measurement and interpretation of elasticities
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Measurement and Interpretation of Elasticities. Chapter 5. Discussion Topics. Own price elasticity of demand Income elasticity of demand Cross price elasticity of demand Other general properties Applicability of demand elasticities. Key Concepts Covered…. - PowerPoint PPT PresentationTRANSCRIPT
Measurementand
Interpretationof Elasticities
Chapter 5
Discussion Topics
Own price elasticity of demandIncome elasticity of demandCross price elasticity of demandOther general propertiesApplicability of demand elasticities
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 curvePoint elasticity = point on the demand curve
Price flexibility = reciprocal of own price elasticity
Own Price Elasticityof Demand
Own Price Elasticity of Demand
Own price elasticity
of demand
Percentage change in quantity
Percentage change in price=
Page 71
Arc Elasticity ApproachArc Elasticity Approach
Own Price Elasticity of Demand
Own price elasticity
of demand
Percentage change in quantity
Percentage change in price=
where:P = (Pa + Pb) 2; Q = (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb)
Arc elasticityOwn price elasticity
of demand= [QP] x [PQ]
Page 71
The subscript “a” here againstands for “after” while “b”stands for “before”
The subscript “a” here againstands for “after” while “b”stands for “before”
Equation 5.3Equation 5.3
Own Price Elasticity of Demand
Own price elasticity
of demand
Percentage change in quantity
Percentage change in price=
where:P = (Pa + Pb) 2; Q = (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb)
Arc elasticityOwn price elasticity
of demand= [QP] x [PQ]
Page 71
The subscript “a” here againstands for “after” while “b”stands for “before”
The subscript “a” here againstands for “after” while “b”stands for “before”
The “bar” over the P andQ variables indicates anaverage or midpoint.
The “bar” over the P andQ variables indicates anaverage or midpoint.
Own Price Elasticity of Demand
Own price elasticity
of demand
Percentage change in quantity
Percentage change in price=
where:P = (Pa + Pb) 2; Q = (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb)
Arc elasticityOwn price elasticity
of demand= [QP] x [PQ]
Page 71
The subscript “a” here againstands for “after” while “b”stands for “before”
The subscript “a” here againstands for “after” while “b”stands for “before”
Specific rangeon curve
Specific rangeon curve
Pb
Pa
Qb Qa
Interpreting the Own Price Elasticity of Demand
If elasticity coefficient is:
Demand is said to be:
% in quantity is:
Greater than 1.0 ElasticGreater than % in price
Equal to 1.0 Unitary elasticSame as % in
price
Less than 1.0 InelasticLess than %
in price
Page 72
Demand Curves Come in a Variety of Shapes
Demand Curves Come in a Variety of Shapes
Perfectly inelasticPerfectly inelastic
Perfectly elasticPerfectly elastic
Page 72
Demand Curves Come in a Variety of Shapes
InelasticInelastic
ElasticElastic
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
Page 73
Example of arc own-price elasticity of demandExample of arc own-price elasticity of demand
Unitary elasticity…a one for one exchange
Unitary elasticity…a one for one exchange
Page 73
Inelastic demandInelastic demand
Elastic demandElastic demand
Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand CurveElastic Demand Curve
0
Cut in price
Cut in price Brings about a larger
increase in the quantity demanded
Brings about a largerincrease in the quantity demanded
c
Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand CurveElastic Demand Curve
What happened toproducer revenue?
What happened to consumer surplus?
What happened toproducer revenue?
What happened to consumer surplus?
0
c
Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand CurveElastic Demand Curve
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
c
Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand CurveElastic Demand Curve
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
c
Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand CurveElastic Demand Curve
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
c
Revenue Implications
Own-price elasticity is:
Cutting the price will:
Increasing the price will:
Elastic Increase revenueDecrease revenue
Unitary elasticNot change revenue
Not change revenue
Inelastic Decrease revenueIncrease revenue
Page 81
Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand CurveElastic Demand Curve
Consumer surplusbefore the price cutwas area Pbca.
Consumer surplusbefore the price cutwas area Pbca.
a
b
0
c
Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand CurveElastic Demand Curve
Consumer surplusafter the price cut isArea Pacb.
Consumer surplusafter the price cut isArea Pacb.
a
b
0
c
Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand CurveElastic Demand Curve
So the gain inconsumer surplusafter the price cut isarea PaPbab.
So the gain inconsumer surplusafter the price cut isarea PaPbab.a
b
0
c
Pb
Pa
Qb Qa
Price
Quantity
Inelastic Demand CurveInelastic Demand Curve
Cut in price
Cut in price
Brings about a smallerincrease in the quantitydemanded
Brings about a smallerincrease in the quantitydemanded
Pb
Pa
Qb Qa
Price
Quantity
Inelastic Demand CurveInelastic Demand Curve
What happened toproducer revenue?
What happened to consumer surplus?
What happened toproducer revenue?
What happened to consumer surplus?
Pb
Pa
Qb Qa
Price
Quantity
Inelastic Demand CurveInelastic Demand Curve
Producer revenuefalls since %P isgreater than %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
Producer revenuefalls since %P isgreater than %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
Pb
Pa
Qb Qa
Price
Quantity
Inelastic Demand CurveInelastic Demand Curve
Producer revenuefalls since %P isgreater than %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
Producer revenuefalls since %P isgreater than %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
Pb
Pa
Qb Qa
Price
Quantity
Inelastic Demand CurveInelastic Demand Curve
Consumer surplusincreased by areaPaPbab
Consumer surplusincreased by areaPaPbab
a
b
0
Revenue Implications
Own-price elasticity is:
Cutting the price will:
Increasing the price will:
Elastic Increase revenue
Decrease revenue
Unitary elastic Not change revenue
Not change revenue
Inelastic Decrease revenue
Increase revenue
Characteristic of agricultureCharacteristic of agriculture Page 81
Retail Own Price Elasticities
• Beef = -.6166• Cheese = -.3319• Bananas = -.4002• Milk = -.2588• Carrots = -.0388
Page 79
InterpretationLet’s 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
Q
10% drop10% drop
1.467% increase1.467% increase
Rice producerRevenue?
Consumer surplus?
Example1. The Dixie Chicken sells 1,500 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 70 cents:
a. 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.
The answer…1. The Dixie Chicken sells 1,500 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 70 cents:
a. How many platters will the chicken sell?__1,110____Solution:-1.30 = %Q%P-1.30= %Q[20%]%Q=(-1.30 × 20) = –26%So the new quantity of burger platters is 1,110, or (1-.26) ×1,500, or .74 ×1,500
The answer…1. The Dixie Chicken sells 1,500 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 70 cents:
a. How many platters will the chicken sell?__1,110____
b. The Chicken’s revenue will change by $__-$588___Solution:Current revenue = 1,500 × $3.50 = $5,250 per monthNew revenue = 1,110 × $4.20 = $4,662 per monthSo revenue decreases by $588 per month, or $4,662minus $5,250
The answer…1. The Dixie Chicken sells 1,500 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 70 cents:
a. How many platters will the chicken sell?__1,110____
b. The Chicken’s revenue will change by $__-$588___
c. Consumers will be __worse___ off as a result of this price change.
Why? Because price increased.
Income Elasticityof Demand
Income Elasticity of Demand
Income elasticity of
demand
Percentage change in quantity
Percentage change in income=
where:
I = (Ia + Ib) 2 Q = (Qa + Qb) 2 Q = (Qa – Qb) I = (Ia – Ib)
= [QI] x [IQ]
Page 74
Indicates potential changes or shifts in the demand curve asconsumer income (I)changes….
Indicates potential changes or shifts in the demand curve asconsumer income (I)changes….
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!
Interpreting the Income Elasticity of Demand
Page 75
Some Examples
Commodity
Own Price elasticity
Income
elasticityBeef -0.6166 0.4549
Chicken -0.5308 .3645
Cheese -0.3319 0.5927
Rice -0.1467 -0.3664
Lettuce -0.1371 0.2344
Tomatoes -0.5584 0.4619
Fruit juice -0.5612 1.1254
Grapes -1.3780 0.4407
Nonfood items -0.9875 1.1773
Inferior goodInferior good Luxury goodLuxury goodElasticElastic
Page 79
ExampleAssume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is .3645.
a. What impact would this tax cut have upon the demand for chicken?
b. Is chicken a normal good or an inferior good? Why?
The Answer1. Assume the government cuts taxes, thereby
increasing disposable income (I) by 5%. The income elasticity for chicken is .3645.
a. What impact would this tax cut have upon the demand for chicken?Solution:.3645 = %QChicken % I.3654 = %QChicken 5 %QChicken = .3645 5 = + 1.8225%
The Answer1. Assume the government cuts taxes, thereby
increasing disposable income by 5%. The income elasticity for chicken is .3645.
a. What impact would this tax cut have upon the demand for chicken? _____+ 1.8225%___
b. 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
Cross Price Elasticityof Demand
Cross Price Elasticity of Demand
Cross Price elasticity of
demand
Percentage change in quantity
Percentage change in another price=
where:
PT = (PTa + PTb) 2
QH = (QHa + QHb) 2
QH = (QHa – QHb)PT = (PTa – PTb)
= [QHPT] × [PTQH]
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Indicates potential changes or shifts in the demand curve asthe price of othergoods change…
Indicates potential changes or shifts in the demand curve asthe price of othergoods change…
If the cross price elasticity is equal to:
The good is classified as:
Positive Substitutes
Negative Complements
Zero Independent
Interpreting the Cross Price Elasticity of Demand
Page 76
Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
Values in red alongthe diagonal are ownprice elasticities…
Values in red alongthe diagonal are ownprice elasticities…
Page 80
Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
Values off the diagonal are all positive, indicating these products are substitutes as prices change…
Values off the diagonal are all positive, indicating these products are substitutes as prices change…
Page 80
Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
Page 80
An increase in the price ofRagu Spaghetti Sauce has a bigger impact on Hunt’sSpaghetti Sauce than viceversa.
An increase in the price ofRagu Spaghetti Sauce has a bigger impact on Hunt’sSpaghetti Sauce than viceversa.
Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
Page 80
A 10% increase in the price ofRagu Spaghetti Sauce increasesthe demand for Hunt’s Spaghetti Sauce by 5.349%…..
A 10% increase in the price ofRagu Spaghetti Sauce increasesthe demand for Hunt’s Spaghetti Sauce by 5.349%…..
Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
Page 80
But…a 10% increase in the price ofHunt’s Spaghetti Sauce increasesthe demand for Ragu Spaghetti Sauce by only 1.381%…..
But…a 10% increase in the price ofHunt’s Spaghetti Sauce increasesthe demand for Ragu Spaghetti Sauce by only 1.381%…..
Example1. 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 percent,
what impact will that have on hamburger consumption?
b. What is the demand relationship between these products?
The Answer1. 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% ______
Solution:-.60 = %QH %PHB
-.60 = %QH 3
%QH = 3 (-.60) = – 3%
The Answer1. 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% _____
b. What is the demand relationship between these products?
The Answer1. 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% _____
b. What is the demand relationship between these products?
These two products are complements as evidenced by the negative sign on this cross-price elasticity.
Another Example2. 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.
a. 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?
The Answer2. 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.
a. If the price of Coca Cola rises by 5 percent, what
impact will that have on Pepsi consumption?
Solution:.70 = %QPepsi %PCoke
.70 = %QPepsi 5 %QPepsi=5*.7=3.5%New quantity sold = 1,000 1.035 = 1,035New value of sales = 1,035 $3.00 = $3,105
The Answer2. 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.
a. 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__
b. What is the demand relationship between these products?
The Answer2. 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.
a. 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__
b. What is the demand relationship between these products?
The products are substitutes as evidenced by the positive sign on this cross-price elasticity!
Price Flexibilityof Demand
Price FlexibilityWe 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.
Price FlexibilityWe 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%!
If supply increases by 2%, price would fall by 8%!
Price FlexibilityWe 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%!
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.
Revenue Implications
Own-price elasticity is:
Increase in supply will:
Decrease in supply will:
Elastic Increase revenue
Decrease revenue
Unitary elastic Not change revenue
Not change revenue
Inelastic Decrease revenue
Increase revenue
Characteristic of agricultureCharacteristic of agriculture Page 81
Short run effects Long run effects
Over time, consumers respond ingreater numbers. This is referredto as a recognition lag…
Over time, consumers respond ingreater numbers. This is referredto as a recognition lag… Page 77
Changing Price Response Over TimeChanging Price Response Over Time
Pb
Pa
Qb Qa
Price
Quantity
Ag’s Inelastic Demand CurveAg’s Inelastic Demand Curve
A small increase in supplywill cause the price of Agproducts to fall sharply.
This situation explains why majorprogram crops receivesubsidies from the federalgovernment.
A small increase in supplywill cause the price of Agproducts to fall sharply.
This situation explains why majorprogram crops receivesubsidies from the federalgovernment.
a
b
0
Increase insupply
Increase insupply
Pb
Pa
Qb Qa
Price
Quantity
Inelastic Demand CurveInelastic Demand Curve
While subsidies increase thecosts of governmentprograms and hencebudget deficits, rememberconsumers benefit fromcheaper food costs.
While subsidies increase thecosts of governmentprograms and hencebudget deficits, rememberconsumers benefit fromcheaper food costs.
a
b
0
Pb
Pa
Qb Qa
Price
a
b
0
In Summary…Know how to interpret all three
elasticitiesKnow how to interpret a price
flexibilityUnderstand 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
Chapter 6 starts a series of chapters that culminates in a market supply curve for food and fiber products….