9 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 If ““closeclose”” to zero, relative unresponsive to zero, relative unresponsive– If If ““farfar”” from zero, relatively responsive 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 This is said to be ““the elasticity of Y with respect to the elasticity of Y with respect to

XX ””

Consider this relationshipConsider this relationship

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

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

Grade

Study Time/week

0

Another exampleAnother example

The elasticity of gradesThe elasticity of grades

with respect to with respect to

alcohol consumptionalcohol consumption

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

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

(relatively responsive)(relatively responsive)

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

(relatively unresponsive)(relatively unresponsive) 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““ElasticElastic”” demand demand

Elastic demandElastic demand– elasticity > 1elasticity > 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 buyersWhen buyers’’ expenditures are a large expenditures are a large part of their income so they shop more part of their income so they shop more carefully—buying a home.carefully—buying a home.

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 . . . . . . ““InelasticInelastic”” demand demand

Inelastic demandInelastic demand– elasticity < 1elasticity < 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. Examples: Door-to-door sales. Complex Examples: Door-to-door sales. Complex products that are hard to compare.products that are hard to compare.

When consumers pay only a fraction of the cost. When consumers pay only a fraction of the cost. Ex.: When insurance covers most of the bill.Ex.: When insurance covers most of the bill.

When the cost of switching would be high. When the cost of switching would be high. Example: When the user has developed Example: When the user has developed expertise in using a product (software).expertise in using a product (software).

When a product is used with another product When a product is used with another product that the consumer uses. that the consumer uses.

Example: Ink cartridges in printers. Example: Ink cartridges in printers.

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 products (e.g., Wal-Mart and other retailers data)retailers 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 know about future events — plan If you know about future events — plan more more precisely (hotels and conventions)precisely (hotels and conventions)

No close substitutes?No close substitutes?

SCI, the largest firm in the U.S. funeral business, SCI, the largest firm in the U.S. funeral business, with 14% of total industry revenue, increased its with 14% of total industry revenue, increased its average revenue per service (its product price) average revenue per service (its product price) by 9% in one year. The number of funeral by 9% in one year. The number of funeral services fell by 5.8%.  services fell by 5.8%. 

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

Was the price increase sensible?Was the price increase sensible?

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

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

How a market changes when prices change

Hong Kong had 80% tariff on wine, so high wine prices.2008: tariff abolished; retail prices fell 30-50%.Sales rose: 34% in ’09; 73% in ‘10 and 40% in ‘11. Elasticity appears near 1.

What else changed?

Little impact in restaurants since Little impact in restaurants since they have large markup already.they have large markup already.

Sale increase was at stores.Sale increase was at stores.

Expanded volume meant increase Expanded volume meant increase need for warehouse space, HK need for warehouse space, HK became largest wine auction site in became largest wine auction site in world in world in ‘‘11 (quarter billion in 11 (quarter billion in auction sales).auction sales).

Wine expos. Greater employment. Wine expos. Greater employment. Smuggling ended.Smuggling ended.

Cross-price elasticitiesCross-price elasticities

Cross-price elasticity of demand Cross-price elasticity of 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 , by

definitiondefinition– If negative, goods are If negative, goods are complementscomplements, ,

by definitionby 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 Elasticity of Income Elasticity of DemandDemand

– Measure of responsiveness of Measure of responsiveness of demanddemand to to changes in income: (%∆ Dx) / (%∆ l)changes in income: (%∆ Dx) / (%∆ l)

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

Recession in U.S.—Incomes down 4%:Recession in U.S.—Incomes down 4%:

‘‘08-09—Budweiser down 7.4%; Busch up 5.3%08-09—Budweiser down 7.4%; Busch up 5.3%

Saks down 26%; Wal-Mart up 3.5%Saks down 26%; Wal-Mart up 3.5%

2010: Concert Ticket Sales fell 15% in U.S.2010: Concert Ticket Sales fell 15% in U.S.

LoweLowe’’s: home repair projects over $500 way s: home repair projects over $500 way down.down.

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

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 -0.6; for premium gasoline was -0.6; for premium gasoline was -0.3.gasoline was -0.3.

Why the difference?Why the difference?