Lecture 7Lecture 7

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:

(%∆Y)/(%∆X)(%∆Y)/(%∆X)– Is said to be “the elasticity of Y with respect to X”Is said to be “the elasticity of Y with respect to X”

An exampleAn exampleConsider this hypothetical Consider this hypothetical relationshiprelationship The elasticity of grades with respectThe elasticity of grades with respect

to to time spent studyingtime spent studying – Likely positiveLikely positive– ηη=(%∆G)/(%∆S)>0=(%∆G)/(%∆S)>0

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

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

– Special case: Special case: ηη=1 “unit elastic”=1 “unit elastic”Grade

Study Time

Another exampleAnother exampleAgain, a purely hypothetical example (you hope!)Again, a purely hypothetical example (you hope!)

The elasticity of grades withThe elasticity of grades with

respect to wine consumptionrespect to wine consumption– Likely negative (?)Likely negative (?)– εε = (%∆G)/(%∆W) < 0 = (%∆G)/(%∆W) < 0

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

(relatively responsive)(relatively responsive)

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

(relatively unresponsive)(relatively unresponsive)

– Special case: |Special case: |εε| = 1 | = 1

““unit elastic”unit elastic”Grades

Wine Consumption

0

The (own) Price Elasticity of The (own) Price Elasticity of DemandDemandProbably the most important elasticity we’ll Probably the most important elasticity we’ll encounterencounter

Measures the responsiveness of quantity Measures the responsiveness of quantity demanded to changes in their (own) price of demanded to changes in their (own) price of a gooda good– 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| |

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 demanded

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 demandedcauses a 10% increase quantity demanded

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 Price change leads to spendingspending

change in opposite directionchange in opposite direction

– Thus,Thus, Higher price → lower Higher price → lower spendingspending Lower price → higher Lower price → higher spendingspending

Demand elasticity Demand elasticity (con’t)(con’t)“Inelastic” demand“Inelastic” demand Inelastic demandInelastic demand

– ||εε| < 1| < 1

– Qd Qd relativelyrelatively unresponsive to price unresponsive to price

– Price change leads to Price change leads to spendingspending

change in same directionchange in same direction

– Thus,Thus, Higher price → higher Higher price → higher spendingspending Lower price → lower Lower price → lower spendingspending

Demand elasticities (con’t)Demand elasticities (con’t)“Unit elastic” demand“Unit elastic” demand

Unit elastic demandUnit elastic demand– ||εε| = 1| = 1

– The knife-edge caseThe knife-edge case

– Spending on the good isSpending on the good is

independentindependent of its price of its price

– Whether price rises or Whether price rises or falls, falls, spendingspending remains remains constantconstant

Why would you care?Why would you care?Some uses of demand elasticitiesSome uses of demand elasticities

Avoid mistakesAvoid mistakes– A higher price is no guarantee of higher revenueA higher price is no guarantee of higher revenue

Interpreting dataInterpreting data– Use of upc scanner to aid in pricing productsUse of upc scanner to aid in pricing products

Solve puzzlesSolve puzzles– Property crime and the price of heroinProperty crime and the price of heroin

The simple path to higher wealth:The simple path to higher wealth:– If revenue rises when price, ask yourself:If revenue rises when price, ask yourself:

Why isn’t price even Why isn’t price even higherhigher ? ?

Real World ElasticitiesReal World ElasticitiesCollected by Assorted Economists Over Collected by Assorted Economists Over TimeTime

Estimated ElasticityEstimated ElasticityProduct or ServiceProduct or Service Short Run Short Run Long Run Long Run

LambLamb 2.652.65 ----BreadBread 0.150.15 ----TiresTires 0.80.8 1.21.2Auto RepairsAuto Repairs 1.41.4 2.42.4Radio & TV RepairsRadio & TV Repairs 0.50.5 3.83.8Theatre & OperaTheatre & Opera 0.20.2 0.310.31MoviesMovies 0.870.87 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 0.60.6

The Linear Demand The Linear Demand CurveCurveIllustrating that elasticity is Illustrating that elasticity is not not a a slopeslope

Top portion is elasticTop portion is elastic

Bottom portion isBottom portion is

inelasticinelastic

The point in the middleThe point in the middle

is unit elasticis unit elastic

εε = [(%∆Qd)/(%∆P)] = [(%∆Qd)/(%∆P)]

Total Revenue and Total Revenue and ElasticityElasticity

Key to a firm is knowing if total revenue will rise Key to a firm is knowing if total revenue will rise or fall if product prices are increased or or fall if product prices are increased or decreased.decreased.

Price/Software Q Software Sold Own Price Elas.Price/Software Q Software Sold Own Price Elas. T.R.T.R.

$$ 00 8080 0.00 0.00 $ 0$ 0

55 7070 - 0.14 - 0.14 350 350

1010 6060 - 0.33 - 0.33 600 600

1515 5050 - 0.60 - 0.60 750 750

2020 4040 - 1.00 - 1.00 800 800

2525 3030 - 1.67 - 1.67 750 750

3030 2020 - 3.00 - 3.00 600 600

3535 1010 - 7.00 - 7.00 350 350

4040 0 0 - - 0 0

Total Revenue and Total Revenue and ElasticityElasticity

We see if demand is elastic, an increase We see if demand is elastic, an increase (decrease) in price will lead to a decrease (decrease) in price will lead to a decrease (increase) in total revenue. If demand is (increase) in total revenue. If demand is inelastic, just the opposite. Total Revenue is inelastic, just the opposite. Total Revenue is maximized when elasticity is one.maximized when elasticity is one.

PriceTotalRevenue

Quantity Quantity

Elastic

Inelastic$20

40

Unit Elasticity

40

$800

Marginal Revenue

Other demand-related Other demand-related elasticitieselasticities

Cross-price elasticity of demand Cross-price elasticity of demand – Measure of responsiveness of Measure of responsiveness of demanddemand to changes in to changes in

prices of substitutes and complements:prices of substitutes and complements:

(%(%∆ Dx)/(%∆ Py)∆ Dx)/(%∆ Py)– If positive, goods are If positive, goods are substitutessubstitutes, by definition, by definition– If negative, goods are If negative, goods are complementscomplements, by definition, by definition

Income elasticity of demandIncome elasticity of demand– Measure of responsiveness of Measure of responsiveness of demanddemand to changes in to changes in

income:income:

(%(%∆ Dx)/(%∆ l)∆ Dx)/(%∆ l)– If positive, good is If positive, good is normalnormal, by definition (>1, superior), by definition (>1, superior)– If negative, good is If negative, good is inferiorinferior, by definition, by definition

Estimates of Cross Estimates of Cross ElasticitiesElasticities

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

Estimates of Income Estimates of Income ElasticitiesElasticities

These are estimates of income elasticities These are estimates of income elasticities from different studies in the U.S.:from different 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)

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

Restaurant mealsRestaurant meals 1.48 1.48 income increases) income increases)

Elasticity of SupplyElasticity of SupplyLikely second most important Likely second most important elasticityelasticity

Measures the responsiveness of quantity Measures the responsiveness of quantity supplied to changes in the (own) price of a supplied to changes in the (own) price of a goodgood

Defined thus:Defined thus:

ηη = [( = [(%%∆ in quantity supplied)/(∆ in quantity supplied)/(%%∆ in price)]∆ in price)]

Or Or ηη = [( = [(%%∆Qs)/(∆Qs)/(%%∆P)]∆P)]

Note that Note that ηη is positive, because supply curves are positively is positive, because supply curves are positively slopedsloped

An example An example

Suppose the supply of unskilled labor in some Suppose the supply of unskilled labor in some geographic region is known to be 0.8geographic region is known to be 0.8

Suppose wage rises by 20% due to an increase in Suppose wage rises by 20% due to an increase in demanddemand

What will be impact on employment of unskilled What will be impact on employment of unskilled workers in region?workers in region?– ηη = (%∆Qs)/(%∆P) = (%∆Qs)/(%∆P)

– We know We know ηη and %∆P, and seek %∆Qs and %∆P, and seek %∆Qs

– Rearranging, %∆Qs = (+0.8)(+20) = +16%Rearranging, %∆Qs = (+0.8)(+20) = +16%

– Thus, employment will rise 16%Thus, employment will rise 16%

Questions About Questions About ElasticityElasticity

In the past 40 years, the In the past 40 years, the percentage of income Americans percentage of income Americans spend on food has fallen while spend on food has fallen while incomes have risen. incomes have risen.

What does this tell us about the What does this tell us about the income elasticity of demand for income elasticity of demand for food?food?

Elasticity QuestionsElasticity Questions

Story in newspaper said: “Detroit bus Story in newspaper said: “Detroit bus system is losing money. It wants to system is losing money. It wants to raise fares but not cut its schedule.”raise fares but not cut its schedule.”

Two questions:Two questions:– For revenue to rise as a result of fare For revenue to rise as a result of fare

hike, what must be true about hike, what must be true about demand elasticity?demand elasticity?

– If fare is raised, what will happen to If fare is raised, what will happen to schedule?schedule?

ElasticitiesElasticities

A marketing study estimated the A marketing study estimated the elasticity of demand for all elasticity of demand for all products of a wide range of products of a wide range of companies to be companies to be

-0.985.-0.985.

What does that mean?What does that mean?

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?

Changing ElasticityChanging Elasticity

For many years, Kodak film For many years, Kodak film completely dominated the U.S. completely dominated the U.S. market and had a large majority market and had a large majority of the world market. of the world market.

What happened to price elasticity What happened to price elasticity when Fuji became a major when Fuji became a major competitor and 3-M entered the competitor and 3-M entered the store-brand market?store-brand market?

Is the Demand for Is the Demand for Prescription Drugs Infinite?Prescription Drugs Infinite?

It is often asserted that prescription It is often asserted that prescription drugs can be sold for any price drugs can be sold for any price because they are patented (protected because they are patented (protected against copying) and people need against copying) and people need them to live. What would you suspect them to live. What would you suspect the elasticity for drugs is? What are the elasticity for drugs is? What are the substitutes for drugs?the substitutes for drugs?