elasticity (baye)

7/31/2019 Elasticity (Baye)

1/29

Michael R. Baye, Managerial Economics and Business Strategy , 6e. The McGraw-Hill Companies, Inc., 2008

Managerial Economics & Business Strategy

Chapter 3Quantitative Demand Analysis


2/29


The Elasticity Concept

How responsive is variable G to a changein variable S

If E G,S > 0, then S and G are directly related.If E G,S < 0, then S and G are inversely related.

S G E S G

=

%%,

If E G,S = 0, then S and G are unrelated.


3/29


The Elasticity Concept UsingCalculus

An alternative way to measure the elasticityof a function G = f(S) is

GS

dS dG E S G =,

If E G,S > 0, then S and G are directly related.If E G,S < 0, then S and G are inversely related.

If E G,S = 0, then S and G are unrelated.


4/29


Own Price Elasticity of Demand

Negative according to the law of demand.

Elastic:

Inelastic:

Unitary:

X

d X

PQ PQ

E X X

=

%%

,

1, > X X PQ E

1, < X X PQ E

1, = X X PQ E


5/29


Perfectly Elastic &Inelastic Demand

)(ElasticPerfectly , = X X PQ E

D

Price

Quantity

D

Price

Quantity

)0, = X X PQ E (InelasticPerfectly


6/29


Own-Price Elasticityand Total Revenue

ElasticQ Increase (a decrease) in price leads to a decrease (an

increase) in total revenue.

InelasticQ Increase (a decrease) in price leads to an increase (a

decrease) in total revenue.

UnitaryQ Total revenue is maximized at the point where demand

is unitary elastic.


7/29


Elasticity, Total Revenue and LinearDemand

QQ

P TR100

0 010 20 30 40 50


8/29



QQ

P TR100

0 10 20 30 40 50

80

800

0 10 20 30 40 50


9/29



QQ

P TR100

80

800

60 1200

0 10 20 30 40 500 10 20 30 40 50


10/29



QQ

P TR100

80

800

60 1200

40

0 10 20 30 40 500 10 20 30 40 50


11/29



QQ

P TR100

80

800

60 1200

40

20

0 10 20 30 40 500 10 20 30 40 50


12/29



QQ

P TR100

80

800

60 1200

40

20

Elastic

Elastic

0 10 20 30 40 500 10 20 30 40 50


13/29



QQ

P TR100

80

800

60 1200

40

20

Inelastic

Elastic

Elastic Inelastic

0 10 20 30 40 500 10 20 30 40 50


14/29



QQ

P TR100

80

800

60 1200

40

20

Inelastic

Elastic

Elastic Inelastic

0 10 20 30 40 500 10 20 30 40 50

Unit elasticUnit elastic


15/29


Demand, Marginal Revenue (MR)and Elasticity

For a linear inversedemand function,MR(Q) = a + 2bQ,where b < 0.

WhenQ MR > 0, demand is

elastic;Q MR = 0, demand is unit

elastic;Q MR < 0, demand is

inelastic.Q

P100

80

6040

20

Inelastic

Elastic

0 10 20 40 50

Unit elastic

MR


16/29


Factors AffectingOwn Price Elasticity

Q Available Substitutes The more substitutes available for the good, the more elastic

the demand.Q Time

Demand tends to be more inelastic in the short term than in

the long term. Time allows consumers to seek out available substitutes.

Q Expenditure Share Goods that comprise a small share of consumers budgets

tend to be more inelastic than goods for which consumersspend a large portion of their incomes.


17/29


Cross Price Elasticity of Demand

If E Q X ,P Y > 0, then X and Y are substitutes.

If E Q X ,P Y < 0, then X and Y are complements.

Y

d X

PQ PQ

E Y X

=

%%

,


18/29


Income Elasticity

If E Q X ,M > 0, then X is a normal good.

If E Q X ,M < 0, then X is a inferior good.

M Q

E d

X M Q X

=

%%

,


19/29


Uses of Elasticities

Pricing. Managing cash flows. Impact of changes in competitors prices. Impact of economic booms and recessions. Impact of advertising campaigns. And lots more!


20/29


Example 1: Pricing and CashFlows

According to an FTC Report by MichaelWard, AT&Ts own price elasticity of demand for long distance services is -8.64.

AT&T needs to boost revenues in order tomeet its marketing goals.

To accomplish this goal, should AT&Traise or lower its price?


21/29


Answer: Lower price!

Since demand is elastic, a reduction in pricewill increase quantity demanded by agreater percentage than the price decline,resulting in more revenues for AT&T.


22/29


Example 2: Quantifying theChange

If AT&T lowered price by 3 percent, whatwould happen to the volume of longdistance telephone calls routed through

AT&T?


23/29


Answer

Calls would increase by 25.92 percent!

( )%92.25%%64.8%3

%3%64.8

%%64.8,

=

=

=

==

d X

d X

d X

X

d

X PQ

QQ

Q

PQ E

X X


24/29


Example 3: Impact of a changein a competitors price

According to an FTC Report by MichaelWard, AT&Ts cross price elasticity of demand for long distance services is 9.06.

If competitors reduced their prices by 4percent, what would happen to the demandfor AT&T services?


25/29


Answer AT&Ts demand would fall by 36.24 percent!

%24.36%%06.9%4

%4%06.9

%%06.9,

=

=

=

==

d X

d X

d X

Y

d X PQ

QQ

Q

PQ E

Y X


26/29


Interpreting Demand Functions Mathematical representations of demand curves.

Example:

Q Law of demand holds (coefficient of P X is negative).Q X and Y are substitutes (coefficient of P Y is positive).Q

X is an inferior good (coefficient of M is negative).

M PPQ Y X d

X 23210 +=


27/29


Linear Demand Functions andElasticities

General Linear Demand Function and Elasticities:

H M PPQ H M Y Y X X d

X ++++=

0

Own PriceElasticity

Cross PriceElasticity

IncomeElasticity

X

X X PQ

Q

P E

X X =

,

X

M M Q Q M

E X

=,

X

Y Y PQ Q

P E

Y X =

,


28/29


Example of Linear Demand

Qd

= 10 - 2P. Own-Price Elasticity: (-2)P/Q. If P=1, Q=8 (since 10 - 2 = 8). Own price elasticity at P=1, Q=8:

(-2)(1)/8= - 0.25.


29/29


Conclusion Elasticities are tools you can use to quantify

the impact of changes in prices, income, andadvertising on sales and revenues. Given market or survey data, regression

analysis can be used to estimate:Q Demand functions.Q Elasticities.Q A host of other things, including cost functions.

Managers can quantify the impact of changes in prices, income, advertising, etc.

elasticity (baye)

Documents