elasticity and demand dr prabha 17.8.11

8/3/2019 Elasticity and Demand Dr Prabha 17.8.11

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Elasticity andElasticity and

DemandDemand

Dr Prabha Bhola, IIT KGP, Managerial


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Elasticity of Demand

A general definition:

Elasticity is a (standard)measure of the degree of sensitivity( or responsiveness) of one variableto changes in another variable

Usespercentage changes - unit freeFour demand elasticities price, income, cross, promotional



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The % change in quantitydemanded, divided by the %change in price.

Price Elasticity ofDemand (E)

% QE % P

=

P& Q are inversely related by the law

of demand soEis always negativeThe larger the absolute value ofE, the

more sensitive buyers are to a change inprice



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Demand ElasticityElastic Demand When % Change in Quantity

Demanded > % Change in Price

Unit Elastic Demand When % Change inQuantity Demanded = % Change in Price

Inelastic Demand When % Change inQuantity Demanded < % Change in Price

Perfectly Elastic Demand When QuantityDemanded Changes by a very large percentage

in response to an almost zero Change in PricePerfectly Inelastic Demand When the

Quantity Demanded remains constant as Pricechanges



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The elasticity of perfectly elasticdemand curve is infinity

Perfectly Elastic DemandCurve

Quantity

D

14

8

6

4

2

10 15 20 25 305

12

10



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Perfectly InelasticDemand Curve

Quantity

D

30

25

20

15

10

5

5 10 15 20 25

The elasticity of perfectly inelasticdemand curve is zero



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Elasticity Responsiveness EElastic

UnitaryElastic

Inelastic

Price Elasticity ofDemand (E)

% Q % P > % Q % P =

% Q % P

1E =1

E

% Q % P = % Q % P


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Significance of Price

Elasticity of Demand


Profit maximization requires that

business set a price that willmaximize the firms profit

Elasticity tells the firm how muchcontrol it has over using price toraise profit


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Factors Affecting Price

Elasticity of DemandAvailability of substitutesThe better & more numerous the

substitutes for a good, the more elastic is

demand

Percentage of consumers budgetThe greater the percentage of the

consumers budget spent on the good, the

more elastic is demand

Time period of adjustmentThe longer the time period consumers

have to adjust to price changes, the more

elastic is demand Dr Prabha Bhola, IIT KGP, Managerial


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Calculating Price Elasticityof Demand

Price elasticity can be calculatedby multiplying the slope of demand(Q/P) times the ratio of price to

quantity (P/Q)

% QE

% P

=

Q

Q

PP

=

100

100

Q P

P Q

=



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Price elasticity can be measured either:Interval (or arc) elasticity: calculated over

an interval (or arc) of a demand curve.

Point elasticity: calculated at a specificpoint on the demand curve rather than overan interval.

Multiply the slope of demand (Q/P),computed at the point of measure, times theratio P/Q, using the values of P and Q at thepoint of measure.

Method of measuring point elasticity dependson whether demand is linear or curvilinear.


Q PE

P Q

=

Average

Average



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Point Elasticity when Demand isLinear


R

R,

Q a bP cM dP

M P

= + + +Given , let income &

price of the related good take specific

values and respectively

R

Q a' bP

a' a cM dP b Q P

= +

= + +=

Then express demand as , where

and the slope parameteris



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Point Elasticity when Demand is Linear

Compute elasticity using either of thetwo formulas below which give the same

value forE P PE b E

Q P A= =

or

Where and are values of price and quantity demandedat the point of measure along demand, andis the price-intercept of demand

P QA ( a'/ b )=



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Point elasticity when Demand isCurvilinear


Compute elasticity using either of twoequivalent formulas below

Q P PEP Q P A

= =

Where is the slope of the curved demand at

the point of measure, and are values of price andquantity demanded at the point of measur e, and isthe price-intercept of the tangent line extende

Q P

P QA

d tocross the price-axis



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If the price change is relatively small, apoint calculation is suitable

If the price change spans a sizable arcalong the demand curve, the interval

calculation provides a better measure


l i i (G ll )


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Elasticity (Generally)Varies Along a Demand

CurveFor linear demand, price and Evary

directly

The higher the price, the more elasticis demand

The lower the price, the less elastic isdemand

For curvilinear demand, no generalrule about the relation between price

and quantity

Special case of which has a constantprice elasticity (equal to ) for all prices

bQ aP

b

=Special case of which has a constantprice elasticity (equal to ) for all prices

bQ aP

b

=



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Slope ofthe

lineardemandcurve isconstan

t butelasticity varies

Elasticity of Straight LineDemand Curve

Quantity

D

11

10

9

8

7

6

5

4

3

2

1

0

Very elastic

e = 6.33

Slightly elastic

Unit elastic

Slightly inelastic

Veryinelastic

e = .29

e =1.0

0 1 2 3 4 5 6 7 8 9 10 11



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Constant Elasticity ofDemand


Demand Function:Q = aPb

EU = P / (P - A)

= 20 / (20-33.33)

= -1.5

EV = P / (P - A)

= 40 / (40-66.67)

= -1.5


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Marginal Revenue,Demand & Price Elasticity

Marginal revenue (MR) is thechange in total revenue per unit

change in output

SinceMR measures the rate ofchange in total revenue as quantity

changes,MR is the slope of the totalrevenue (TR) curve

TRMR

Q

=



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Marginal Revenue andDemand

Unit sales (Q) Price TR = P Q MR = TR/Q

0 $4.50 $ 0 --

1 4.00 4.00 $ 4.00

2 3.50 7.00 3.00

3 3.10 9.30 2.30

4 2.80 11.20 1.90

5 2.40 12.00 0.80

6 2.00 12.00 0

7 1.50 10.50 -1.50


MR < P for allbut the 1stunit soldbecauseprice must

be loweredinorder tosell moreunits.

Inframarginal

units: units ofoutput thatcould havebeen sold ata higher

price had afirm not

MR = Price Revenue lost bylowering

price on theinframarginal units


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Demand, MR and TR

Panel A Panel B



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Demand and MarginalRevenue

When inverse demand is linear,P =A + BQ

Marginal revenue is also linear,intersects the vertical (price) axis atthe same point as demand, & is twiceas steep as the inverse demand

function.

The equation of the linear marginalcurve is:

MR = A + 2BQ Dr Prabha Bhola, IIT KGP, Managerial

Linear Demand MR &


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Linear Demand, MR, &Elasticity

Q = 120

2P



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MR, TR & Price Elasticityof Demand

Marginalrevenue

Total revenue Price elasticityof demand

MR> 0 TR increases as Q

increases

Elastic (E> 1)

MR = 0 TR is maximized Unit elastic (E=1)

MR < 0 TR decreases as Qincreases

Inelastic (E< 1)

Unit Elastic

(E= 1)

Inelastic

(E< 1)

Elastic

(E> 1)



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Marginal Revenue & PriceElasticity

For all demand & marginal revenuecurves, the relation betweenmarginal revenue, price, &

elasticity can be expressed as:

11

MR P E

= +



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Income Elasticity

Income elasticity (EM):A measure ofthe responsiveness of quantitydemanded to changes in income,

holding all other variables in thegeneralized function constant. Positive for a normal good

Negative for an inferior good

d d

M

d

% Q Q ME% M M Q

= =



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Cross-Price Elasticity

Cross-price elasticity (EXR):A measure

of the responsiveness of quantity

demanded (of goodX) to changes in the

price of related good (R), when all othervariables in the generalized demandfunction remain constant. Positive when the two goods are substitutes

Negative when the two goods arecomplements X X Y

XY

Y Y X

% Q Q P E

% P P Q

= =



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Interval ElasticityMeasures

To calculate interval measures ofincome & cross-price elasticities, thefollowing formulas can be employed

M

Q ME

M Q=

Average

Average

R

XR

R

PQEP Q

=

AverageAverage



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Point Elasticity Measures

X X YQ a bP cM dP ,= + + +

For the linear demand function

point

measures of income & cross-price

elasticities can be calculated as

M

ME c

Q=

R

XR

PE d

Q=



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Promotional Elasticity ofDemand

Purpose Product Differentiation(Branding)

To make the demand for a

product greater


It measures the responsiveness ofdemand to the advertisementexpenditure of the firm

E = % change in the demand for X

% change in the ad. exp. on X


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Determining the level of outputand prices

Helpful in price discriminationFixation of rewards for factors of

production

Determining Govt. policiesHelpful in international trade

Helps in demand forecasting

Importance of Elasticity

elasticity and demand dr prabha 17.8.11

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