chapter 6 elasticities of demand

© Pilot Publishing Company Ltd. 2005

Chapter 6 Elasticities of Demand


• Elasticity of Demand• Classification of Elasticities of Demand• Price Elasticity of Demand• Price Elasticity & Demand Curve • Price Elasticity of Demand, Total Revenue & Total Expenditure • Income Elasticity of Demand• Cross Elasticity of Demand

Contents:


• Advanced Material 6.1: Price Consumption Curve and Price Elasticity• Advanced Material 6.2: Income Consumption Curve and Income Elasticity

Contents:


Elasticity of Demand


Elasticity of demand (需求彈性 , Ed)

• is a measure of the responsiveness of the quantity demanded of a good to a change in an exogenous variable.

Elasticity of demand

• % change in X_________ % change in exogenous variable

Why?


Classification of

Elasticities of Demand


Type of elasticity of demand

Exogenous variable concerned

Price elasticity of demand

(價格需求彈性 , pEd)

Income elasticity of demand

(所得需求彈性 , iEd)

Cross elasticity of demand

(交叉需求彈性 , cEd)

Classification according to the exogenous variable concerned

Price of the good

Income

Price of related good


Classification according to the formula adopted in calculation

Point elasticity of demand

% Δ= X2 – X1 x 100%

X1

Situations applied: when the % change are _________

Arc elasticity of demand

% Δ= X2 – X1 x 100%

(X1+ X2)/2Situations applied: when the % change are _________

very small

significant


vertical

Classification according to the size of the elasticity

• Perfectly inelastic (Ed = 0)

• The exogenous variable changes but X remains unchanged

i.e. % Δ in X =_______.

• In the case of price elasticity,

the demand curve is _________.

D0

vertical

Px

X0



2. Inelastic (Ed < 1) % in X ____ % in exogenous variable

3. Unitarily elastic (Ed = 1) % in X ____ % in exogenous variable

4. Elastic (Ed > 1) % in X ____ % in exogenous variable


horizontal

D


5. Perfectly elastic (Ed = infinity)

• A negligible change in the exogenous variable brings an infinite change in Qd

i.e. % Δ in X =_________.

• In the case of price elasticity,

the demand curve is ___________.

infinity

horizontal

Px

X0


Price Elasticity of Demand


What is price elasticity?

Price elasticity of demand (價格需求彈性 , pEd) is equal to the percentage change in quantity demanded of a good divided by the percentage change in its own price.

good the of price in %

demanded quantity in %Edp


What is price elasticity? (Con’t)

According to the first law of demand, pEd is ________.negative

positive

However, if Giffen good existed, its pEd would be ________.


ΔPx

ΔXX

X1

P1

0

C

B

A

Px

DC

Point elasticity of demand -- on a linear demand curve (DC)

1

1

X X

P

P

X

1

1

X X

P

P

X

Mathematical measure:

pEd at point A:

Graphical measure:

OX

BX

CP

OP

AC

AB

1

1

1

1 OX

BX

CP

OP

AC

AB

1

1

1

1


ΔPx

ΔX

Point elasticity of demand – on a non-linear DC

XX1

P1

0

C

B

A

Px

DC

1

1

X X

P

P

X

1

1

X X

P

P

X


pEd at point A:

Graphical measure:

OX

BX

CP

OP

AC

AB

1

1

1

1 OX

BX

CP

OP

AC

AB

1

1

1

1


Price Elasticity Price Elasticity &&

Demand Curve Demand Curve


X0

Px

Demand curve

M (mid-point): |pEd|= 1 (unitarily elastic)

|pEd| > 1 (elastic)

|pEd| < 1 (inelastic)

Point elasticity of demand -- on a linear DC


AD

d1 d2 XO

Px

B

C

P

E

pEd at point A on d1 =BAAC

=OPPC

EDDC

=

= pEd at point D on d2

Price elasticity at points on different DCs• If two linear DCs have the same y-intercept

they will have the same pEd at every price.


pEd at point A on d1 (with a smaller y-intercept)

=OPPF

EDDF

= pEd at point D on d2 (with a larger y-

intercept)

>

Price elasticity at points on different DCs

A D

XO

Px

B

C

P

Ed1

d2

F OPPC

=BAAC

=If 2 linear DCs have different y-intercepts

The curve with a smaller y-intercept will have a larger price elasticity than the curve with a larger y-intercept at every price.


D (on d2)

XO

Px

A on (d1)

B

C

P

E

F

d1 d2

pEd at point A on a d1 (with a larger slope)

OPPF

EDDF

=

= pEd at point D on d2

(with a smaller slope)

<

Price elasticity of points on different DCs

OPPC

=BAAC

=If 2 linear DCs intersect,

the one with a gentler slope will have a larger price elasticity at the intersection point.


Price Elasticity of Demand, Total Revenue &

Total Expenditure


Total expenditure paid by a consumer

= Price x Quantity transacted (or P x Q)

= Total revenue received by a producer

Price elasticity, total expenditure (TE) and total revenue (TR)


Change in TE and TR

When demand or supply changes, price & quantity transacted vary.

Subsequently, total expenditure & total revenue are affected.


D2

P2

X2

in TRin TR in TRin TR

Increase in demand

D P & Q TR

Px

XD1

S1

P1

X10


D2

P2

X2

Decrease in demand

D P & Q TR Px

X

D1

S1

P1

X10

in TRin TR in TRin TR


Increase in supply

P but X

Δ in TR depends onthe relative % Δ inP & Q, i.e., the pEd.

X

S2

Px

D

S1

P1

X1

P2

X20


S2

a. Demand is elastic

P2

X2

When supply increases, if demand is elastic,

• %in X % in P

• TR

Px

XD

S1

P1

M

in TR

in TR

X10


S2

b. Demand is unitarily elastic

%in X %in P

TR remains constant

in TR

in TRP2

X2

Px

XD

S1

P1

M

X1

0


S2

c. Demand is inelastic

%in X % in P

TR

Px

XD

S1

P1

M

in TR

in TR

X1

P2

X20


P but X

Decrease in supply

Px

XD

S1

S2

P2

P1

X1X20

Δ in TR depends onthe relative % Δ in P & Q, i.e., the pEd


S2

a. Demand is elastic

When supply decreases, if demand is elastic,

• % in X % in P

• Δ in TR

Px

X

D

S1

P2

X2

P1

M

X1

in TR

in TR


S2

b. Demand is unitarily elastic

% in X = % in P

TR remains constant Px

XD

S1

P1

M

in TR

in TR X1

P2

X2


S2

c. Demand is inelastic

%in X % in P

Δin TR

P2

X2

D

M

Px

X

S1

P1

X1

in TR

in TR


Q6.6:

(a) If the demand is inelastic, to increase the TR, should a producer raise the price or should he cut the price?

(b) After raising the price of a good, a producer finds that the total revenue falls. What is the reason?


Unit elasticity and total revenue

% Δ in X = % Δ in P

TR remains constant despite a change in P or Q.

If one spends the whole amount (or a fixed amount) of his income on a good no matter what its price is, its pEd must be equal to / greater than /smaller than one.

For a unitarily elastic demand:

equal to


Xx


1. Number of close substitutes:

more close substitutes

more elastic demand.

Factors affecting price elasticity

Why?

Why?

2. Degree of necessity:

necessities & habit-forming goods

less elastic demand.


3. Number of possible uses:

more different uses more elastic demand.

Factors affecting price elasticity (Con’t)

Why?

4. Durability:

more durable more elastic demand.

5. Proportion of income spent:

a larger proportion of one’s expenditure

more elastic demand.

Why?

Why?


6. Time of adjustment:

longer time for adjustment more elastic demand

(Second law of demand)

Shift of DC as time passes

Px

X

P0

P1

X0 X3X2X1 X40

Why?


Q6.7:

The demand for salt is inelastic. List all possible reasons.


Income Elasticity of Demand


Income elasticity of demand (所得需求彈性 , iEd) is equal to the percentage change in quantity demanded divided by the percentage change in income.

incomein %

demandedquantity in %Edi

What is income elasticity?


Superior good X is _________ related to income. iEd is ________.

luxuries necessities

positive

(Options: positive / negative / luxuries / necessities / positively / negatively )

iEd 1

iEd 1

positively


Inferior good

X is _________ related to income.

iEd is __________.negative

(Options: positive / negative / luxuries / necessities positively / negatively)

negatively


X

II1

X1

C 0

B

A ΔX

Δ I

Good X is an inferior good

Graphical measure:


CI

OI

OX

BX

AC

AB

1

1

1

1di A point at E

1

1

X

I

I

X

X

II1

X1

C0

B

A ΔXΔ I

Good X is a superior good


Cross Elasticity of Demand


Cross elasticity of demand (交叉需求彈性 , cEd) is equal to the percentage change in quantity demanded of a good (e.g., good X) divided by the percentage change in price of another good (e.g., good Y).

Y good of pricein %

X good of demandedquantity in % Edc

What is cross elasticity?


The cross elasticity of substitutes is positive, why?

The cross elasticity of complements is negative, why?

Cross elasticity of demand

when PY Y and X (substitute of Y) thus, PY and X are positively related.

when PY Y and X (complement of Y) thus, PY and X are negatively related.


•Graphical measure:

•Mathematical measure:1

1

X

P

P

X Y

Y

PY

X

C

0B

A

ΔX

ΔPY

X1

PY1

Good X and good Y are substitutes

PY

X

C

0 B

A

ΔX

ΔPY

X1

PY1

Good X and good Y are complements

CP

OP

OX

BX

AC

AB

Y

Y

1

1

1

1dc A point at E


Q6.9:

For each of the following commodities, suggest a good with a positive cross elasticity and a good with a negative cross elasticity related to the commodity.

Shoes Pencil Broom Camera Map


Advanced Material 6.1:Price elasticity and price consumption curve

As income remains unchanged and the expenditure ongood Y , the expenditure on good X must __________.

As the expenditure on good X (when Px and X ),the % in X must be ___________ the % in PX.

So, the demand for good X must be the demand for good X must be _______.

If PCC is _upward sloping_, when Px, both the consumption of good X and good Y __________.

PCCY

X0

increase

decrease

smaller than

inelastic


Shape of PCC

Consumption and

expenditure on Y

Expenditure on X

(= I - PY Y)

Relative size

of % Δ in

X () and P

x ()

Price elasticity

of demand for X

Upward sloping %in X

%in Px

Horizontal Unchanged Unchanged

%in X

% in Px

Downward sloping

%in X

% in Px

< Inelastic

>

=

Elastic

Unitarily elastic


Price elasticity and price consumption curve

• Graphical measure:

PCC (|pEd|<1)

Y

X0

PCC (|pEd|=1)

Y

X0

PCC (|pEd|>1)

Y

X0


ICC1

ICC2

ICC5

ICC4

ICC3

Shape of ICC

iEd of X

iEd of Y

ICC1

ICC2

ICC3

ICC4

ICC5

Y

XI1 I3I20

Advanced Material 6.2:Income elasticity and income consumption curve

+ve-ve

+ve0

+ve+ve

0+ve

-ve+ve


Correcting Misconceptions:

1. The gentler the slope of a demand curve, the larger its price elasticity.

2. A price rise must raise the total revenue.

3. If one spends a fixed amount of his income on a good, his demand for the good is perfectly inelastic.

4. It is impossible for all the goods consumed to be luxuries, because one must consume some necessities.


Survival Kit in Exam

Question 6.1:

After a rise in the price of coffee,

what will happen to the total revenues of

(a) coffee,

(b) sugar and

(c) tea respectively?

chapter 6 elasticities of demand

Documents

iedcross elasticity

arc elasticity of demand

larger price elasticity

d2 price elasticity

case of price elasticity

elasticity of demandelasticity

law of demand

price consumption curve