Agri 2312 chapter 5 measurement and interpretation of elasticities 1

Introduction to Agricultural Economics, 5th edPenson, Capps, Rosson, and Woodward

© 2010 Pearson Higher Education,Upper Saddle River, NJ 07458. • All Rights

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Measurementand

Interpretationof Elasticities

Chapter 5



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Discussion Topics

Own price elasticity of demandIncome elasticity of demandCross price elasticity of demandOther general propertiesApplicability of demand elasticities



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Key Concepts Covered…

Own price elasticityIncome elasticityCross price elasticity

Pages 70-76



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What is Elasticity of Demand?

• We define elasticity of demand as responsiveness of the quantity demanded to a change in the price.– Degree of responsiveness is measured by an

elasticity coefficient—frequently called elasticities.

• Invented by the British Economist Alfred Marshall



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Own price elasticity =

%Qbeef for a given %Pbeef

Income elasticity =

%Qbeef for a given %Income

Cross price elasticity =

%Qbeef for a given %PchickenPages 70-76



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Arc elasticity = range along the demand curve

Point elasticity = point on the demand curve

Pages 70-76



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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

Pages 70-76



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Own Price Elasticityof Demand



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Own Price Elasticity of Demand

Own price elasticity

of demand

Percentage change in quantity

Percentage change in price=

Point Elasticity ApproachPoint Elasticity Approach

Pages 70-72



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Point elasticity:

= [QP] × [PaQa]Own price elasticity of

demand

Own price elasticity of

demand

Percentage change in quantity Percentage change in price

=

Q = (Qa – Qb); and

P = (Pa – Pb)

The subscript “a” herestands for “after” while “b”stands for “before”


Pages 70-72



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Point elasticity:

= [QP] × [PaQa]


of demand


of demand



Q = (Qa – Qb); and

P = (Pa – Pb)



Single pointon curve

Single pointon curvePa

Qa

Pages 70-72



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of demand



Page 72

Arc Elasticity ApproachArc Elasticity Approach



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of demand



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]

The subscript “a” here againstands for “after” while “b”stands for “before”


Equation 5.3Equation 5.3

Page 72



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of demand








The “bar” over the P andQ variables indicates anaverage or mean.

The “bar” over the P andQ variables indicates anaverage or mean.

Page 72



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of demand








Specific rangeon curve

Specific rangeon curve

Pb

Pa

Qb Qa

Page 72



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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 72



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Demand Curves Come in a Variety of Shapes



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Perfectly inelasticPerfectly inelastic

Perfectly elasticPerfectly elastic

Page 72



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InelasticInelastic

ElasticElastic



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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



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• Demand curves often exhibit all three rangesof elasticity in a single curve.– Always true when a

demand curve is astraight line.

Straight line demand curvesare elastic with respect to priceat relatively high prices, and inelastic at relatively low prices.



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Page 73

Example of arc own-price elasticity of demandExample of arc own-price elasticity of demand

Unitary elasticity…a one for one exchangeUnitary elasticity…a one for one exchange



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Page 73

Inelastic demandInelastic demand

Elastic demandElastic demand



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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



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Pb

Pa

Qb Qa

Price

Quantity


What happened toproducer revenue?

What happened to consumer surplus?



0

c



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Pb

Pa

Qb Qa

Price

Quantity


Producer revenueincreases since %Pis less that %Q.

Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.



a

b

0

c



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Pb

Pa

Qb Qa

Price

Quantity






a

b

0

c



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Pb

Pa

Qb Qa

Price

Quantity






a

b

0

c



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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

Page 81



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Pb

Pa

Qb Qa

Price

Quantity


Consumer surplusbefore the price cutwas area Pbca.

Consumer surplusbefore the price cutwas area Pbca.

a

b

0

c



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Pb

Pa

Qb Qa

Price

Quantity


Consumer surplusafter the price cut isArea Pacb.

Consumer surplusafter the price cut isArea Pacb.

a

b

0

c



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Pb

Pa

Qb Qa

Price

Quantity


So the gain inconsumer surplusafter the price cut isarea PaPbab.

So the gain inconsumer surplusafter the price cut isarea PaPbab.a

b

0

c



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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



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Pb

Pa

Qb Qa

Price

Quantity








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Pb

Pa

Qb Qa

Price

Quantity


Producer revenuefalls since %P isgreater than %Q.




a

b

0



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Pb

Pa

Qb Qa

Price

Quantity






a

b

0



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Pb

Pa

Qb Qa

Price

Quantity


Consumer surplusincreased by areaPaPbab

Consumer surplusincreased by areaPaPbab

a

b

0



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Cutting the price will:

Increasing the price will:


Decrease revenue


Not change revenue


Increase revenue

Characteristic of agricultureCharacteristic of agriculture Page 81



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Retail Own Price Elasticities

• Beef and veal= .6166• Milk = .2588• Wheat = .1092• Rice = .1467• Carrots = .0388

• Non food = .9875

Page 79



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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?



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Example1. 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:

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.



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The answer…1. The Dixie Chicken sells 1,500 Freddie Burger platters


a. 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= %Q0.1333%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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a. 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 monthNew revenue = 1,440 × $4.00 = $5,760 per monthSo revenue increases by $510 per month, or $5,760minus $5,250



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b. The Chicken’s revenue will change by $__+$510___

c. Consumers will be __worse___ off as a result of this price change.

Why? Because price increased.



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Another Example1. The Dixie Chicken sells 1,500 Freddie Burger platters


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.



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a. How many platters will the chicken 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= %Q0.1333%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



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b. The Chicken’s revenue will change by $__- $290___Solution:Current revenue = 1,500 × $3.50 = $5,250 per monthNew revenue = 1,240 × $4.00 = $4,960 per monthSo revenue decreases by $290 per month, or $4,960 minus $5,250



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b. The Chicken’s revenue will change by $__- $290___

c. Consumers will be __worse___ off as a result of this price change.

Why? Because the price increased.



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Income Elasticityof Demand



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Income Elasticity of Demand

Income elasticity of

demand


Percentage change in income=

where:

I = (Ia + Ib) 2 Q = (Qa + Qb) 2 Q = (Qa – Qb) I = (Ia – Ib)

= [QI] x [IQ]

Page 74-75

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….



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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



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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



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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?



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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 .05 %QChicken = .3645 .05 = .018 or + 1.8%



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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? _____+ 1.8%___

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



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Cross Price Elasticityof Demand



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Cross Price Elasticity of Demand

Cross Price elasticity of

demand


Percentage change in another price=

where:

PT = (PTa + PTb) 2

QH = (QHa + QHb) 2

QH = (QHa – QHb)PT = (PTa – PTb)

= [QHPT] × [PTQH]

Page 75

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…



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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



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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



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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



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Prego -2.5502 .8103 .3918

Ragu .5100 -2.0610 .1381

Hunt’s 1.0293 .5349 -2.7541

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.

Page 80



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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%…..



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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%…..



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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?



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The Answer1. The cross price elasticity for hamburger demand


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 .05

%QH = .05 (-.60) = -.03 or – 3%



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impact will that have on hamburger consumption? ___ - 3% _____




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impact will that have on hamburger consumption? ___ - 3% _____


These two products are complements as evidenced by the negative sign on this cross price elasticity.



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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?




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The Answer2. Assume that a retailer sells 1,000 six-packs of



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 = 1,035New value of sales = 1,035 $3.00 = $3,105



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impact will that have on Pepsi consumption? __35 six-packs or $105 per day__




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impact will that have on Pepsi consumption? __35 six-packs or $105 per day__


The products are substitutes as evidenced by the positive sign on this cross price elasticity!



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Price Flexibilityof Demand



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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.



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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%!




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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%



Note: make sure you use the negative sign for both the elasticity and the flexibility.



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Increase in supply will:

Decrease in supply will:


Decrease revenue


Not change revenue


Increase revenue

Characteristic of agricultureCharacteristic of agriculture Page 81



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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



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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 explains why majorprogram crops receiveSubsidies from the federalgovernment.

A small increase in supplywill cause the price of Agproducts to fall sharply.

This explains why majorprogram crops receiveSubsidies from the federalgovernment.

a

b

0

Increase insupply

Increase insupply



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Pb

Pa

Qb Qa

Price

Quantity


While this increases thecosts of governmentprograms and hencebudget deficits, rememberconsumers benefit fromcheaper food costs.

While this increases thecosts of governmentprograms and hencebudget deficits, rememberconsumers benefit fromcheaper food costs.

a

b

0

Pb

Pa

Qb Qa

Price

a

b

0



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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?



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The Market Demand CurvePrice

Quantity

What causes movement along a demand curve?

What causes movement along a demand curve?



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The Market Demand CurvePrice

Quantity

What causes the demand curve to shift?

What causes the demand curve to shift?



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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



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

Business

Agri 2312 chapter 5 measurement and interpretation of elasticities 1