Session5-Elasticity and Its Application-1

8/3/2019 Session5-Elasticity and Its Application-1

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Economic AnalysisEconomic Analysis

for Businessfor Business

Session IV: Elasticity and its ApplicationSession IV: Elasticity and its Application--11

InstructorInstructorSandeep BasnyatSandeep [email protected][email protected]


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You design websites for local businesses.You charge $200 per website, and currently sell

12 websites per month.

Your costs are rising (including the opp. cost of

your time), so youre thinking of raising theprice to $250.

The law of demand says that you wont sell as

many websites if you raise your price. Howmany fewer websites? How much will your

revenue fall, or might it increase?

You design websites for local businesses.You charge $200 per website, and currently sell

12 websites per month.

Your costs are rising (including the opp. cost of

your time), so youre thinking of raising theprice to $250.

The law of demand says that you wont sell as

many websites if you raise your price. Howmany fewer websites? How much will your

revenue fall, or might it increase?

A scenarioA scenario


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ElasticityElasticityy

Basic idea: Elasticity measures how muchone variable responds to changes in another

variable.

One type of elasticity measures how much demand

for your websites will fall if you raise your price.

y Definition:Elasticity is a numerical measure of the

responsiveness of Qd or Qs to one of itsdeterminants.

y Elastic and Inelastic demand and supply.


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Price Elasticity ofDemandPrice Elasticity ofDemand

y Price elasticity of demand measures howmuch Qdresponds to a change in P.

Price elasticity

of demand=

Percentage change in Qd

Percentage change in P


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Price Elasticity ofDemandPrice Elasticity ofDemand

Priceelasticity

of demand

equals

P

Q

D

Q2

P2

P1

Q1

P rises

by 10%

Q falls

by 15%

15%

10%= 1.5

Price elasticityof demand

= Percentage change in Qd


Example:

What does elasticity = 1.5 mean?


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Calculating Percentage ChangesCalculating Percentage Changes

P

Q

D

$250

8

B

$200

12

A

CalculatePrice

Elasticity of

Demand

Standard methodof computing the

percentage (%) change:

end value start value

start value x 100%


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Calculating Percentage ChangesCalculating Percentage Changes

P

Q

D

$250

8

B

$200

12

A

Demand for

your websites

Problem:

FromA to B,

Prises 25%, Qfalls 33%,elasticity = 33/25 = 1.33

From B toA,

Pfalls 20%, Qrises 50%,

elasticity = 50/20 = 2.50

How to solve this confusion?


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Calculating Percentage ChangesCalculating Percentage Changesy So, we instead use the midpoint method:

end value start value

midpointx 100%

The midpoint is the number halfway betweenthe start & end values, also the average of

those values.

It doesnt matter which value you use as the

start and which as the end you get the

same answer either way!

What is PED using midpoint method?


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Calculating Percentage ChangesCalculating Percentage Changesy Using the midpoint method, the % change

in Pequals

$250 $200

$225x 100% = 22.2%

The % change in Qequals

12 8

10x 100% = 40.0%

The price elasticity of demand equals

40/22.2 = 1.8


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AACC TT II VV E LE L EE AA RR NN II NN GG 11::

Calculate an elasticityCalculate an elasticity

Use the followinginformation to

calculate the

price elasticity

of demandfor hotel rooms using

midpoint method:

ifP= $70, Qd

= 5000

ifP= $90, Qd = 3000

10


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AnswersAnswers

Use midpoint method to calculate% change in Qd

(5000 3000)/4000 = 50%

% change in P

($90 $70)/$80 = 25%

The price elasticity of demand equals

11

50%

25%= 2.0


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Calculating Price Elasticity ofDemandCalculating Price Elasticity ofDemand

y Arc Elasticity:

where ( indicates change.

y Example

If a 1% increase in price results in a 3% decrease in quantity

demanded, the elasticity of demand is I = -3%/1% = -3.

Q

p

p

Q

p

p

Q

Q

p

Q

(

(!

(

(

!(

(!

%

%I

Two Ways: Arc elasticity Calculation and PointElasticity Calculation

Important Note:

Along a D curve, Pand

Q move in oppositedirections, which wouldmake price elasticity

negative most of thecases. (E


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y Use of derivative: dQ/dP : denotes rate at which quantitychanges with respect to Price: similar to:

So, replace by dQ /dP in the Arc elasticity formula,

So the elasticity of demand is:

)/(QpdPdQ

Qp

pQ !(

(

!I

Point Elasticity: Elasticity at a particular point (price)

p

Q

(

(

Note: The derivative of Qn = nQn-1


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y The estimated linear demand function for pork is:

Q = 286 -20p

where Q is the quantity of pork demanded in million kg

per year and p is the price of pork in $ per year. At the equilibrium point ofp = $3.30 and Q = 220 Find

the elasticity of demand for pork:


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y The estimated linear demand function for pork is:

Q = 286 -20p

where Q is the quantity of pork demanded in million kg

per year and p is the price of pork in $ per year. At the equilibrium point ofp = $3.30 and Q = 220 the

elasticity of demand for pork:

3.0220

30.320)/( !v!!

Q

pdPdQI


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Numerical exampleNumerical example

y

Consider a competitive market for which thequantities demanded and supplied (per year) at

various prices are given as follows:

Price($) Demand (millions) Supply (millions)

60 22 14

80 20 16

100 18 18

120 16 20Calculate the price elasticity of demand when the

price is $80. When the price is $100.


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Solution to Numerical exampleSolution to Numerical example

.

PQ

QP

P

PQ

Q

E D

D

D

D

D(

(!(

(

!

From the above question, with each price increase of$20, the quantity

demanded decreases by 2. Therefore,

(QD(P

!

2

20! 0.1.

At P = 80, quantity demanded equals 20 and

ED !80

20 0.1 ! 0.40.

Similarly, at P = 100, quantity demanded equals 18 and

ED !100

18

0.1

! 0.56.


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NonNon--linear demand functionlinear demand function--Numerical ExampleNumerical Example

y C

onsider the following non-linear demand function:Q = P

If the value of = -2, is the demand Price elastic or

inelastic?


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NonNon--linear demand functionlinear demand function--Numerical ExampleNumerical Example

y C

onsider the following non-linear demand function:Q = P. Find price elasticity ofdemand for thisfunction.

Solution:

Differentiating Q = P

dQ/dP = P-1

Therefore, E = P-1 (P /Q) = ( P-1+1) / Q = ( P) / Q

Since,Q = P

E =


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What determines the Elasticity ofDemand?What determines the Elasticity ofDemand? EXAMPLEEXAMPLE 1:1:

WaiWaiWaiWai vs.vs. Yogurt or curdYogurt or curd

y The prices of both of these goods rise by 20%.

For which good does Qd drop the most? Why?

WaiWai has lots of close substitutes

(e.g., Rum Pum, Mayoz etc.),so buyers can easily switch if the price rises.

Yogurt has no close substitutes,

so consumers would probably not

buy much less if its price rises.

y Lesson: Price elasticity is higher when close

substitutes are available.


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EXAMPLE 2:EXAMPLE 2:

Blue Jeans vs. ClothingBlue Jeans vs. Clothing

y

The prices of both goods rise by 20%.For which good does Qd drop the most? Why?

For a narrowly defined good such as

blue jeans, there are many substitutes

(khakis, shorts, Speedos, or even cotton pant).

There are fewer substitutes available for broadly

defined goods.

(Can you think of a substitute for clothing,

other than living in a nudist colony?)

y Lesson: Price elasticity is higher for narrowlydefined goods than broadly defined ones.


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Insulin vs. Caribbean CruisesInsulin vs. Caribbean Cruises

y The prices of both of these goods rise by 20%.

For which good does Qd drop the most? Why?

To millions of diabetics, insulin is a necessity.

A rise in its price would cause little or nodecrease in demand.

A cruise is a luxury. If the price rises,

some people will forego it.

y Lesson: Price elasticity is higher for luxuries thanfor necessities.


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Gasoline in the Short Run vs. Gasoline in the LongGasoline in the Short Run vs. Gasoline in the Long

RunRuny The price of gasoline rises 20%. Does Qd drop more

in the short run or the long run? Why?

Theres not much people can do in the

short run, other than ride the bus or carpool.

In the long run, people can buy smaller cars

or live closer to where they work.

y Lesson: Price elasticity is higher in thelong run than the short run.


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The Determinants ofPrice Elasticity:The Determinants ofPrice Elasticity:A SummaryA Summary

The price elasticity of demand depends on:

the extent to which close substitutes are

available

whether the good is a necessity or a luxury

how broadly or narrowly the good is defined

the time horizon: elasticity is higher in the longrun than the short run.

The price elasticity of demand depends on:

the extent to which close substitutes are

available

whether the good is a necessity or a luxury

how broadly or narrowly the good is defined

the time horizon: elasticity is higher in the longrun than the short run.


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The Variety ofDemand CurvesThe Variety ofDemand Curves

y

Economists classify demand curves according totheir elasticity.

y The price elasticity of demand is closely relatedto the slope of the demand curve.

y Rule of thumb:The flatter the curve, the bigger the elasticity.The steeper the curve, the smaller the elasticity.

y The next 5 slides present the differentclassifications, from least to most elastic.


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Q1

P1

D

Perfectly inelastic demandPerfectly inelastic demand (one extreme case)(one extreme case)

P

Q

P2

P fallsby 10%

Q changes

by 0%

0%

10% = 0

Price elasticity

of demand =

% change in Q

% change in P =

Consumers

price sensitivity:

D curve:

Elasticity:

vertical

0

0


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D

Inelastic demandInelastic demand

P

QQ1

P1

Q2

P2

Q rises less

than 10%

< 10%

10% < 1

Price elasticity

of demand =

% change in Q

% change in P =

P fallsby 10%

Consumers

price sensitivity:

D curve:

Elasticity:

relatively steep

relatively low

< 1


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D

Unit elastic demandUnit elastic demand

P

QQ1

P1

Q2

P2

Qrises by 10%

10%

10% = 1

Price elasticity

of demand =

% change in Q

% change in P =

P fallsby 10%

Consumers

price sensitivity:

Elasticity:

intermediate

1

D curve:

intermediate slope


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D

Elastic demandElastic demand

P

QQ1

P1

Q2

P2

Q rises more

than 10%

> 10%

10% > 1

Price elasticity

of demand =

% change in Q

% change in P =

P fallsby 10%

Consumers

price sensitivity:

D curve:

Elasticity:

relatively flat

relatively high

> 1


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D

Perfectly elastic demandPerfectly elastic demand (the other extreme)(the other extreme)

P

Q

P1

Q1Pchanges

by 0%

Q changes

by any %

any %

0% = infinity

Q2

P2 =Consumers

price sensitivity:

D curve:

Elasticity:

infinity

horizontal

extreme

Price elasticity

of demand =

% change in Q

% change in P =


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Elasticity of a Linear Demand CurveElasticity of a Linear Demand Curve

The slopeof a linear

demand

curve is

constant,but its

elasticity

is not.

P

Q

$30

20

10

$00 20 40 60

200%

40%= 5.0E=

67%67%

= 1.0E=

40%

200%= 0.2E=


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Price Elasticity and Total RevenuePrice Elasticity and Total Revenuey Continuing our scenario, if you raise your price

from $200 to $250, would your revenue rise or fall?

Revenue = Px Q

y A price increase has two effects on revenue:

Higher Pmeans more revenue on each unityou sell.

But you sell fewer units (lower Q), due to

Law ofDemand.

y Which of these two effects is bigger?

It depends on the price elasticity of demand.


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Price Elasticity and Total RevenuePrice Elasticity and Total Revenue

y If demand is elastic, then

price elast. of demand > 1

% change in Q > % change in P

y The fall in revenue from lower Q is greaterthan the increase in revenue from higher P,

so revenue falls.

Revenue = Px Q

Price elasticityof demand

= Percentage change in QPercentage change in P


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Elastic demand(elasticity = 1.8) P

Q

D

$200

12

IfP= $200,

Q= 12 and

revenue = $2400.

When D is elastic,

a price increase

causes revenue to fall.

$250

8

IfP= $250,

Q= 8 and

revenue = $2000.

lost

revenue

due to

lowerQ

increased

revenue due

to higherP

Demand foryour websites


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y If demand is inelastic, then

price elast. of demand < 1% change in Q < % change in P

y The fall in revenue from lower Q is smaller

than the increase in revenue from higher P,

so revenue rises.

y In our example, suppose that Q only falls to 10(instead of 8) when you raise your price to $250.

Revenue = Px Q

Price elasticityof demand =Percentage change in Q



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Price Elasticity and Total RevenuePrice Elasticity and Total RevenueNow, demand is

inelastic:elasticity = 0.82 P

Q

D

$200

12

IfP= $200,

Q= 12 and

revenue = $2400. $250

10

IfP= $250,

Q= 10 and

revenue = $2500.When D is inelastic,

a price increase

causes revenue to rise.

lost

revenue

due to

lowerQ

increasedrevenue due

to higherP

Demand foryour websites


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AnswersAnswers

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A. Pharmacies raise the price of insulin by 10%.Does total expenditure on insulin rise or fall?

Expenditure = Px Q

Since demand is inelastic, Q will fall lessthan 10%, so expenditure rises.


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AnswersAnswers

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B. As a result of a fare war, the price of a luxury cruisefalls 20%.Does luxury cruise companies total revenuerise or fall?

Revenue = Px Q

The fall in Preduces revenue,but Q increases, which increases revenue. Which

effect is bigger?

Since demand is elastic, Q will increase more than20%, so revenue rises.


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Thank youThank you

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Session5-Elasticity and Its Application-1