Lecture 9Lecture 9

ElasticitiesElasticities

Elasticities are measures of responsivenessElasticities are measures of responsiveness– The response of one variable to changes in anotherThe response of one variable to changes in another– Can be positive or negativeCan be positive or negative– If “close” to zero, relative unresponsiveIf “close” to zero, relative unresponsive– If “far” from zero, relatively responsiveIf “far” from zero, relatively responsive

Calculated as the ratio of two percentage Calculated as the ratio of two percentage changes:changes:

E = (%∆Y)/(%∆X)E = (%∆Y)/(%∆X)– This is said to be “the elasticity of Y with respect to This is said to be “the elasticity of Y with respect to

X”X”

Consider this hypothetical Consider this hypothetical relationshiprelationship

The elasticity of grades The elasticity of grades

with respect towith respect to

time spent studyingtime spent studying

– Likely positiveLikely positive– ΕΕ = (%∆G)/(%∆S) > 0 = (%∆G)/(%∆S) > 0

– If E > 1, we say “elastic” If E > 1, we say “elastic” (relatively responsive)(relatively responsive)

– If E < 1, we say “inelastic” If E < 1, we say “inelastic” (relatively unresponsive)(relatively unresponsive)

Grade

Study Time/week

0

Another hypothetical Another hypothetical exampleexample The elasticity of gradesThe elasticity of grades

with respect to with respect to

alcohol consumptionalcohol consumption

– Likely negative Likely negative – E = (%∆G)/(%∆W) < 0E = (%∆G)/(%∆W) < 0

– If |E|If |E| >1, we say “elastic” >1, we say “elastic”

(relatively responsive)(relatively responsive)

– If |E| < 1, we say “inelastic” If |E| < 1, we say “inelastic”

(relatively unresponsive)(relatively unresponsive)

Real elasticity computation regarding alcohol: a 10% price Real elasticity computation regarding alcohol: a 10% price increase leads to a 5.8% decline in traffic fatalities.increase leads to a 5.8% decline in traffic fatalities.

Grades

Alcohol Consumption/week

0

The (own) Price Elasticity of The (own) Price Elasticity of DemandDemand

Measures the responsiveness of quantity Measures the responsiveness of quantity demanded to changes in the price of the demanded to changes in the price of the good itselfgood itself– Defined thus: Defined thus:

εε = [(%∆in quantity demanded)/(%∆ in price)] = [(%∆in quantity demanded)/(%∆ in price)] Or Or εε = [(%∆Qd)/(%∆P)] = [(%∆Qd)/(%∆P)]

Note that Note that εε mustmust be negative (Law of Demand) be negative (Law of Demand)

Sometimes convenient to refer to the absolute Sometimes convenient to refer to the absolute value |value |εε| so we can ignore the negative sign | so we can ignore the negative sign

Examples of demand Examples of demand elasticitieselasticities

Suppose a 10% rise in the price of a good Suppose a 10% rise in the price of a good causes a 20% reduction in the quantity causes a 20% reduction in the quantity demanded in a measured time perioddemanded in a measured time period

εε = -20%/+10% = -2 = -20%/+10% = -2

Suppose a 15% decline in the price of a good Suppose a 15% decline in the price of a good causes a 10% increase quantity demanded in causes a 10% increase quantity demanded in a measured time perioda measured time period

εε = +10%/-15% = -0.67 = +10%/-15% = -0.67

Categories of demand Categories of demand elasticitieselasticities“Elastic” demand“Elastic” demand

Elastic demandElastic demand– ||εε| > 1| > 1

– Qd Qd relativelyrelatively responsive to price responsive to price

– Price change leads to spending Price change leads to spending

change in opposite directionchange in opposite direction

– Thus,Thus, Higher price → lower spendingHigher price → lower spending Lower price → higher spendingLower price → higher spending

Price

Q/time

Demand

When is a good likely to When is a good likely to have sensitive elasticity?have sensitive elasticity?

If a product is not unique so it has many If a product is not unique so it has many close substitutes and consumers know close substitutes and consumers know about the alternatives.about the alternatives.

When buyers’ expenditures are a large When buyers’ expenditures are a large part of their income so they shop part of their income so they shop more carefully.more carefully.

The product is an input in production The product is an input in production that is price sensitive, so the producer that is price sensitive, so the producer will keep close watch on input prices.will keep close watch on input prices.

Demand elasticityDemand elasticity . . . . . . “Inelastic” demand“Inelastic” demand

Inelastic demandInelastic demand– ||εε| < 1| < 1

– Qd Qd relativelyrelatively unresponsive to price unresponsive to price

– Price change leads to spending Price change leads to spending

change in same directionchange in same direction

– Thus,Thus, Higher price → higher spendingHigher price → higher spending Lower price → lower spendingLower price → lower spending

Price

Q/time

Demand

When is elasticity likely When is elasticity likely to be less sensitive?to be less sensitive?

When comparisons to substitutes is difficult. When comparisons to substitutes is difficult. Door-to-door sales. Complex products that Door-to-door sales. Complex products that are hard to compare.are hard to compare.

When consumers pay only a fraction of the When consumers pay only a fraction of the cost—when insurance covers most of the cost—when insurance covers most of the bill.bill.

When the cost of switching would be high—When the cost of switching would be high—when the consumer has developed when the consumer has developed expertise in using a product.expertise in using a product.

When a product is used with another When a product is used with another product that the consumer is committed product that the consumer is committed to—such as ink cartridges.to—such as ink cartridges.

No close substitutes?No close substitutes?

In 2006 SCI, the largest player in the funeral In 2006 SCI, the largest player in the funeral business, with 14% of total industry revenue business, with 14% of total industry revenue saw its average revenue per service (its saw its average revenue per service (its product price) rise by 9%.  product price) rise by 9%. 

At the same time, the number of funeral services At the same time, the number of funeral services performed fell by 5.8 percent.  performed fell by 5.8 percent. 

The price elasticity of demand for its services is –The price elasticity of demand for its services is –(-5.8/9) = 0.64.  Its price and quantity (-5.8/9) = 0.64.  Its price and quantity demanded suggest that its demand is inelasticdemanded suggest that its demand is inelastic—and we thus know from this calculation that —and we thus know from this calculation that its total revenue increased from these services its total revenue increased from these services increases. increases.

Some uses of demand elasticitiesSome uses of demand elasticities

More Accurate PricingMore Accurate Pricing– Use of UPC bar codes to aid in pricing Use of UPC bar codes to aid in pricing

products (e.g., Wal-Mart and other retailers products (e.g., Wal-Mart and other retailers data)data)

Trying to Maximize ProfitsTrying to Maximize Profits– A higher price is no guarantee of higher A higher price is no guarantee of higher

revenue (will study below)revenue (will study below)

Plan aheadPlan ahead– – If you think you know about future trends — If you think you know about future trends — plan more plan more precisely (hotels and conventions)precisely (hotels and conventions)

Real World Elasticities Real World Elasticities (all negative numbers)(all negative numbers)

Estimated Estimated ElasticityElasticity

Product or ServiceProduct or Service Short Run Short Run Long Run Long Run

LambLamb 2.652.65 ----BreadBread 0.150.15 ----CoffeeCoffee 0.160.16 ----TiresTires 0.80.8 1.21.2Auto RepairsAuto Repairs 1.41.4 2.42.4Theatre & OperaTheatre & Opera 0.20.2 0.30.3MoviesMovies 0.90.9 3.73.7Foreign Travel by U.S. ResidentsForeign Travel by U.S. Residents 0.10.1 1.81.8Public TransportationPublic Transportation 0.60.6 1.21.2ElectricityElectricity 0.10.1 1.81.8Jewelry & WatchesJewelry & Watches 0.40.4 0.60.6Alcohol and TobaccoAlcohol and Tobacco 0.30.3 0.90.9RecreationRecreation 1.11.1 3.53.5

ExampleExample

The The Macon Telegraph Macon Telegraph sponsored a road sponsored a road race for charity. Entry fee was $12 race for charity. Entry fee was $12 per runner. 1,600 runners per runner. 1,600 runners participated. Fees were $19,200.participated. Fees were $19,200.

To raise more money, fee raised to $20 To raise more money, fee raised to $20 the next year. Same weather. 900 the next year. Same weather. 900 runners participated. Fees $18,000.runners participated. Fees $18,000.

Price elasticity (arc) of demand? 1.12 Price elasticity (arc) of demand? 1.12

ExampleExample

ESPN football videogame:ESPN football videogame: 2003 price: $402003 price: $40 2004 price: $20 (50% decrease)2004 price: $20 (50% decrease) 2003 Q2003 Qdd: 400,000: 400,000

2004 Q2004 Qdd: 2.7 million (575% increase): 2.7 million (575% increase) E = 575%/50% = 11.5E = 575%/50% = 11.5 Note: major competitor, Madden Note: major competitor, Madden

football, did not change price; its sales football, did not change price; its sales rose less than 10% from 2003 to 2004 rose less than 10% from 2003 to 2004

ExampleExample

Kelkoo.com, owned by Yahoo!, is 3Kelkoo.com, owned by Yahoo!, is 3rdrd largest largest retail website in UK; 10 million users per retail website in UK; 10 million users per month.month.

Data for sales of PDAs in 100 days in 2003:Data for sales of PDAs in 100 days in 2003:18 models sold by 19 retailers. If click on one 18 models sold by 19 retailers. If click on one

model, may get prices offered by 12 retailers.model, may get prices offered by 12 retailers.Price elasticities of demand for various models Price elasticities of demand for various models

offered by different retailers ranged from -offered by different retailers ranged from -1.75 to -14.7. Average was -4.6.1.75 to -14.7. Average was -4.6.

Lowest price retailer saw demand rise 60.4%.Lowest price retailer saw demand rise 60.4%.

Cross-price elasticitiesCross-price elasticities

Cross-price elasticity of Cross-price elasticity of demand demand – Measure of responsiveness of Measure of responsiveness of

demanddemand to changes in prices of to changes in prices of substitutes and complements:substitutes and complements:

(%∆ Dx) / (%∆ Py)(%∆ Dx) / (%∆ Py)– If positive, goods are If positive, goods are substitutessubstitutes, ,

by definitionby definition– If negative, goods are If negative, goods are

complementscomplements, by definition, by definition

Estimates of Cross Estimates of Cross ElasticitiesElasticities

These are estimates of cross elasticities of These are estimates of cross elasticities of various goods (goods that are substitutes) in various goods (goods that are substitutes) in the U.S.:the U.S.:

Electricity and natural gasElectricity and natural gas 0.20 (weak 0.20 (weak substitutes)substitutes)

Beef and PorkBeef and Pork 0.200.20

Natural gas and fuel oilNatural gas and fuel oil 0.440.44

Margarine and butterMargarine and butter 0.81 (strong 0.81 (strong substitutes)substitutes)

Income ElasticityIncome Elasticity

Income elasticity of demandIncome elasticity of demand– Measure of responsiveness of Measure of responsiveness of

demanddemand to changes in income: to changes in income:

(%∆ Dx) / (%∆ l)(%∆ Dx) / (%∆ l)– If positive, good is If positive, good is normalnormal, by , by

definition (>1, superior)definition (>1, superior)– If negative, good is If negative, good is inferiorinferior, by , by

definitiondefinition

Estimates of Income Estimates of Income ElasticitiesElasticities

Estimates of income elasticities from different Estimates of income elasticities from different studies in the U.S.:studies in the U.S.:

FlourFlour -0.36 (inferior good)-0.36 (inferior good)

MargarineMargarine -0.20 (inferior good)-0.20 (inferior good)

Milk and creamMilk and cream 0.07 0.07 (little change)(little change)

BeefBeef 0.51 to 1.05 0.51 to 1.05

ApplesApples 1.32 1.32

Dental ServicesDental Services 1.41 1.41 (highly responsive to (highly responsive to

Restaurant mealsRestaurant meals 1.48 1.48 income increases) income increases)

Personal air travelPersonal air travel 1.8 1.8

Endless ElasticitiesEndless Elasticities

Many measures of elasticity can be Many measures of elasticity can be performed simultaneously.performed simultaneously.

The demand for cans of Coke varies The demand for cans of Coke varies across state. Even when price is the across state. Even when price is the same, sales are higher in Southern same, sales are higher in Southern states (Georgia has highest states (Georgia has highest consumption) compared to Northern consumption) compared to Northern (ND lowest).(ND lowest).

What factors could you consider?What factors could you consider?

ElasticityElasticity

A study of gasoline sales found A study of gasoline sales found that price elasticity for regular that price elasticity for regular gasoline was -.6 and for premium gasoline was -.6 and for premium gasoline was -.3.gasoline was -.3.

What does that mean?What does that mean?