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
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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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Price elasticity of demand: example
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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Price elasticity of demand: example
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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Price elasticity of demand: example
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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Demand Elasticity and Revenue
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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Demand Elasticity and Revenue
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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Demand Elasticity and Revenue
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.
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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)
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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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Extremes of Demand Elasticity
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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Extremes of Demand Elasticity
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.
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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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The Cross-Elasticity of Demand
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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The Cross-Elasticity of Demand
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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The Cross-Elasticity of Demand
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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Elasticity of Supply
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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Elasticity of Supply
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