emba sem i managerial economics session3-elasticity and its application (1)

8/10/2019 EMBA Sem I Managerial Economics Session3-Elasticity and Its Application (1)

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Managerial EconomicsExecutive MBA Program

Session 3: Elasticity and itsApplication

InstructorSandeep [email protected]


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Elasticity Basic idea: Elasticity measures how much

one variable responds to changes inanother variable.

One type of elasticity measures how much

demand for your websites will fall if you raiseyour price.

Definition:

Elasticityis a numerical measure of theresponsiveness of Qd or Qs to one of itsdeterminants.

Elastic and Inelastic demand and supply.


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Price Elasticity of Demand

Price elasticity of demandmeasureshow much Qdresponds to a change in P.

Price elasticityof demand

=Percentage change in Qd

Percentage change in P


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Price Elasticity of Demand

Priceelasticityof demand

equals

P

Q

D

Q2

P2

P1

Q1

P risesby 10%

Q fallsby 15%

15%

10%= 1.5

Price elasticityof demand =

Percentage change in Qd


Example:

What does elastic i ty = 1.5 mean?


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Calculating Percentage Changes

P

Q

D

$250

8

B

$200

12

A

CalculatePrice

Elasticity ofDemand

Standard method

of computing thepercentage (%) change:

end valuestart value

start valuex 100%


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Calculating Percentage Changes

P

Q

D

$250

8

B

$200

12

A

Demand foryour websites

Problem:

From A to B,

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

From B to A,

Pfalls 20%, Qrises 50%,

elasticity = 50/20 = - 2.50

How to solve th is confus ion?


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Calculating Percentage Changes So, we instead use the midpoint method:

end valuestart 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 Changes Using the midpoint method, the % change

in Pequals

$250$200

$225x 100% = 22.2%

The % change in Qequals

812

10x 100% = - 40.0%

The price elasticity of demand equals

- 40/22.2 = -1.8


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ACTIVE LEARNING 1:Calculate an elasticity

Use the followinginformation tocalculate theprice elasticity

of demandfor hotel rooms usingmidpoint method:

if P= $70, Qd

= 5000if P= $90, Qd= 3000

10


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ACTIVE LEARNING 1:Answers

Use midpoint method to calculate% change in Qd

(50003000)/4000 = 50%

% change in P

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

The price elasticity of demand equals

11

50%

- 25%= - 2.0


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Calculating Price Elasticity ofDemand

Arc Elasticity:

where Dindicates change.

Example

If a 1% increase in price results in a 3% decrease inquantity demanded, the elasticity of demandis e= -

3%/1% = -3.

Q

p

p

Q

p

p

Q

Q

p

Q

D

D

D

D

D

D

%

%e

Two Ways:Arc elasticity Calculation and Point

Elasticity CalculationImportant Note:

Along a Dcurve, Pand Qmove inopposite directions,which would makeprice elasticitynegative most of thecases. (E


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Numerical example

Consider a competitive market for which the

quantities demanded and supplied (peryear) at various prices are given as follows:

Price($) Demand (millions) Supply

(millions)60 22 14

80 20 16

100 18 18

120 16 20

Calculate the price elasticity of demand whenthe price is $80. When the price is $100.


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Solution to Numerical example

.P

Q

Q

P

P

P

Q

Q

E DD

D

D

DD

D

D

D

From the above question, with each price increase of $20, the quantitydemanded decreases by 2. Therefore,

DQDDP

220

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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The estimated linear demand function for porkis:

Q= 286 -20p

where Qis the quantity of pork demanded in millionkg per year and p is the price of pork in $ per year.

At the equilibrium point ofp = $3.30 and Q= 220Find the elasticity of demand for pork:


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Demand

Use of derivative: dQ/dP: denotes rate at whichquantity changes with respect to Price: similar to:

So, replace by dQ/dP in theArc elasticity formula,

So the elasticity of demand is:

)/( Q

pdPdQQ

p

p

Q

D

D

e

Point Elasticity: Elasticity at a particular point (price)

p

Q

D

D


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The estimated linear demand function for porkis:

Q= 286 -20p

where Qis the quantity of pork demanded in millionkg per year and p is the price of pork in $ per year.

At the equilibrium point ofp = $3.30 and Q= 220 theelasticity of demand for pork:

3.0220

30.320)/(

Q

pdPdQe


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Numerical ProblemsConsider a market with Demand curve q = 16 10pand Supply curve

q = 8 + 20p.(Here q is in millions of kgs and p is in dollars/kg)

(a) Determine the market equilibrium price and quantity and the total

revenue in this market.

(b) Calculate the price elasticity of demand and the price elasticity of

supply at the market equilibrium.

Answer (a):

P = $0.8/kg q = 8 million kgs. TR = $6.4 millions

Answer (b):PED = -1PES = 2


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What determines the Elasticity of Demand?EXAMPLE 1:

Wai Wai vs. Yogurt or curd

The prices of both of these goods rise by 20%.For which good doesQddrop the most? Why?

Wai Wai 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.

Lesson: Price elast ic i ty is h igher when closesubs ti tutes are avai lable.


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EXAMPLE 2:

Blue Jeans vs. Clothing

The prices of both goods rise by 20%.

For which good doesQddrop the most? Why? For a narrowly defined good such as

blue jeans, there are many substitutes

(khakis, shorts, Speedos, or even cottonpant).

There are fewer substitutes available for

broadly defined goods.

(Can you think of a substitute for clothing,

other than living in a nudist colony?)

Lesson: Price elast ic i ty is h igher for narrow ly

def ined goods than broadly def ined ones.


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EXAMPLE 3:

Insulin vs. Caribbean Cruises

The prices of both of these goods rise by 20%.For which good doesQddrop the most? Why?

To millions of diabetics, insulin is a

necessity.

A rise in its price would cause little or no

decrease in demand.

A cruise is a luxury. If the price rises,

some people will forego it.

Lesson: Price elast ic i ty is h igher for lu xu r iesthan for necess i t ies.


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EXAMPLE 4:

Gasoline in the Short Run vs. Gasoline in the

Long Run

The price of gasoline rises 20%. Does Qddropmore 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.

Lesson: Price elast ic i ty is higher in thelong run than the shor t run.


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The Determinants of Price Elasticity:A Summary

The price elasticity of demand dependson:

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

long run than the short run.


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The Variety of Demand Curves

Economists classify demand curves

according to their elasticity.

The price elasticity of demand is closelyrelated to the slope of the demand curve.

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

elasticity. The next 5 slides present the different

classifications, from least to most elastic.


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Q1

P1

D

Perfectly inelastic demand (one extreme case)

P

Q

P2

P fallsby 10%

Q changesby 0%

0%

10%= 0

Price elasticity

of demand

=% change in Q

% change in P=

Consumers

price sensitivity:

Dcurve:

Elasticity:

vertical

0

0


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D

Inelastic demand

P

QQ1

P1

Q2

P2

Q rises lessthan 10%

< 10%

10%< 1

Price elasticity

of demand

=% change in Q

% change in P=

P fallsby 10%

Consumers

price sensitivity:

Dcurve:

Elasticity:

relatively steep

relatively low

< 1


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D

Unit 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

Dcurve:

intermediate slope


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D

Elastic demand

P

QQ1

P1

Q2

P2

Q rises morethan 10%

> 10%

10%> 1

Price elasticity

of demand

=% change in Q

% change in P=

P fallsby 10%

Consumers

price sensitivity:

Dcurve:

Elasticity:

relatively flat

relatively high

> 1


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D

Perfectly elastic demand (the other extreme)

P

Q

P1

Q1Pchanges

by 0%

Q changesby any %

any %

0%= infinity

Q2

P2=Consumers

price sensitivity:

Dcurve:

Elasticity:

infinity

horizontal

extreme

Price elasticity

of demand

=% change in Q

% change in P=


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Elasticity of a Linear Demand Curve

The slopeof a lineardemandcurve is

constant,but itselasticityis 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 Revenue Continuing our scenario, if you raise your price

from $200 to $250, would your revenue rise or fall?Revenue = Px Q

A price increase has two effects on revenue:

Higher Pmeans more revenue on each unit

you sell.

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

Law of Demand.

Which of these two effects is bigger?It depends on the price elasticity of demand.


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Price Elasticity and Total Revenue

If demand is elastic, thenprice elast. of demand > 1

% change in Q > % change in P

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 Q



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Elastic demand

(elasticity = 1.8) P

Q

D

$200

12

If P= $200,

Q= 12 and

revenue = $2400.

When Dis elastic,

a price increase

causes revenue to fall.

$250

8

If P= $250,

Q= 8 and

revenue = $2000.

lostrevenuedue tolower Q

increased

revenue dueto higher P



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If demand is inelastic, then

price elast. of demand < 1

% change in Q < % change in P

The fall in revenue from lower Qis smallerthan the increase in revenue from higher P,

so revenue rises.

In our example, suppose that Qonly falls to 10(instead of 8) when you raise your price to

$250.

Revenue = Px Q

Price elasticity

of demand =

Percentage change in Q



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Price Elasticity and Total RevenueNow, demand is

inelastic:elasticity = 0.82 P

Q

D

$200

12

If P= $200,

Q= 12 and

revenue = $2400. $250

10

If P= $250,

Q= 10 and

revenue = $2500.When Dis inelastic,

a price increase

causes revenue to rise.

lostrevenuedue to

lowerQ

increased

revenue dueto higher P



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A. Pharmacies raise the price of insulin by10%. Does total expenditure on insulinrise or fall?

Expenditure = Px QSince demand is inelastic, Qwill fall lessthan 10%, so expenditure rises.


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B. As a result of a fare war, the price of a luxurycruise falls 20%.Does luxury cruise companies total revenue

rise or fall?

Revenue = Px Q

The fall in Preduces revenue,but Qincreases, which increases revenue.

Which effect is bigger?Since demand is elastic, Qwill increase morethan 20%, so revenue rises.


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Income Elasticity of Demand The income elasticity of demandmeasures the

response of Qdto a change in consumer income.

Income elasticityof demand

=Percent change in Qd

Percent change in income


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Calculating Income Elasticity of Demand

Arc Elasticity:

where Ystands for income.

Example

If a 1% increase in income results in a 3% decrease inquantity demanded, the income elasticity of demandis x= -3%/1% = -3.

Q

Y

Y

Q

YY

Q

Q

Y

Q

D

D

D

D

D

D

%

%x

N i l E l


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Numerical Example

a) Suppose the demand for an automobile as a functionof income per capita is given by:

Q = 50,000 + 5I

What is the income elasticity of demand when per capita

income increases from $10,000 to $11,000? (Using midpoint

method)

N i l E l


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Numerical Example

a) Suppose the demand for an automobile as a functionof income per capita is given by:

Q = 50,000 + 5I

What is the income elasticity of demand when per capita

income increases from $10,000 to $11,000? (Using midpoint

method)

Solution:

When I1= 10,000 Q1= 100,000

When I2= 11,000, Q2= 105,000

Percentage Change in Q = 4.88Percentage Change in I = 9.52

Income Elasticity of Demand = 4.88 / 9.52 = 0.512


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Numerical Example-Point Income Elasticity

b) Suppose the demand for an automobile as a function

of income per capita is given by:Q = 50,000 + 5I

What is the income elasticity of demand at the income level

of $10,500?


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Numerical Example

b) Suppose the demand for an automobile as a function

of income per capita is given by:Q = 50,000 + 5I

What is the income elasticity of demand at the income level

of $10,500?

Solution:

When I = 10,500; Q = 102,500

dQ / dI = 5

Income Elasticity of Demand = b x (P/Q)

= 5 x (10500 / 102500)

E = 0.512

Necessities Inferior goods and


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Necessities, Inferior goods andluxuriesElasticity measurement as:

E < 0 : Inferior goods (negative)

0 < E 1: Normal goods or necessities

E > 1 : Luxuries

An increase in income causes an increase in

demand for a normalgood and luxuries.

An increase in income causes a decrease indemand for inferior goods.

C P i El ti it f D d


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Cross Price Elasticity of Demand The cross-price elasticity of demandmeasures the

response of demand for one good to changes in theprice of another good.

Cross-price elast.

of demand

=% change in Qd for good 1

% change in price of good 2

For substitutes, cross-price elasticity > 0 (positive)

E.g., an increase in price of goat meat causes an

increase in demand for chicken.

For complements, cross-price elasticity < 0

(Negative)

E.g., an increase in price of computers causes

decrease in demand for software.

Calculating Cross Price Elasticity of


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Calculating Cross Price Elasticity ofDemand

Arc Elasticity,

wherePostands for price of another good.

Example

If a 1% increase in the price of a related good results in a3% decrease in quantity demanded, the cross-priceelasticity of demandis = -3%/1% = -3.

Q

p

p

Q

pp

Q

Q

p

Q o

o

o

oo D

D

D

D

D

D

%

%

Numerical Example


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Numerical ExampleDemand for a publishers book is given as:

Qx= 12,0005,000Px+ 5I+ 500Pc Px = Price of the book = $5

I = Income per capita = $10,000

Pc

= Price of the books from competingpublishers = $6

Numerical Example


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Numerical Example1) a) Find Price elasticity of demand for the book.

b) What effect a price increase would have on total

revenues?Solution:

a) Substituting the values of I and Pc

Qx= 12,0005,000Px+ 5(10000) + 500(6)

Or, Qx= 65,0005,000Px

When Px = $5 (given), Qx = 40,000Now, dQx/dPx= - 5000

Therefore, E p = -5000 x (5 / 40000) = - 0.625

b) Since, the demand for the book is inelastic, anincrease in the price of the book would increasetotal revenue.

Numerical Example


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Numerical Example2) a) Find income elasticity of demand for the book.

b) Find if the book is inferior good, normal good or luxury.

Solution:

a) Substituting the values of Px and PcQx= 12,0005,000(5) + 5I+ 500(6)

Or, Qx= - 10,000 + 5I

When I= $10000 (given), Qx = 40,000Now, dQx/dI = b = 5Therefore, E I = 5 x (10000 / 40000) = 1.25

b) Since, the E I> 1 for the book, the book is luxury.

Numerical Example


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Numerical Example3) a) Assess the probable impact on demand for the book

if competing publishers raise their prices.

b) Are the books substitute for each other orcomplementsSolution:

a) Substituting the values of Px and IQx= 12,0005,000(5) + 5(10000) + 500Pc

Or, Qx

= 37,000 + 500Pc

When Pc = $6 (given), Qx = 40,000

Now, dQx/dPc= b = 500

Therefore, Cross price elasticity of demand for the book

E c = 500 x (6 / 40000) = 0.0751% increase in competitors book price will increase the

demand for the book by 0.075%

b) Since, the E C> 0 for the book, the book is substitute to

competing producers book.

P i El ti it f S l


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Price Elasticity of Supply

Price elasticity of supplymeasures

how much Qs

responds to a change inP.

Price elasticityof supply =

Percentage change in Qs


P i El ti it f S l


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Q2

Price Elasticity of Supply

Priceelasticityof supplyequals

P

Q

S

P2

Q1

P1

P risesby 8%

Q risesby 16%

16%

8%= 2.0

Price elasticityof supply =

Percentage change in Qs


Example:

The Variety of Supply Curves


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The Variety of Supply Curves

Economists classify supply curves

according to their elasticity.

The slope of the supply curve is closelyrelated to price elasticity of supply.

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

elasticity. The next 5 slides present the different

classifications, from least to most elastic.

P f tl i l ti


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S

Perfectly inelastic (one extreme)

P

QQ1

P1

P2

Q changesby 0%

0%

10%

= 0Price elasticity

of supply

=% change in Q

% change in P

=

P risesby 10%

Sellers

price sensitivity:

Scurve:

Elasticity:

vertical

0

0

I l ti


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S

Inelastic

P

QQ1

P1

Q2

P2

Q rises lessthan 10%

< 10%

10%

< 1Price elasticity

of supply

=% change in Q

% change in P

=

P risesby 10%

Sellers

price sensitivity:

Scurve:

Elasticity:

relatively steep

relatively low

< 1

U it l ti


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S

Unit elastic

P

QQ1

P1

Q2

P2

Q risesby 10%

10%

10%

= 1Price elasticity

of supply

=% change in Q

% change in P

=

P risesby 10%

Sellers

price sensitivity:

Scurve:

Elasticity:

intermediate slope

intermediate

= 1


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P f tl l ti (th th t )


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S

Perfectly elastic (the other extreme)

P

Q

P1

Q1Pchanges

by 0%

Q changesby any %

any %

0%

= infinityPrice elasticity

of supply

=% change in Q

% change in P

=

Q2

P2=Sellers

price sensitivity:

Scurve:

Elasticity:

horizontal

extreme

infinity


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A C T I V E L E A R N I N G 3:


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ACTIVE LEARNING 3:Elasticity and changes in equilibrium

The supply of beachfront property isinelastic. The supply of new cars iselastic.

Suppose population growth causesdemand for both goods to double(at each price, Qddoubles).

For which product will Pchange themost?

For which product will Qchange themost?

60



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61

Beachfrontproperty (inelastic

supply):P

Q

D1 D2S

Q1

P1 A

B

Q2

P2

When supplyis inelastic,

an increase in

demand has a

bigger impacton price than

on quantity.



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62

New cars(elastic supply):

P

Q

D1 D2

S

Q1

P1

A

Q2

P2

B

When supplyis elastic,

an increase in

demand has a

bigger impacton quantity

than on price.

How the Price Elasticity of Supply Can Vary


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S

How the Price Elasticity of Supply Can Vary

P

Q

Supply oftenbecomesless elasticas Qrises,

due tocapacitylimits.

$15

525

12

500

$3

100

4

200

elasticity> 1

elasticity< 1


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Thank you

emba sem i managerial economics session3-elasticity and its application (1)

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