand
5
Own Price Elasticity of Demand
Point Elasticity Approach:
Own price elasticity of
demand
Q = (Qa – Qb)
P = (Pa – Pb)
Pages 70-72
Pa
Qa
a
a a a
PQQ PQ P P Q
The subscript• a stands for after price change• b stands for before price change
$
Q
Pb
Qb
Own price elasticity of
demand
Percentage change in quantity demanded (Q)
Percentage change in its own price (P)ηii =
6
Single pointon curve
Single pointon curve
% Δ in Q% Δ in P
Own Price Elasticity of Demand
Percentage change in quantity Percentage change in own priceηii =
where:P = (Pa + Pb) 2 Q = (Qa + Qb) 2 Q = (Qa – Qb) P = (Pa – Pb)
Arc Elasticity Approach:Own price elasticity of
demand
Page 72
Q PQ PQ P P Q
The subscript• a stands for after price change• b stands for before price change
The subscript• a stands for after price change• b stands for before price change
Avg Price
Avg Quantity
Equation 5.3Equation 5.3
Pa
Pb
Qa Qb
Specific rangeon curve
Specific rangeon curve$
Q
P
Q
Own price elasticity of
demand
7
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
Greater than –1.0 Inelastic
Less than % in Price
Page 728
Note: The %Δ in Q is in terms of the absolute valueof the change
Own Price Elasticity of Demand
9
Snow Leopard was a previousversion of Apple’s OS
Own Price Elasticity of Demand
10
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
Own Price Elasticity of Demand
11
ηii = -0.2 to -0.3
Own Price Elasticity of Demand
12
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
tonsSS
2.50tons – 2.25tons $300 / ton $350 / tonη
2.50tons $300 / ton
0.25tons $50 ton 0.25 502.50tons $300 ton 2.50 300
0.100.60
0.167
Own Price Elasticity of Demand
13
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
lbsSS
5000lbs – 4,500lbs $0.150 / lb $0.175 / lbη
5,000lbs $0.150 / lb
500lbs $0.025 lb 500 0.0255,000 lbs $0.150 lb 5,000 0.150
0.100.60
0.167
←Same as previous value
Demand Curves Come in a Variety of Shapes
$
Q
14
Demand Curves Come in a Variety of Shapes
Page 72
$
Q
Perfectly ElasticPerfectly Elastic
Perfectly InelasticPerfectly Inelastic
Perfectly Inelastic: A price change does not change quantity purchased Can you think of a
good that would have this characteristic?
∆P
15
The two extremes
Demand Curves Come in a Variety of Shapes
Inelastic DemandInelastic Demand
Elastic DemandElastic Demand
∆P
∆Q
∆P
∆Q
$
Q
16 Page 73
Demand Curves Come in a Variety of Shapes
Inelastic where (–%Q )< % PInelastic where (–%Q )< % P
Elastic where (–%Q ) > % P Elastic where (–%Q ) > % P
Page 73
Unitary Elastic where (–%Q) = % P Unitary Elastic where (–%Q) = % P
$
Q
17
A single demand curve can exhibitvarious types of own-price elasticity
Page 73
Example of Arc Own-Price Elasticity of DemandExample of Arc Own-Price Elasticity of Demand
Unitary elasticity–% Change in Q = % Change in
Pηii= –1.0
Unitary elasticity–% Change in Q = % Change in
Pηii= –1.0
18
Page 73
Inelastic demandInelastic demand
Elastic demandElastic demand
19
Pb
Pa
Qb
$
Q
Elastic Demand CurveElastic Demand Curve
With the price decrease from Pb to Pa
What happens to producer revenue (or consumer expenditures)?
0 Qa
20
Pb
Pa
Qb Qa
$
Q
Elastic Demand CurveElastic Demand Curve
0
Cut in price
Cut in price
An elastic demand curve → a larger % ↑in quantity demanded than the absolute value of the % price change (a price decrease)
An elastic demand curve → a larger % ↑in quantity demanded than the absolute value of the % price change (a price decrease)
21
Pb
Pa
Qb
Q
Elastic Demand CurveElastic 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
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 0PaBQaA
B
0
C
$
Qa
22
Pb
Pa
Qb
Q
Elastic Demand CurveElastic Demand Curve
Change in revenue (∆TR) is TRa – TRb
→ ∆TR = 0PaBQa – 0PbAQb
→ ∆TR = QbDBQa – PaPbAD
→TR ↑%Q ↑ is greater than %P ↓
A
B
0
C
$
Qa
D
Red Box Purple Box
When you have elastic demand ↑ in price → ↓ total
revenue (expenditures) ↓ in price → ↑ total
revenue (expenditures)
23
Pb
Pa
Qb Qa
$
Q
Inelastic Demand CurveInelastic Demand Curve
Cut in price
Cut in price
Results in smaller %increase in quantitydemanded
Results in smaller %increase in quantitydemanded
24
Pb
Pa
Qb Qa
$
Q
Inelastic Demand CurveInelastic Demand Curve
With price decrease from Pb to Pa
What happens to producer revenue or consumer expenditures)?
25
Pb
Pa
Qb Qa
$
Q
Inelastic Demand CurveInelastic Demand Curve
A
B
0
Producer revenue (TR) = price x quantityRevenue 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
26
Pb
Pa
Qb Qa
$
Q
Inelastic Demand CurveInelastic Demand Curve
A
B
0
Change in revenue (∆TR) is TRa – TRb
∆TR = 0PaBQa – 0PbAQb
∆TR = QbDBQa – PaPbAD
→TR ↓% Q increase is less than %P decrease
D
Red Box Purple Box
When you have inelastic demand ↑ in price → ↑ total
revenue ↓ in price → ↓ total
revenue
27
Revenue ImplicationsOwn-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
Not Change Revenue
Inelastic(-1< ηii < 0)
Decrease Total Revenue
Increase Total Revenue
Page 8128Typical of Agricultural CommoditiesTypical of Agricultural Commodities
Pb
Pa
Qb
$
Q
Elastic Demand CurveElastic Demand Curve
Consumer surplus (CS)Before price cut CS is area PbCAAfter the price cut CS is area PaCB
A
B
0
C
Qa
29
Pb
Pa
Qb Qa
$
Q
Elastic Demand CurveElastic Demand Curve
A
B
0
C
The gain in consumer surplus after the price cut is area PaPbAB = PaCB – PbCA
30
Pb
Pa
Qb Qa
$
Q
Inelastic Demand CurveInelastic Demand Curve
A
B
0
Inelastic demand and price decreaseConsumer surplus increases
by area PaPbAB
31
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
Page 79Source: Huang, (1985)32
InterpretationLet’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%
$
Q
10% drop10% drop
1.5% increase1.5% increase
With a price drop What is the impact on rice
producer revenues? What is the impact on
consumer surplus from rice consumption?
DemandCurve
Pb
Pa
A
B
0 QB Qa
33
Own Price Elasticity Example1. 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
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?_________
Inelastic demand
34
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? 1,440Solution:
-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= %Q0.1333→ %Q=(-0.30 × 0.1333) = -0.04 or –4%→ New quantity = (1–0.04)×1,500 = 0.96×1,500 =
1,440
P Avg. Price
%P
35
The answer…b. The Chicken’s revenue will change by +$510Solution:
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 - $5,250c. Consumers will be __worse___ off as a result of this price change
Why? Because price has increased
36
Another Example1. 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¢:
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?
Elastic demand
37
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? 1,240Solution:-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= %Q0.1333%Q=(-1.30 × 0.1333) = -0.1733 or –17.33%→ New quantity = (1 Y 0.1733)×1,500 = 0.8267
×1,500 = 1,24038
The answer…1. b. The Chicken’s revenue will change by –$290
Solution:Current revenue = 1,500 × $3.50 = $5,250/moNew 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 changeWhy? Because the price increased.
39
Income Elasticityof Demand
40
Income Elasticity of Demand
Income elasticity of
demand
Percentage change in quantity demanded (Q)
Percentage change in income (I)ηY =
where:
I = (Ia + Ib) 2 Q = (Qa + Qb) 2 Q = (Qa – Qb) I = (Ia – Ib)
Page 74-75
ηY : A quantitative measure of changes or shifts in quantity demanded (ΔQ) resulting from changes in consumer income (I)
yQ IQ I
ηQ I I Q
41
When the income elasticity is: The good is classified as:
Greater than 0.0 A normal good
Greater than 1.0A 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
Interpreting the Income Elasticity of Demand
Page 7542
ExampleAssume 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?
44
The Answer1. 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
45
Cross Price Elasticityof Demand
46
Cross Price Elasticity of Demand
Cross Price elasticity of
demand
Percentage change in quantity demanded
Percentage change in another good’s priceηij =
where:
Pj = (Pja + Pjb) 2
Qi = (Qia + Qib) 2
Qi = (Qia – Qib)Pj = (Pja – Pjb)
Page 75
ηij provides a quantitative measure of the impacts of changes or shifts in the demand curve as the price of other goods change
jj iiij
i j j i
PP QQη
Q P P Q
i and j are goods(i.e., apples, oranges, peaches)
47
Cross Price Elasticity of Demand
Page 75
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 bunsIf commodities i & j are independent (ηi j= 0):
Pi↑→Qi↓, Qj is not impactedi.e., peanut butter and Miller Lite
48
If the Cross-Price Elasticity is:
The Good is Classified as a:
Positive Substitute
Negative Complement
Zero Independent
Interpreting the Cross Price Elasticity of Demand
Page 7649
Some Examples
Quantity Changing
Price That is Changing
Prego Ragu Hunt’s
Prego -2.550 0.810 0.392
Ragu 0.510 -2.061 0.138
Hunt’s 1.029 0.535 -2.754
Page 80
Off diagonal values are all positive → These products are substitutes
Off diagonal values are all positive → These products are substitutesValues in red along
the diagonal are ownprice elasticities
Values in red alongthe diagonal are ownprice elasticities
50
Spaghetti Sauce
Price Change
Prego Ragu Hunt’s
Prego -2.550 0.810 0.392
Ragu 0.510 -2.061 0.138
Hunt’s 1.029 0.535 -2.754
Some Examples
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)
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 8051
Spaghetti Sauce
Price Change
Prego Ragu Hunt’s
Prego -2.550 0.810 0.392
Ragu 0.510 -2.061 0.138
Hunt’s 1.029 0.535 -2.754
Some Examples
Page 80
A 10% increase in Ragu spaghetti sauce price increases the demand for Hunt’s spaghetti sauce by 5.35%
A 10% increase in Ragu spaghetti sauce price increases the demand for Hunt’s spaghetti sauce by 5.35%
52
Spaghetti Sauce
Price Change
Prego Ragu Hunt’s
Prego -2.550 0.810 0.392
Ragu 0.510 -2.061 0.138
Hunt’s 1.029 0.535 -2.754
Some Examples
Page 80
A 10% increase in Hunt’s spaghetti sauce price increases Ragu spaghetti sauce demand by 1.38%
A 10% increase in Hunt’s spaghetti sauce price increases Ragu spaghetti sauce demand by 1.38%
53
Example1. The cross price elasticity for hamburger demand
with respect to the price of hamburger buns is equal to –0.60a. 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?
54
The Answer1. The cross price elasticity for hamburger demand
with respect to the price of hamburger buns is equal to –0.60a. 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
55
Another Example2. 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?
56
The Answera. 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 packsNew 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
57
Price Flexibilityof Demand
58
Price FlexibilityThe 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
59
Price FlexibilityThis 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%
→If supply ↑ by 2%, price would ↓ by 8%
Note: make sure you use the negative sign for both the elasticity and the flexibility.
60
Revenue ImplicationsOwn-Price Elasticity
Resulting Price Flexibility
Increase in Supply Will
Decrease in Supply Will
Elastic < -1.0Increase Revenue
Decrease Revenue
Unitary elastic = -1.0 Not Change
RevenueNot Change Rrevenue
Inelastic Between 0 and -1.0
Decrease Revenue
Increase Revenue
Page 81Characteristic of a large number of agricultural commodities
Characteristic of a large number of agricultural commodities
61
Short run effects Long run effects
Page 77
Changing Price Response Over TimeChanging Price Response Over Time
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
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 curve62
Pb
Pa
Qb Qa
$
Q
Implications of Agriculture’sInelastic Demand Curve
Implications of Agriculture’sInelastic Demand Curve
Small ↑ in supply will cause agricultural product prices to ↓ sharplyExplains why major
program crops receive Federal government subsidies
Small ↑ in supply will cause agricultural product prices to ↓ sharplyExplains why major
program crops receive Federal government subsidies
A
0
Increase insupply
Increase insupply
63
Pb
Pa
Qb Qa
Price
Quantity
Inelastic Demand CurveInelastic Demand Curve
While this ↑ the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs.
While this ↑ the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs.
A
0
Pb
Pa
Qb Qa
B
0
64
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
The Market Demand CurvePrice
Quantity
What causes movement along a demand curve?
What causes movement along a demand curve?
66
The Market Demand CurvePrice
Quantity
What causes the demand curve to shift?
What causes the demand curve to shift?
67
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
Chapter 6 starts a series of chapters that culminates in a market supply curve for food and fiber products….
69