Elasticity

MB MC

ElasticityElasticity

MB MC

Copyright c 2007 by The McGraw-HillCompanies, Inc. All rights reserved.

Chapter 4: Elasticity Slide 2

Learning Objectives

1. Define and calculate price elasticity of demand

2. Determinants of price elasticity of demand

3. Graphical interpretation of price elasticity of demand

4. Understand how changes in price affect total revenue; relate to price elasticity of demand

5. Define income elasticity and cross-price elasticity

6. Define and calculate price elasticity of supply

7. Determinants of price elasticity of supply

MB MC



Elasticity Does a business make more money or less

by offering goods on sale?

Does the government earn higher or lower tax revenues by raising taxes on goods, say cigarettes?

Does the total wage earnings of all trade union members as a whole rise after the union negotiates a wage hike for its members?

MB MC



Elasticity and Illegal Drugs Is greater enforcement in the illegal drug market

likely to reduce crime? Hypothesis

Drug users steal to buy drugs Increased drug enforcement will decrease theft

AnalysisIncreased enforcement reduces supply of drugs

Price of drugs increases; Quantity demanded falls

Theft goes down only if drug users spend less to buy drugs

How responsive is quantity demanded to price?

MB MC



The Effect of Extra Border Patrols on the Market for Illicit Drugs

Q(1,000s of ounces/day)

P($

/ou

nce

)

50

50

S

D

80

40

S’

Total Expenditure = P x QS $2500 = $50 x 50S’ $3200 = $80 x 40

MB MC



Elasticity

Say the price of salt rises by 50%. By how much will you reduce your salt consumption?

Not a whole lot because salt does not have very good substitutes.

Now say the price of only one brand, Morton salt, rises by 50%. How does your salt consumption respond?

Buy other brands of salt because for most people Morton and Wal-Mart brands will be perfect substitutes.

MB MC



Elasticity

Clearly, for a 50% change in the price, demand for Morton salt is more responsive than the demand for salt in general.

We say that the demand for Morton salt is more elastic than the demand for salt.

Elasticity, in general, is a measure of the extent to which quantity demanded and/or quantity supplied responds to variations in price, income, and other factors.

MB MC



Price Elasticity of Demand

Measure of responsiveness of quantity demanded to changes in price

It is defined as the absolute value of the percentage change in the quantity demanded of good A divided by the percentage change in the price of good A.

If the price of pork falls by 2% and the quantity demanded increases by 6%, then the price elasticity of demand for pork is 6% divided by 2% = 3

ε = (-) Percentage change in quantity demanded

Percentage change in price

MB MC




Quantity

Pri

ce

1.00

D

A

400

0.97

404

B

Another example

MB MC



The elasticity going from A (old) to B (new) is 0.33 [(PB - PA)/PA] x 100 = -3%; [(QB - QA)/QA] x 100 = 1%; Price

elasticity of demand = 0.33 But going from B (old) to A (new) the calculation is: [(PA - PB)/PB] x 100 = -3.09278%; [(QA - QB)/QB] x 100 =

0.99%; Price elasticity of demand = 3.123 So economists use Midpoint Average Formula.


Old (A) New (B) % Change

Price $1.00 (PA) $0.97 (PB) 3%

Quantity 400 (QA) 404 (QB) 1%

MB MC




Price Elasticityof Demand

=(Q1 – Q2) / 0.5 (Q1 + Q2)

(P1 – P2) / 0.5 (P1 + P2)

Price Elasticityof Demand

=(Q1 – Q2) / (Q1 + Q2)

(P1 – P2) / (P1 + P2)

MB MC




Suppose that 100 shoes are demanded when price is $20. When price rises to $40, quantity of shoes demanded falls to 40. So P1=$20, Q1=100; P2=$40 and Q2=40. Then the price elasticity of demand is:

(Q1 – Q2) / (Q1 + Q2)

(P1 – P2) / (P1 + P2)

=(100 – 40) / (100 + 40)

(20 – 40) / (20 + 40) = 9/7

MB MC



Elastic, Inelastic and Unit Elastic Demand

Demand is said to be elastic if the price elasticity of demand is greater than 1.

Percentage change in quantity is greater than percentage change in price; quantity demanded is responsive to price

Demand is said to be inelastic if the price elasticity of demand is less than 1.

Percentage change in quantity is less than percentage change in price; quantity demanded is not very responsive to price

Demand is said to be unit elastic if the price elasticity of demand is equal to 1: price and quantity change by the same percentage

MB MC



Price Elasticity Estimates for Selected Products

Good or service Price elasticity

Green peas 2.80

Restaurant meals 1.63

Automobiles 1.35

Electricity 1.20

Beer 1.19

Movies 0.87

Air travel (foreign) 0.77

Shoes 0.70

Coffee 0.25

Theater, opera 0.18

MB MC



Determinants of Price Elasticity of Demand

Nature of the goods - Necessities have rather inelastic demand. The short run price elasticity of demand for gasoline is 0.26 (long run 0.58). Luxuries, on the other hand have relatively elastic demand (e.g., restaurant meals).

Availability of close substitutes - Price Elasticity of demand is expected to be high for goods with close substitutes. If the price of Crest toothpaste rises most people will switch brands and the quantity of Crest toothpaste demanded will fall by a large amount. The same cannot be said for toothpaste in general.

MB MC



Determinants of Price Elasticity of Demand

Fraction of Income Spent (budget share) - Lower (higher) the fraction of income spent on a good, the lower (higher) will be its price elasticity of demand. Example – salt.

Length of time - Price elasticity of demand is greater in the long run than in the short run. If high-efficiency washers become cheaper by 25%, many people will buy a washer immediately. These would be people shopping for a washer at the time. But as time passes, (assuming electricity and non he washer prices stay the same) more and more people will buy these he washers.

MB MC



Economic Naturalist

Will higher taxes on cigarettes curb teenage smoking?

Although cigarette demand is expected to be inelastic, they may be quite elastic for teenagers because the cost may be a fair share of their budget.

Teenagers smoke because their peers do. Cutbacks by some will influence peers to cut back too and the total effect of reduced consumption may be significant.

MB MC



Economic Naturalist

In 1990 Congress imposed a luxury tax on yachts costing > $100,000. Instead of yielding higher revenues, it led to revenue loss and unemployment in the US boating industry. Why?

Foreign made yachts (which are perfect substitutes) were exempt from the tax. A tax imposed on a good with a high price elasticity of demand stimulates large rearrangements of consumption but yields little revenue.

MB MC



A Graphical Interpretationof Price Elasticity

Let ΔP be a small change in priceThen ΔP / P is the percentage change in price

Suppose that when price changes by ΔP, quantity demanded changes by ΔQThen ΔQ/ Q is percentage change in quantity

demanded So the price elasticity of demand is:

ε = ΔQ / Q

ΔP / P

MB MC



A Graphical Interpretation of Price Elasticity of Demand

Quantity

Pri

ce

P

D

A

Q

P - P

Q + Q

Q

P

slopeQ

P A

1 at elasticity icePr

MB MC



Calculating Price Elasticity of Demand

20

Quantity

Pri

ce

1

D

A

2 3 4 5

16

12

8

4

45

20

intercept horizontal

intercept verticalslope

3

2

12

8

4

1x

3

8A

MB MC



D1

D2

12

4 6 12

6

4

Price Elasticity and the Steepness of the Demand Curve

Quantity

Pri

ceWhat is the price elasticity ofDemand for D1 & D2 when P = $4?

2

1

612

1

4

41D

2

126

1

4

42D

MB MC



Price Elasticity and the Steepness of the Demand Curve

12

Quantity

Pri

ce

D1

D2

4 6 12

6

4

ObservationIf two demand curves have a point in common, the steeper curve must be less elastic with respect to price at that point

MB MC



Price Elasticity Regions along a Straight-Line Demand Curve

Quantity

Pri

ce

b/2

a/2

a

b

1

1

1

ObservationPrice elasticity varies at every point along a straight-line demand curve

MB MC



Perfectly Elastic Demand Curve

Quantity

Pri

ce

) y (elasticit demand

elastic Perfectly

0 curve demandc theof Slope

MB MC



Perfectly Inelastic Demand Curve

Quantity

Pri

ce

)0 y (elasticit demand

inelasticPerfectly

curve demandc theof Slope

MB MC



Elasticity and Total Expenditure

When will a university generate higher revenues by raising tuition?When the demand for education at the university

is inelastic. When will a business earn higher revenues

by cutting prices?When the demand for the good is elastic.

MB MC



Elasticity and Total Expenditure

Total Expenditure = P x QMarket demand measures the quantity (Q)

at each price (P) Total Expenditure = Total Revenue

MB MC



D

A

Total Expenditure = $1,000/day

The Demand Curve for Movie Tickets

12

Quantity (100s of tickets/day)

Pri

ce (

$/ti

cket

)

1 3 4 5 6

10

8

6

4

2

0 2

MB MC



D

B

Total Expenditure = $1,600/day

The Demand Curve for Movie Tickets

12


Pri

ce (

$/ti

cket

)

1 3 4 5 6

10

8

6

4

2

0 2

MB MC



Quantity Demanded and Total Expenditure as a Function of Price

Price $12 $10 $8 $6 $4 $2 $0

Quantity 0 100 200 300 400 500 600

Expenditure $0 $1,000 $1,600 $1,800 $1,600 $1,000 $0

Elasticity 5 2 1.00 0.05 0.02 0

Demand for movie Tickets again

MB MC



Total Expenditure as a Function of Price

1,800

Price ($/ticket)

To

tal

ex

pe

nd

itu

re (

$/d

ay

)

2 6 8 10 12

1,600

1,000

0 4

12


Pri

ce

($

/tic

ke

t)

1 3 4 5 6

10

8

6

4

2

0 2

Total revenue is at a maximum at themidpoint on a straight-line demand curve

1

1

1

1

TEQP ,,,1

TEQP ,,,1

MB MC



Income Elasticity of Demand

Income Elasticity of DemandThe percentage by which quantity

demanded changes in response to a 1 percent change in income

MB MC


04/22/23 Sudeshna C. Bandyopadhy

ay

35

Income Elasticityof Demand =

(Q1 – Q2) / 0.5 (Q1 + Q2)

(I1 – I2) / 0.5 (I1 + I2)

Income Elasticityof Demand

(Q1 – Q2) = *

(I1 - I2)

(I1 + I2)


(Q1 + Q2)

MB MC



ay

36

7.8… Income Elasticity of Demand

Suppose that when income is $1000 per week, the number of CDs demanded (per week) is 4. When income rises to $2000, weekly demand for CDs rises to 7. So I1=$1000 Q1=4; I2=$2000 and Q2=7. Then the income elasticity of demand for CDs is:

eI(4 – 7)

= * (1000 - 2000)

(1000 + 2000)

(4 + 7) = 9/11

MB MC



ay

37


Good A is a normal good if the income elasticity of demand is positive.

Good A is an inferior good if the income elasticity of demand is negative.

MB MC



Cross Price Elasticity of Demand

Cross-Price Elasticity of DemandThe cross price elasticity of demand for X is

the percentage by which quantity demanded of X changes in response to a 1 percent change in the price of a different good, Y.

MB MC



ay

39

Cross Price Elasticityof Demand for X =

(Q1X – Q2

X) / 0.5 (Q1X + Q2

X)

Cross Price Elasticityof Demand for X

(Q1X – Q2

X )

= *


(P1Y – P2

Y) / 0.5 (P1Y + P2

Y)

(Q1X + Q2

X )

(P1Y + P2

Y )

(P1Y - P2

Y )

*

MB MC



ay

40

eX,Y

(25 – 100) = *

(1.00 – 1.50)

(1.00 + 1.50)

(25 + 100) = 3

Substitutes

Consider an example with substitute goods. Suppose that 25 two liter bottles of coke are demanded when Pepsi sells for $1 per 2 liter bottle. When the price of a bottle of Pepsi rises to $1.50, quantity of coke demanded rises to 100 bottles. So P1

Y = $1, Q1X = 25; P2

Y = $1.50, Q2X = 100.

Then the cross price elasticity of demand for coke (good X) is:

*

MB MC



ay

41

Complements

Suppose that 30 bottles of soda is demanded when a slice of Pizza sells for $1 per slice. When the price of a slice of pizza rises to $2 per slice, the quantity of soda demanded falls to 10 bottles. Here good X is soda and good Y is pizza. So P1

Y = $1, Q1X = 30; P2

Y = $2, Q2X =

10. Then the cross price elasticity of demand for soda (good X) is:

MB MC



ay

42

eX,Y

(30 – 10) = *

(1.00 – 2.00)

(1.00 + 2.00)

(30 + 10) = -3/2

Complements

Consider and example with complement goods. Suppose that 30 bottles of soda is demanded when a slice of Pizza sells for $1 per slice. When the price of a slice of pizza rises to $2 per slice, the quantity of soda demanded falls to 10 bottles. Here good X is soda and good Y is pizza. So P1

Y = $1, Q1X = 30; P2

Y = $2, Q2X = 10. Then the cross

price elasticity of demand for soda (good X) is:

MB MC



ay

43


The cross price elasticity of demand is negative for complements.

The cross price elasticity of demand is positive for substitutes.

The cross price elasticity of demand is zero for goods which are unrelated in consumption.

MB MC



The Price Elasticity of Supply

Price Elasticity of SupplyThe percentage change in the quantity

supplied that occurs in response to a 1 percent change in price

PP

QQ supply of elasticity Price

slope

1

Q

P supply of elasticity Price

MB MC



2

8A

22128 A

3

10B

3

521310 B

Price Elasticity of Supply Declines as Quantity Rises for a supply curve with a +ve Y Intercept

Quantity

Pri

ce

0

4

S

MB MC



15

5B

P

Q

15/1515/5 B

S

12

4A

14/1212/4 A

A Supply Curve with zero intercept has Price Elasticity of Supply = 1

Quantity

Pri

ce

0

MB MC



Mid point Average Formula

Price Elasticityof Supply

=(Q1 – Q2) / 0.5 (Q1 + Q2)

(P1 – P2) / 0.5 (P1 + P2)

Price Elasticityof Supply

=(Q1 – Q2) / (Q1 + Q2)

(P1 – P2) / (P1 + P2)

MB MC



Flexibility of inputsUses adaptable inputs, more elastic

Mobility of inputsResources move where needed, more elastic

Ability to use substitute inputsAlternative inputs easy to find, more elastic

TimeLong run, more elastic

Determinants of Supply Elasticity

MB MC



A Perfectly Inelastic Supply Curve

Quantity

Pri

ce

($/a

cre

)

0

SElasticity = 0 at everypoint along a verticalsupply curve

Slope of a verticalsupply curve = infinity

MB MC


LO 4 - 6

Examples of Perfectly Inelastic Supply

Land on ManhattanSupply is completely fixed

Any one-of-a-kind item has perfectly inelastic supplyWork of art (Mona Lisa)Hope Diamond

MB MC



Quantity of lemonade

(cups/day)

Pri

ce (

cen

ts/c

up

)

0

14 S

Supply elasticity is infinite for a horizontal straight line supply curve; Slope = 0. Happens when MC is constant

A Perfectly Elastic Supply Curve

MB MC



Infinite price elasticity of supplySell all you can at a fixed price

Inputs purchased at a constant priceNo volume discounts

Constant proportions of production Lemonade example

Cost of production is 14¢ at all levels of QMarginal cost

P = 14¢

Examples of Perfectly Elastic Supply

MB MC



Why are gasoline prices so much more volatile than car prices?

Differences in marketsDemand for gasoline is more inelasticGasoline market has larger and more frequent

supply shifts Price volatility is seen in markets where

demand is relatively inelastic and supply fluctuates sharply and often.

Economic Naturalist

MB MC



Gasoline Market

Quantity(millions of gallons/day)

Pri

ce (

$/g

allo

n)

0 6

1.69

S’

D

1.02

7.2

S

Gasoline: Inelastic demand; large and frequent supply shifts

MB MC



Price volatility is also common in markets where supply is highly inelastic and demand curves fluctuates sharply.Supply of electricity in the short run is essentially

fixed. If demand increases significantly, prices can rise dramatically – story of California’s unregulated market for wholesale electricity in summer 2000.

Price Volatility

MB MC



Automobile Market

Pri

ce (

$1,0

00s/

car)

D

17

S’

11Quantity

(1,000s of cars/day)Cars

16.4

12

S

Cars: Relatively elastic demand; small supply shifts

MB MC



Why do star players get paid in hundreds of millions of dollars for a contract?Because they supply unique and essential

inputs in the production process, which are the true supply bottlenecks, thereby significantly reducing the elasticity of supply in the long run.

Supply Bottlenecks

MB MC

End ofChapterEnd of

Chapter

Elasticity

Documents

Transcript of Elasticity