Chapter 4 Demand Elasticity
KEY CONCEPTS
elasticity
• endogenous variables
• exogenous variables
• point elasticity
• arc elasticity
• price elasticity of demand
• elastic demand
• unitary elasticity
• inelastic demand
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optimal price formula
substitute
complement
cross-price elasticity
income elasticity
normal goods
inferior goods.
counter-cyclical
noncyclical normal goods
cyclical normal goods
OVERVIEW
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Measuring Market Demand
Demand Sensitivity Analysis: Elasticity
Price Elasticity of Demand
Price Elasticity and Marginal Revenue
Price Elasticity and Optimal Pricing
Policy
Cross-price Elasticity of Demand
Income Elasticity
一. General meaning of Elasticity
1.Definetion
Elasticity: the responsiveness of
dependent variable to a given change
in one of its determinants.
• Y=f(x1,x2,x3……xn)
2. calculation
Point elasticity reflects sensitivity of
Y to small changes in X,
Ex = ∂Y/Y ÷ ∂X/X
•
Arc elasticity reflects sensitivity of Y
to big changes in X,
EX = (Y2–Y1)/(Y2+Y1) ÷ (X2-X1)/(X2+X1).
3. types of elasticity
二. Price Elasticity of Demand
1.Definetion:
the responsiveness of Qd to a given change in
the price of that good.
εP =%△Qd/ %△P
εP < 0
Price elasticity of demand =
% change in quantity demanded
% change in price
2.Formula
– Point price elasticity,
εP = ∂Q/Q ÷ ∂P/P.
Price elasticity of dem and =
(Q 2 - Q 1 ) / [(Q 1 + Q 2 ) / 2]
(P 2 - P 1 ) / [(P 1 + P 2 ) / 2]
_ ARC elasticity of D
P
Qd TR
Ed
conclusion
9
15
?Fill the blanks
7
5
25
35
?Draw the D
curve
3
45
3.Classification of εP with Graphs
1. │εP│> 1, D is elastic.
2. │εP│< 1, D is inelastic.
3. │εP│= 1, D is unit elastic
4. │εP│= 0, D is perfectly inelastic.
5. │εP│= ∞, D is perfectly elastic
4. The εP of a linear D curve:
Ⅰ：At upper part of the D curve, │εP│>
1.
.
Ⅱ：At lower part of the D curve, │εP│<
1.
Ⅲ：At mid point of the D curve, │εP│=
1.
三. Price Elasticity and TR
TR= P*Q
?? How to increase TR by changing price?
if │εP│> 1.
if │εP│= 1.
if │εP│< 1.
if │εP│= 0
if │εP│= ∞
四.Price Elasticity and MR
If Qd=6-P
??Demand curve
?? Total revenue curve
?? P= 2,3,5 elasticity=?
??Relation between elasticity and MR
– MR > 0 if │εP│> 1.
– MR = 0 if │εP│= 1.
– MR < 0 if │εP│< 1.
五.Price Elasticity and Optimal
Pricing Policy P87
1. Optimal Price Formula
MR = P/[1+(1/ εP)].
Optimal P* = MC/[1+(1/ εP)].
• 2.Optimal Pricing Policy Example
• 六.Determinants of Price Elasticity
– Essential goods have low│εP│.
– Nonessential goods have high│εP│.
1.The number and closeness of substitutes.
2.Definition of the market
Example: beef and meat.
3.Luxury versus necessity
Necessities: poor substitutes
Luxuries: many substitutes
4.Proportion of income spent on that good
5.The time period.
Example: SR │εP│for gasoline = 0.2;
LR│εP│ =0.7
│εP│
Good or
service
for selected goods
│εP│
Electricity 0.13
(household)
Clothing
0.49
Motor
1.14
vehicles
Medical
0.31
care
Eggs
0.32
Good or
service
│εP│
Telephone
service
Gasoline
0.26
Beef
1.27
0.60
Restaurant 2.27
meal
Milk
0.63
Applications of price elasticity of D
1. Bumper crops
Can Good News for Farming Be Bad News
for Farmers?
(Ed for farm products is between 0.2—
0.25)
2.Eexcise taxes
What goods should be taxed?
3.Decriminalization of drug dealing
Proponents: Ed ﹤1
Opponents: Ed﹤1 for addicts;
Ed﹥1 for dabbler
七.Cross-price Elasticity of Demand
Definition: demand sensitivity to
changes in other prices.
– εPX = ∂QY/QY ÷ ∂PX/PX.
• Substitutes have εPX > 0.
• Complements have εPX > 0.
• Independent goods have εPX > 0.
• Cross-price Elasticity Example
八. Income Elasticity
Definition:
Income elasticity shows demand
sensitivity to changes in income.
εI = ∂Q/Q ÷ ∂I/I.
Types of Goods:
Normal goods:εI > 0.
Inferior goods:εI < 0.
• Types of Normal Goods
– Noncyclical goods: 0 < εI < 1.
– Cyclical goods: εI > 1.