measurement and interpretation of elasticities

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=

Arc Elasticity ApproachArc Elasticity Approach

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

of demand

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

of demand

Specific rangeon curve

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

Less than 1.0 InelasticLess than %

in price

Demand Curves Come in a Variety of Shapes

Perfectly inelasticPerfectly inelastic

Perfectly elasticPerfectly elastic

InelasticInelastic

ElasticElastic

Inelastic where %Q < % PInelastic where %Q < % P

Elastic where %Q > % P Elastic where %Q > % P

Unitary Elastic where %Q = % P Unitary Elastic where %Q = % P

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

Unitary elasticity…a one for one exchange

Inelastic demandInelastic demand

Elastic demandElastic demand

Quantity

Elastic Demand CurveElastic Demand Curve

Cut in price

Cut in price Brings about a larger

increase in the quantity demanded

Brings about a largerincrease in the quantity demanded

Quantity

What happened toproducer revenue?

What happened to consumer surplus?

Quantity

Producer revenueincreases since %Pis less that %Q.

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

Quantity

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

Quantity

Consumer surplusbefore the price cutwas area Pbca.

Quantity

Consumer surplusafter the price cut isArea Pacb.

Quantity

So the gain inconsumer surplusafter the price cut isarea PaPbab.

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

Quantity

Inelastic Demand CurveInelastic Demand Curve

Cut in price

Brings about a smallerincrease in the quantitydemanded

Quantity

Producer revenuefalls since %P isgreater than %Q.

Quantity

Consumer surplusincreased by areaPaPbab

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

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%.

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

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

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

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 income=

where:

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

= [QI] x [IQ]

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

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

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 another price=

where:

PT = (PTa + PTb) 2

QH = (QHa + QHb) 2

QH = (QHa – QHb)PT = (PTa – PTb)

= [QHPT] × [PTQH]

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

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…

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…

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.

Prego -2.5502 .8103 .3918

Ragu .5100 -2.0610 .1381

Hunt’s 1.0293 .5349 -2.7541

A 10% increase in the price ofRagu Spaghetti Sauce increasesthe demand for Hunt’s Spaghetti Sauce by 5.349%…..

Prego -2.5502 .8103 .3918

Ragu .5100 -2.0610 .1381

Hunt’s 1.0293 .5349 -2.7541

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

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%

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

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?

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 5 %QPepsi=5*.7=3.5%New quantity sold = 1,000 1.035 = 1,035New value of sales = 1,035 $3.00 = $3,105

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!

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.

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%!

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%!

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

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

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.

Increase insupply

Quantity

While subsidies increase thecosts of governmentprograms and hencebudget deficits, rememberconsumers benefit fromcheaper food costs.

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….

measurement and interpretation of elasticities

incomecross price elasticity

price elasticity of

demand curvepoint elasticity

pchickenarc elasticity

pbeefincome elasticity

price cutwas area pbca

price cut isarea pacb

demand curveprice flexibility

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