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

Own Price Elasticity of Demand

Point Elasticity Approach:

Own price elasticity of

demand

Q = (Qa – Qb)

P = (Pa – Pb)

Pages 70-72

PQQ PQ P P Q

The subscript• a stands for after price change• b stands for before price change

demand

Percentage change in quantity demanded (Q)

Percentage change in its own price (P)ηii =

Single pointon curve

% Δ in Q% Δ in P

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

Q PQ PQ P P Q

The subscript• a stands for after price change• b stands for before price change

Avg Price

Avg Quantity

Equation 5.3Equation 5.3

Specific rangeon curve

Specific rangeon curve$

demand

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

Note: The %Δ in Q is in terms of the absolute valueof the change

Snow Leopard was a previousversion of Apple’s OS

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

ηii = -0.2 to -0.3

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

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

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

←Same as previous value

Demand Curves Come in a Variety of Shapes

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?

The two extremes

Inelastic DemandInelastic Demand

Elastic DemandElastic Demand

16 Page 73

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

A single demand curve can exhibitvarious types of own-price elasticity

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

Inelastic demandInelastic demand

Elastic demandElastic demand

Elastic Demand CurveElastic Demand Curve

With the price decrease from Pb to Pa

What happens to producer revenue (or consumer expenditures)?

Cut in price

An elastic demand curve → a larger % ↑in quantity demanded than the absolute value of the % price change (a price decrease)

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

•Revenue after the change is (TRa) is Pa x Qa Represented by the area 0PaBQaA

Change in revenue (∆TR) is TRa – TRb

→ ∆TR = 0PaBQa – 0PbAQb

→ ∆TR = QbDBQa – PaPbAD

→TR ↑%Q ↑ is greater than %P ↓

Red Box Purple Box

When you have elastic demand ↑ in price → ↓ total

revenue (expenditures) ↓ in price → ↑ total

revenue (expenditures)

Inelastic Demand CurveInelastic Demand Curve

Cut in price

Results in smaller %increase in quantitydemanded

With price decrease from Pb to Pa

What happens to producer revenue or consumer expenditures)?

Producer revenue (TR) = price x quantityRevenue before the change (TRb) is Pb x Qb

Revenue after the change is (TRa) Pa x Qa Represented by the area 0PaBQa

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

When you have inelastic demand ↑ in price → ↑ total

revenue ↓ in price → ↓ total

revenue

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

Inelastic(-1< ηii < 0)

Decrease Total Revenue

Increase Total Revenue

Typical of Agricultural CommoditiesTypical of Agricultural Commodities

Consumer surplus (CS)Before price cut CS is area PbCAAfter the price cut CS is area PaCB

The gain in consumer surplus after the price cut is area PaPbAB = PaCB – PbCA

Inelastic demand and price decreaseConsumer surplus increases

by area PaPbAB

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)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%

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

0 QB Qa

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

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 =

P Avg. Price

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

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

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.

Income Elasticityof Demand

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)

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

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

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?

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

Cross Price Elasticityof Demand

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)

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)

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 bunsIf commodities i & j are independent (ηi j= 0):

Pi↑→Qi↓, Qj is not impactedi.e., peanut butter and Miller Lite

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

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

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

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)

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

A 10% increase in Ragu spaghetti sauce price increases the demand for Hunt’s spaghetti sauce by 5.35%

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

A 10% increase in Hunt’s spaghetti sauce price increases Ragu spaghetti sauce demand by 1.38%

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?

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

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?

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

Price Flexibilityof Demand

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

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%

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

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

Characteristic of a large number of agricultural commodities

Short run effects Long run effects

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

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

Increase insupply

Quantity

While this ↑ the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs.

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?

The Market Demand CurvePrice

Quantity

What causes movement along a demand curve?

The Market Demand CurvePrice

Quantity

What causes the demand curve to shift?

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

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

measurement and interpretation of elasticities chapter 5

price elasticity of

price elasticity slide

price change b

p slide

price page

demand curve price flexibility

price decrease

price cut

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