micro economics - elasticity measuring responsiveness

8/3/2019 Micro Economics - Elasticity Measuring Responsiveness

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MICROECONOMICSP R O F . R U S H E N C H A H A L

Elasticity: Measuring Responsiveness

2/12/2012Prof. Rushen Chahal


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Chapter 5

y Elasticity Midpoint formula

y Demand elasticity

y Demand elasticity and total revenue

y Extremes of demand elasticity

y Income elasticity

y Cross-elasticity of demandy Supply elasticity



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Learning Objectives

y Discuss how elasticity is used to measurethe responsiveness of quantity changes toprice.

y Compute the elasticity of demand.

y Describe the conditions under which a price

ch

ange would increase, decrease, or notchange a firms total revenue.

y Discuss the significance of the incomeelasticity of demand, the cross elasticity ofdemand, and the elasticity of supply.



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Elasticity

y If you increase the amount of time you study by25%, what percentage will your grades increase?

y If I spend 10% more time in front of the mirror inthe mornings, how much better looking will I be?

y If I increase the amount I exercise by 50%, whatpercentage of my body weight will I lose?

yAll of these questions are asking questions aboutelasticity



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Elasticity

y Elasticity measures the responsiveness of onething (Y) to another (X), specifically, thepercentage change in Y divided by the percentagechange in X.

y In other words: What percent will one variable will change when

another variable changes?

Elasticity = Percentage change in one variable (Y)

Percentage change in another variable (X)



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Elasticity

y How do we calculate this percentage change in avariable?

y If I am 100lbs and gain weight until Im 150lbs, Ive

gained 50% of my bodyweighty If Im 150lbs and lose weight until Im 100lbs, Ive

lost 33.3% of my bodyweight

y Clearly, comparing the change to the original value

isnt going to worky So instead were going to use the midpoint

formula



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Midpoint Formula

y The measure of percentage changes is provided bythe midpoint formula. The formula computes a percentage change as the change in

the variable divided by an amount halfway between the

starting and ending amount.

Percentage change in Y= change in Y/Y midpoint

Divided by

Percentage change in X= change in X/X midpoint



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Midpoint Formula

y Say I increase my studying time from 2 hours tothree hours

y As a result my test grade increases from 75 to 95

y Whats my elasticity of test grade with respect tostudy time?

y Lets use the midpoint formula to calculate it



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Midpoint Formula

y Whats the change in my study time? 1 hour

y Whats the midpoint of my study time?

(2+3)/2 = 2.5y Whats the change in my grade?

20 points

y Whats the midpoint of my grades? (75+95)/2 = 85



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Midpoint Formula

y Change in study time = 1

y Midpoint of study time = 2.5

y Change in grades = 20

y Midpoint of grades = 85

2085______

_1_

2.5

= 0.588

This means that every onepercentage point increase ofstudy time results in a 0.588percentage increase in mygrades



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Midpoint Formula

y Again, the midpoint formula to calculate thepercentage change in Y caused by a 1 percentagechange of X is:

Change in YY midpoint

=Change in X

X midpoint

( Y1 Y0 )

0.5 (Y0 + Y1)_________________ __________________

______________

( X1 X0 )

0.5 (X0 + X1)

______________



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Midpoint Formula

y Im a farmer

y When I use 40 pounds of fertilizer, I can grow 100bushels of tomatoes

y When I use 50 pounds of fertilizer I can grow 130bushels of tomatoes

y Calculate the elasticity of bushels of tomatoes withrespect to fertilizer used



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Midpoint Formula

y Change in tomato crop: 130100=30

y Tomato crop midpoint: (130+100)/2=115

y Change in fertilizer: 50-40=10y Fertilizer midpoint: (50+40)/2=45

y Elasticity=

30

115_______10_

45

= 1.17

This means that a one percentchange in the amount offertilizer used results in a 1.17percent increase in the

tomatoes I can grow 2/12/2012Prof. Rushen Chahal


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Elasticity

y Elasticityhas a broad range of applications.

Price elasticity of demand

Price elasticity of supply

Cross price elasticity

Income Elasticity



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Price Elasticity of Demand

yWe have seen that demand is downwardssloping

y This means that an increase in price will lead

to a decrease of quantity demandedy But how much will an increase in price

decrease quantity demanded?

y This idea is called the price elasticity of

demandy Because price and quantity demanded are

inversely related, the value will be negative

y For simplicity we always make elasticity of

demand positive (absolute value) 2/12/2012Prof. Rushen Chahal


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Price Elasticity of Demand

y How do we calculate elasticity of demand?

Price%

Quantity%E

(

(!

p

Again, we will be using the midpoint formula to calculate

the percentage change in quantity and price

=

( Q1 Q0 )0.5 (Q0 + Q1)

______________

( P1 P0 )

0.5 (P0 + P1)

______________

Change in YY midpoint

=Change in X

X midpoint

_________________ ________________



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The Elasticity of Demand

y Note: The slope of the demand curve is NOT theelasticity of demand

y Slope measures change in price related to change

in quantity demanded in absolute termsy Elasticity measures change in price related to

change in quantity demanded as a percentage

y Slope makes no calculation for percentage changes



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Price elasticity of demand: example

y Lets calculate my elasticity of demand for t-shirts

y At $10 a t-shirt, I will buy 12 t-shirts a year

y At 8$ a t-shirt I will buy 18 t-shirts a year

y Whats my elasticity of demand for t-shirts?



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y Whats the change in t-shirts demanded? 18-12=6 t-shirts

y Whats the midpoint of t-shirts?

(18+12)/2=15 t-sh

irtsy Whats the percentage change in t-shirts?

6/15



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y Whats the change in price?

$10-$8 = $2

y Whats the midpoint price?

($10+$8)/2 = $9

y Whats the percentage change of price? 2/9



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y What percentage has quantity demanded changed asa result of a price change?

y Percentage change Q

Percentage change Y

6/15 2/9 = 1.8 This means a 1% changein price will result in a1.8% change in quantitydemanded



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The Price Elasticity of Demand

y Categories of Demand Elasticity

Inelastic demand: 0 < EP < 1

A 1% change in price will result in a less than 1% change inquantity demanded

Unit elasticity of demand: EP = 1

A 1% change in price will result in exactly 1% change inquantity demanded

Elastic demand: EP > 1A 1% change in price will result in a larger than 1% change

in quantity demanded



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The Price Elasticity of Demand

y Factors affecting demand elasticity

Ease of substitution

The greater availability of substitutes, the greater will be theelasticity.

Proportion of total expenditures

The larger the proportion of a consumers income is used forthe product, the greater its elasticity.

Length of time

Over a longer period of time you can find more alternatives.

Necessity or Luxury?

Demand for necessities is inelastic; demand for luxuries iselastic.



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The Range of the Elasticity ofDemand

0

Inelastic Elastic

Elasticity of DemandElasticity of Demand

1

Unit

Elastic

This value can rangeThis value can range

from zero to infinityfrom zero to infinity

(in absolute value)(in absolute value)



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Estimates of DemandElasticities

ProductProduct Elasticity ofElasticity ofDemandDemand

BeefBeef 0.350.35

FishFish 0.390.39

Public TransitPublic Transit 0.400.40

Peak use business electricityPeak use business electricity .47.47

Physician servicesPhysician services 0.600.60

PoultryPoultry 0.640.64

FruitFruit 0.710.71

Peak use residential electricityPeak use residential electricity 1.51.5

Restaurant mealsRestaurant meals 2.32.3

Kelloggs Fruit LoopsKelloggs Fruit Loops 2.32.3

CheeriosCheerios 3.63.6

CokeCoke 3.83.8

Mountain DewMountain Dew 4.44.4

Fresh TomatoesFresh Tomatoes 4.64.62/12/2012Prof. Rushen Chahal


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The Effect of Elasticity on Price and Quantity

y Why do we care about price elasticity of demand?

y A response to change in supply is largely determinedby price elasticity.

y

Both price and quantity will be affected, but byhowmuch depends in part on elasticity.

y Lets look at an example:



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The Effect of Elasticity of Demand on Priceand Quantity

10 20 30 40 50

1

2

3

4

5

6

78

9

10 S1S2

D1

Here we have a demand curve

that is relatively elastic.

Equilibrium is at P = 4 and

Q=29.

Now there is a decrease in

supply.

You can see that price

only increases by a smallamount ($0.50) but

quantity decreases by a

large amount, about 9.

P2

P

P1

Q2 Q1



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on Price and Quantity

y Elastic demand curve

if supply decreases, prince increases a little and quantity decreases alot.

If supply increases, price decreases a little and quantity increases alot.

Small changes in price and large changes in quantity.

y Example: luxury goods



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The Effect of Elasticity of Demand on Priceand Quantity

10 20 30 40 50

1

2

3

4

5

6

78

9

10 S1S2Lets look at a demand

curve with that is more

inelastic.

Now we shift supply in by

the exact same amount.

With this curve price rises

by much more ($2) but

quantity only decreases byabout 3

D2

P2

P1

Q2

Q1



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on Price and Quantity

y Inelastic demand curve

if supply decreases, prince increases a lot and quantity decreases a

little.

If supply increases, price decreases a lot and quantity increases alittle.

Large changes in price and small changes in quantity.

y Example: necessities



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Demand Elasticity and Revenue

y Another more important aspect of demand elasticityis its effect on revenue - Price x Quantity, or P xQ

y A decrease in price will also be accompanied by anincrease in quantity demanded

y Will this cause revenue to increase or decrease?



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Elasticity and Total Revenue

Total Revenue = PriceTotal Revenue = Price vv QuantityQuantity

When PWhen Poo

TRo

TR constant

TRqDepending upon the elasticityDepending upon the elasticity



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Total Revenue

Quantity

$

Price

Quantity

demanded

Total revenue = price x quantity

which is the area of the shaded

rectangle.

Demand



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Demand Elasticity and Total RevenueIf we raise the price and:Demand is inelastic, we will see an increase in totalrevenue

Demand is elastic, we will see a decrease in totalrevenue

Demand is unit elastic, revenue remains constant



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If we decrease the price and:

Demand is inelastic we will see a decrease in totalrevenue

Demand is elastic we will see an increase in totalrevenue

Demand is unit elastic, revenue remains constant



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P

Q

Here we are at a point onthe demand curve that isrelatively inelastic.

Revenue is represented byP x Q, or the shaded area.Now price falls, and quantityrises.Total revenue falls.

When demand is inelastic, adecrease in price decreasestotal revenue.

P1

P2

Q1 Q2



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P

Q

Here we are at a point onthe demand curve that isrelatively elastic.

Revenue is represented byP x Q, or the shaded area.Now price falls, and quantityrises.Total revenue rises.

When demand is elastic, adecrease in price increasestotal revenue.

P1

P2

Q1 Q2



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The Effect of a Change inTotal Revenue

Change in Price Effect on Total Revenue

Higher PriceHigher Price If demand is inelastic, totalIf demand is inelastic, totalrevenue rises.revenue rises.

If demand is unit elastic, totalIf demand is unit elastic, totalrevenue remains constant.revenue remains constant.

If demand is elastic, totalIf demand is elastic, totalrevenue falls.revenue falls.

Lower priceLower price If demand is inelastic, totalIf demand is inelastic, total

revenue falls.revenue falls.If demand is unit elastic, totalIf demand is unit elastic, total

revenue remains constant.revenue remains constant.

If demand is elastic, totalIf demand is elastic, totalrevenue rises.revenue rises.

2/12/2012 Prof. Rushen Chahal


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Demand Elasticity for Newspapers

y A French newspaper Le Quotidien, wanted to gain acompetitive edge

y They therefore lowered the price of a paper from FF6to FF4

y Circulation increased from 30,000 to 40,000

y But total revenues decreasedfrom FF180,000 toFF160,000



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Demand Elasticity for Newspapers

y In this example, was demand for this newspaperrelatively elastic or inelastic?

y

It seems th

at th

ey miscalculated th

e elasticity ofdemand for the newspaper, as the price decrease wasnot accompanied by as large of a quantity demandedincrease



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Demand Elasticity

y Demand elasticity willbe different on differentparts of the demand curve

y With downward sloping straight line demand curves:

Demand is unit elastic at the midpoint Demand is elastic above the midpoint

Demand is inelastic below the midpoint



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Demand elasticity

y Why?

y At high prices and low quantities, a small

percentage change in price causes a largerpercentage change in quantity (elasticity)

y At low prices and high quantities, a largepercentage change in price causes a small

percentage change in quantity (inelasticity)


ll ll


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Midpoint: Unit Elastic

Quantity

Price

($s)

Elastic

Inelastic

Example:Example:The price is 100 RMB. A change inThe price is 100 RMB. A change inprice of 2 RMB is a large or smallprice of 2 RMB is a large or smallpercentage?percentage?

SmallSmall

The price is 10 RMB. A change inThe price is 10 RMB. A change inprice of 2 RMB is a large or smallprice of 2 RMB is a large or smallpercentage?percentage?

LargeLarge

Example:Example:The quantity is 100. A change inThe quantity is 100. A change inquantity of 4 is a large or smallquantity of 4 is a large or smallpercentage?percentage?

SmallSmall

The quantity is 10. A change inThe quantity is 10. A change inquantity of 4 is a large or smallquantity of 4 is a large or smallpercentage?percentage?

LargeLarge

High price (small

% change),Low quantity (big% change)

Low price (big % change,

high quantity (small % change)

Elasticity = % change in quantity

% change in price

= smallbig

= bigsmall



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Demand, Elasticity, TotalRevenue

Elastic

Inelastic

Unit Elastic

Total Revenue

Demand

Quantity

Do

llars

Total revenue is maximized

when demand is unit elastic.

Each firm produces in

the elastic range of its

demand curve. 2/12/2012Prof. Rushen Chahal


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Extremes of Demand Elasticity

y Sometimes quantity demanded isnt affected by priceat all

y No matter what the price is, the quantity demandedwill always be the same

y This would be called perfectly inelastic

y E.g. medicine needed to keep people alive: insulin fordiabetics



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y Sometimes its going to be impossible to raise prices

y If you raise prices even just a little bit, nobody willbuy your product

y

Th

is is called perfectly elasticy For example you are one firm in an industry with

1000 firms, all selling at the same price



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y Sometimes total revenue will be the exact same, nomatter what price you charge

y This is called unit elastic

y This may be the case where consumers have a fixedbudget to spend on a good, no matter what the price



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QuantityQuantity QuantityQuantity Quantity

DemandDemand

DemandDemandDemandDemand

22 44 1212

66

33

11

1. Perfectly Inelastic

Elasticity = 0

2. Unit Elastic

Elasticity =1

3. Perfectly Elastic

Elasticity = g



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Income Elasticity

y If your income rises, youre going to buy more of(almost) everything

y If your income rises by 10%, how many more DVDs

will you buy?y If your income rises by 10%, how much more

electricity will you consume?

y This is determined by income elasticity



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Income Elasticity

Y

QEY

(

(!%

%

y Income Elasticity of Demand measures howdemand responds to income; computed as thepercentage change in quantity demanded divided

by the percentage change in income.

y Y means Income



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Income Elasticity

y Normal goods 0 < EY Income elasticity is POSITIVE

Demand INCREASES as income increases

y Inferior goods EY< 0

Income elasticity isNEGATIVE

Demand decreases as income increases if you have more money,you buys less of this inferior good.

2/12/2012 Prof. Rushen Chahal


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Income Elasticity of Demand

Change in Income Change in Demand Income Elasticity Type of Good

Increase Increases Positive Normal

Increase Decreases Negative Inferior

Decrease Increases Negative Inferior

Decrease Decreases Positive Normal



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The Cross-Elasticity of Demand

y So far we have been looking at how changes inprice affects changes in quantity demanded ofone product

y What would happen to the demand for Coca-cola if the price of Pepsi-cola rose?

y What would happen to the demand for bicyclelocks if the price of bicycles rose?



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The Cross Elasticity of Demand

y How much is demand for a product changed when athere is a price change in a substitute or complement(related products)?

y To answer this we must look at the cross-elasticity ofdemand.



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B

A

X

P

QE

(

(!

%

%

y Cross-elasticity of demand measures how thedemand for one good responds to changes in theprice of another good; computes as the percentage

change in the quantity demanded of one good (A)divided by the percentage change in the price ofanother good (B).



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y The sign of cross-elasticity for substitutes ispositive.

In other words: if the cross elasticity of two goods is positive,then those two goods are substitutes.

Example: if the price ofCoca cola rises (positive change), thenthe quantity demanded of Pepsi cola increases (positivechange).

(+ number) (+ number) = + number



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y The sign of cross-elasticity for complements isnegative.

In other words: if the cross elasticity of two goods is negative, then

th

ose two goods are complements. Example: if the price of bicycles rises (positive change), then the

quantity demanded of bicycle locks falls (negative change). (+ number) (- number) = - number



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Cross Elasticity of Demand

Change in the

Price of

Another Good

Change in Demand

for the First Good

Cross Elasticity

Between

the Goods

Relationship

Between

the Goods

Increase Increases Positive Substitutes

Increase Decreases Negative Complements

Decrease Increases Negative Complements

Decrease Decreases Positive Substitutes



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Elasticity of Supply

y Demand is not the only thing affected by price

yWe have seen that supply is also affected by price

yAn increase in price will result in an increase of

quantity suppliedy But byhow much?

y This is determined by elasticity of supply



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Price%

SuppliedQuantity%E

(

(!

S

y Price Elasticity of Supply measures theresponsiveness of quantity supplied to price;computed as the percentage change in quantity

supplied divided by the percentage change inprice.

y Elasticity of supply is 0 or POSITIVE. It is nevernegative.



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y When the supply curve is more elastic, a change indemand will cause a small change in price and alarge change in quantity demanded.

y

When the supply curve is less elastic, a change indemand will cause a large change in price and asmall change in quantity demanded.



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The Extremes of SupplyElasticity

Quantity Quantity Quantity

SupplySupply

SupplySupply

1. Perfectly Inelastic

Elasticity = 0

2. Unit Elastic

Elasticity =1

(only if the line is at a

45 degree angle)

3. Perfectly Elastic

Elasticity = g

SupplySupply



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TH E E L A S T I C I T Y O F S U P P L Y M E A S U R E S TH ER E S P O N S I V E N E S S O F Q U A NT ITY S U P P L I E D TO P R I C E .

ELASTICITY OF SUPPLY CAN FALL WITHINTHE FOLLOWING THREE RANGES:

INELAST

IC SUPPLY

:ELASTICITY OF SUPPLY LIES

BETWEEN 0 AND 1.

UNIT ELASTIC SUPPLY:

ELASTICITY OF SUPPLY = 1.

ELASTIC SUPPLY:

ELASTICITY OF SUPPLY IS

THE ELASTICITYOF SUPPLY

micro economics - elasticity measuring responsiveness

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