Download Price Elasticity of Demand

Chapter 4
Elasticity
Elasticity:
 The
responsiveness of dependent
variable to change in independent
variable
 A measure of the extent to which
quantity demanded and quantity
supplied respond to variations in
price, income, and other factors.
Price Elasticity of Demand
% change in Qd due to 1%
change in P.
 Application: change in price on
 Definition:
– total revenue for sellers
– total expenditure for buyers
– effectiveness of policy in influencing
individual behaviors
Exercise: 4.1, P.99

Known:
– P=$400, Qd=10K;
– P=$380, Qd=12K
Solve for: Ed
 Is D elastic?
 Should P go down from $400 to $380?

Elastic Demand
 |Ed|
> 1: (|Ed| →∞) Elastic
– price changes by 1%, quantity
demanded changes by more than 1%.
– price and total revenue are negatively
related
Inelastic Demand :
 |Ed|
< 1, (|Ed| = 0) Inelastic
– price changes by 1%, quantity
demanded changes by less than 1%
– price and total revenue are positively
related
Unit Elastic Demand
 |Ed|
= 1, Unit Elastic
– price changes by 1%, quantity
demanded also changes by 1%
– total revenue is maximized
Perfectly Elastic and Perfectly
Inelastic Demand Curves
Figure 4.8, P.106
Mid-Point Method

Change in Q = Q2 - Q1
 Change in P = P2 - P1
 E = {(Q2-Q1)/[(Q2+Q1)/2]}
/ {(P2-P1)/[(P2+P1)/2]}
Example:
1998
1999
P
$3.70
$2.72
Qd
1.74B
1.9B
Calculation
Change in Qd = 1.9 – 1.74 = 0.16
 Change in P = 2.72 – 3.70 = - 0.98
 Average Qd = (1.74 + 1.9) / 2 = 1.82
 Average P = (3.70 + 2.72) / 2 = 3.21
 E = (0.16/1.82) / (-0.98/3.21) = - 0.29
 TR1998 = 6.438, TR1999 = 5.168

What does it mean?
Elastic? (Ed = -0.29 absolute value <
1)
 Impact on TR when P decreases
 Possible type of good

Factors Affecting Elasticity of Demand
Substitutability
 Share in budget
 Necessity vs. Luxury
 Time span: short term vs. long term

Price Elasticity of Demand
% change in Qd due to 1%
change in P.
 Formula:
Ed = %ΔQd / %ΔP
= (ΔQd / Qd ) / (ΔP/P)
= (Δ Qd /ΔP) x P/Qd
 Definition:
Slope of D
Initial position
Determinants of Elasticity
Slope of the demand curve at the price
 Position of the point (price level) on the
demand curve

Price Elasticity and the Steepness of the
Demand Curve
Figure 4.5, P.104
Fig. 4.5, P.104

Elasticity affected by both slope and
position
– At (4,4)
• Ed on D1=1/2
• Ed on D2=2
– On D2
• Ed at (4,4) = 2
• Ed at (1, 10) = 1/5
Figure 4.7
Price Elasticity Regions along a Straight-Line
Demand Curve
Conclusions:
For Straight-line Demand Curves:
 Ed at mid-point = 1
– P > Pm  Elastic
– P < Pm  Inelastic

To increase TR
– P > Pm: Lower P  Higher TR
– P < Pm: Higher P  Higher TR
Figure 4.12
Total Expenditure as a Function of Price
Cross-Price Elasticity
 Responsiveness
of demand for one
good to changes in the price of a
related goods.
 Ec = (Δ Qx/ ΔPy) x (Py/Qx)
 Ec > 0, substitutes
 Ec < 0, complements
Income Elasticity of Demand

The responsiveness of demand to changes
in consumer income
 % change in Q divided by % change in Y
 Em = (Δ Q/ ΔY) x (Y/Q)
Income Elasticity of Demand

0 < Em < 1: (Em = 0) Income Inelastic
Income changes by 1%, quantity demanded
changes by less than 1%.
 Em > 1: Income Elastic
Income changes by 1%, quantity demanded
changes by more than 1%.
Income Elasticity of Demand
 Em
= 1: Income Unit Elastic
Income changes by 1%, quantity
demanded changes by 1%.
Categories based on elasticity

Em > 0: Normal goods
– Em > 1: Luxury goods
– Em < 1: Necessity
 Em < 0: Inferior goods
Engel’s Law
with a given set of tastes and
preferences, as income rises, the
proportion of income spent on food falls,
even if actual expenditure on food rises
 the income elasticity of demand of food
is less than 1 (necessity)

Engel’s Coefficient


% change in food expenditure / % change in total
expenditure
% change in food expenditure / % change in income
– EC > 59%: absolutely poverty (绝对贫困);
– 50% < EC <59%: barely enough food and clothing
（温饱）;
– 40% < EC < 50%: moderately well-off （小康）
– 30% <EC < 40%: well-to-do （富足）
– EC < 30%: wealthy （富裕）
Summary: Elasticity of Demand
Price Elasticity
Cross-Price
Elasticity
Income
Elasticity
%ΔQd / %ΔP
%ΔQd(x)/ %ΔP(y)
%ΔQd / %ΔY
Elastic (horizontal) Complements
Inelastic (vertical) Substitutes
Unitary elastic
Luxury/necessity
Substitutability
Normal vs.
inferior
Luxury
vs.necessity
Price Elasticity of Supply
% change in Qs due to 1%
change in P.
 Formula:
Es = %ΔQs / %ΔP
= (ΔQs / Qs ) / (ΔP/P)
= (Δ Qs /ΔP) x P/Qs
 Definition:
Again: slope and position
S’
14
Es at Point A:
On S: (8/2)(1/2)=2
On S’: (14/2)(1/6)=7/6
Es on S:
At A: (8/2)(1/2)=2
At B: (10/3)(1/2)=5/3
Conclusions:
Es declines as Q increases
Es declines faster if slope is steeper
Special Case: fig.4.14, P.113
Es = 1 everywhere
If S is straight and
passes through origin
Special cases:
Perfectly inelastic and Perfectly elastic supply curves
Fig.4.15, P. 113
Fig. 4.16, P.114
Price Elasticity of Supply
> 1: (Es →∞) Elastic
price changes by 1%, quantity supplied
changes by more than 1%.
 Es < 1, (Es = 0) Inelastic
price changes by 1%, quantity supplied
changes by less than 1%
 Es
Unit Elastic Supply
 Es
= 1, Unit Elastic
price changes by 1%, quantity
supplied also changes by 1%
Factors Affecting Elasticity of Supply

Availability of inputs:
– Flexibility; mobility; substitute
 Length of production period
 Difficulty of production
 Technology
Incidence of Excise Tax
Who bears the real burden of tax, the
buyer or the seller?
Effect of an Excise Tax Levied on
the Sales of Taxi Rides
Effect of an Excise Tax Levied on
Purchases of Taxi Rides
The Revenue from an Excise Tax