ch 6 demand elasticity

8/8/2019 Ch 6 Demand Elasticity

1/20

Demand Elasticity

Measuring Buyer Responsiveness

to Changes in Demand

Determinants


2/20

Objectives of Discussion

Review the concept ofdemand elasticity

Discuss the factors that affect a firms demand

elasticity

Illustrate calculation of demand elasticity

Illustrate the relationship between demand

elasticity & a firms Total Revenue & Marginal

Revenue

Review the other frequently used elasticity

indices--Income Elasticity & Cross Elasticity


3/20

Measuring Responsiveness of Demand

Elasticity provides a means forcomparing responsiveness of demandof a given product:

To changes in one of its DemandDeterminants

To responsiveness of other products tochanges in theirDemand Determinants

Between different groups of consumers

At different points in time


4/20

Price Elasticity of Demand (E)

Index measuring buyers responsiveness to changesin own-price of a good

Needs to be independent of the base volume andscale ofmeasurement of the good

Ratio of the %( Q to % (P provides such an index

Eis always negative because of Law of Demand

Eis calculated for price changes along a given demand

curve--all other demand determinants are constant


5/20

Price Elasticity of Demand (E)

Elasticity Responsiveness E

Elastic

Unitary Elastic

Inelastic

% Q % P ( " (

% Q % P ( ! (

% Q % P ( (

E " 1

E 1

E 1

|E| ranges from 0 to g


6/20

Price Elasticity Examples

Elastic Demand:

(P = -10% and %(Qresponds by +15%

Inelastic Demand:


Unitary elastic


Question: IfE= -1.6, what(P is needed to increasesales by 20%?

Question: IfE= -0.6 whateffect will a +10%(P have onQd?

5.1%10

%15 !

!E

5.010

5!

!E

0.1%10

%10 !

!E

%5.126.1

%20%% !

!(

!(E

QP d

%606.

%10%% !

!!E

PQd


7/20

Factors Affecting Demand

Elasticity Availability of substitutes:

Number and closeness of substitutes--more and closer means greater

elasticity

A related factor is how widely, or narrowly, a market is defined:

Demand for travel is much more inelastic than demand for train travel

Demand for a product is more elastic at the firm level than the industry level

Percent of consumers budget spent on item

The smaller the percent, the more inelastic

Nature of the good

Demand for necessities tends to be more inelastic than non-necessities

Demand for durable goods tends to be more elastic than for non-

durable

Length of time period over which elasticity is measured

Demand is more inelastic in short run than long-run


8/20

Calculating Price Elasticity of Demand

If the price change isrelatively small, apoint calculation issuitable

If the price changespans a sizable arcalong the demandcurve, the intervalcalculation provides abetter measure

Q PE

P Q

(! v

(

Average

Average

Q

P

P

QE y

(

(!


9/20

Calculating Elasticity at a Point

First requirement is to determine the slope of the

demand curve at the point in question

For linear demand curve, slope is a negative constant

For non-linear demand curve, slope is found by finding slope

of tangent to demand curve at point in question

Point Elasticity Formula:

Where (Q/ (P is the slope of the demand function

With some algebraic manipulation can show that:

)/ ( aPPE !

Where a is intercept of inverse direct demand curve on price axis

Q

P

P

Q

PP

QQ

E y(

(!

(

(

!


10/20

Elasticity (Generally) Varies Along a

Demand Curve

For linear demand, price and Evary directly The higher the price, the more elastic is demand

The lower the price, the less elastic is demand

For curvilinear demand,

slope changes at each point on demand curve

no general rule about the relation between price and

elasticity

Exception to rule:

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

bQ aP

b

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

bQ aP

b

!y


11/20

Constant Elasticity of Demand(Figure 6.3)


12/20

Price Elasticity & Total Revenue (TR)

TR = P x Q

Price and quantity move in opposite directions on a

demand curve

Move on demand curve has a price effect & an

opposing quantity effect

price effect is effect on TR from a price change holding Q

fixed

quantity effect is effect on TR from a quantity change

holding P fixed

Impact on TR depends on two things:

Which effect is stronger

The direction of the movement on the demand curve (i.e. P

increase vs P decrease)


13/20

Price Elasticity & Total Revenue

Elastic

Quantity-effect

dominates

Unitary elastic

No dominant effect

Inelastic

Price-effect dominates

Pricerises

Pricefalls

TR

lls

TR ris s

N g i TR

N g i TR

TR ris s

TR lls

% Q % P ( " ( % Q % P ( ! ( % Q % P ( (


14/20

TR, MR & the Demand Curve

TR = P x Q

Linear demand curve: P = a + bQ

Substituting in TR forP

TR = (a + bQ)Q = aQ + bQ2

MR is change in TR from selling one more unit ofQ

Using some simple calculus we can show that:

bQa

d

d2

Q

(TR)MR !!

From above we can see that MR has same intercept on price axis as the

demand curve and is twice as steep

@ we can show that when MR = 0, Q is at one-half the amount that it

attains when P = 0 on the demand curve


15/20

Linear Demand, MR, & Elasticity(Figure 6.5)

Inverse D: P = 6 - .05Q

MR= 6 - .10Q

TR= PxQ= (6 - .05Q)xQ=6Q- .05Q2

Q=40: TR= 160

Q=60: TR= 180

Q=65: TR= 178.75

160


16/20

MR, TR, & Price Elasticity

Marginal

revenue Total revenuePrice elasticity of

demand

MR > 0 Elastic (E>

1)

MR = 0 Unit elastic (E=1)

MR < 0 Inelastic (E 1)

TR decreases asQ increases(Pdecreases)

TR is maximized

TR increases

as Q increases(Pdecreases)


17/20

MR & Price Elasticity

Saw earlier that the effect on TR of a price change depends on

size of price elasticity coefficient, E

Recalling that MR is change in TR associated with unit changes

in output, we can express this as:

dQ

dPQ

dQ

dQP yy!MR

dQQPd

dQTRdMR )()(

y

!!

Using the product rule for derivatives, we can show:

Manipulating some of the terms in the above expression we can show:

Definition of price

elasticity

1dQ

dP

P

QPMR y! )

11(

Q

P

dP

dQP

y

! )1

1(E

P !


18/20

Price Elasticity & MR

Since E is always negative, we can express the

above as:

)1

1(MRE

P !

)

1

1(MR EP!

From the above we can see that:

when E> 1, the term in ..) will be positive so MR will bepositive for each unit increase in quantity

when E< 1, the term in ..) will be negative so MR will benegative for each unit increase in quantity

when E= 1, the term in ..) will be zero, so MR will also be 0

Since MR is the change in TR associated with a change in Q, the effects

of elasticity on TR follow from the above


19/20

Income Elasticity

Income elasticity is measured as ratio of % change in Q to

% change in income, holding all other demand

determinants fixedparibusceteris

%

%

M

QE

M

(

(!

EM is positive for most commodities--i.e. normal goods

j EM is smaller for necessities than for non-necessities

y EM

is negative for goods that are considered relatively

inferior in consumption

y EM can be calculated using either an arc approach or a

point approach


20/20

Cross Elasticity

Cross elasticity is measured as ratio of % change in Q to

% change in price of some other good, holding all other

demand determinants fixed

paribusceteris%

%

B

A

X

P

Q

E (

(

!

Primary use of EX is to measure closeness of substitutes

and complements

EX is positive for substitute commodities

EX is negative for complements

ch 6 demand elasticity

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