Download Unit 7 - Elasticities of Demand

Unit 7
Economics - 6th
year
Price Elasticity of
Demand
Unit 7
Elasticities of Demand
The Expenditure
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Economics - 6th year
EURSC
2007/2008
Contents
Unit 7
Economics - 6th
year
Price Elasticity of
Demand
The Expenditure
Price Elasticity of Demand
The Expenditure
Income Elasticity of Demand
Cross-price Elasticity of Demand
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Price Elasticity of Demand
Definition
Unit 7
Economics - 6th
year
Price Elasticity of
Demand
The Expenditure
I
Price Elasticity: Response in quantity demanded to
changes in price measured in percentage units.
Base Formula
Price Elasticity ≡ ε = −
I
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Percentage change in Q
Percentage change in P
NOTE: The minus sign in front is for having positive
numbers.
Price Elasticity of Demand
Alternative formulae
Using two points of the demand function
You are given (P1 , Q1 ) and (P2 , Q2 ), two points of the
demand function. Say ∆P = P2 − P1 and ∆Q = Q2 − Q1 .
ε=−
∆Q/Q1
∆Q P
=−
∆P/P1
∆P Q
Problem: This formula is not consistent. Sometimes
apply the “mean point” corrected version where
P̄ = (P1 + P2 )/2 and Q̄ = (Q1 + Q2 )/2:
ε=−
∆Q P̄
∆P Q̄
Unit 7
Economics - 6th
year
Price Elasticity of
Demand
The Expenditure
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Price Elasticity of Demand
Unit 7
Economics - 6th
year
Alternative formulae
Price Elasticity of
Demand
Using the math expression of the demand function
The Expenditure
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
dQ P
ε=−
dP Q
An expression for elasticity
It is possible to give a general expression for elasticity,
once we know the demand function. If demand function
mP
is: Q = C − mP then dQ
dP = −m and thus, ε = C−mP or
C
else ε = Q
− 1.
Price Elasticity of Demand
Unit 7
Economics - 6th
year
Type of demand by elasticity
Price Elasticity of
Demand
The Expenditure
Elastic and Inelastic Demand
Perfectly Inelastic
Inelastic
Cross-price
Elasticity of
Demand
Elastic
Perfectly
elastic
0
1
Unitary elasticity
Income Elasticity
of Demand
Price Elasticity of Demand
Graphical Representation
Unit 7
Economics - 6th
year
Price Elasticity of
Demand
The Expenditure
I
Elasticity changes as we move along the demand
function even for a linear demand (fig. 8.2)
I
I
I
I
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In point A: Q = 0 =⇒ ε → ∞
In point C: P = 0 =⇒ ε = 0
In point B: Q = C/2 =⇒ ε = 1
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Elasticity in a linear demand can be also measured
graphically as BC/AB.
Demand curves with constant elasticity (fig. 8.3).
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I
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Demand curve perfectly inelastic: Q = C
Demand curve perfectly elastic: P = P̄
Demand curve with unit elasticity Q = P −ε
Price Elasticity of Demand
Factors affecting elasticity
Unit 7
Economics - 6th
year
Price Elasticity of
Demand
I
The slope of the demand curve (1/m) does not
uniquely determine elasticity (see figure 8.4)
The Expenditure
I
Q = 10 − P and Q = 10 − 2P have the same
elasticity at Q = 5 but second is flatter.
Cross-price
Elasticity of
Demand
I
Always remeber that elasticity is not something
absolute: it changes along the demand curve!!
The demand is more or less elastic if:
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I
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Availability of substitutes: Having closer substitutes
will make the demand reduce for each price and
being flatter (more elastic)
Lapse of time: The longer the period, the more
elastic is the demand of a product.
Income Elasticity
of Demand
The Expenditure
Elasticity affects expenditure
Unit 7
Economics - 6th
year
Price Elasticity of
Demand
The Expenditure
I
Why is important to study elasticity?
I
Elasticity allows one to study the expected effect of
changes in price in total sales revenue.
I
What do you prefer: selling a lot at a cheap price or
selling very little at a high price?
I
The answer depends on the elasticity of the good
you are selling
The Expenditure
Elasticity affects expenditure
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Unit 7
Economics - 6th
year
Price Elasticity of
Demand
I
You have a clothing shop. Expenditure (E) = Q × P.
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Q=20, P=5, then E=100. Now, you plan to increase
prices 1 EUR (20%)
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If ε = 1, Q reduces 20% and Q’=16.666, E=100
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If ε = 0.5, Q reduces 10% and Q’=18.18, E=109.1
I
If ε = 2, Q reduces 40% and Q’=14.28, E=85.71
I
The success of your price strategy depends on
elasticity!!
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The price elasticity of expenditure can be
aproximated as 1 − ε.
The Expenditure
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Income Elasticity of Demand
Unit 7
Economics - 6th
year
Definition
Price Elasticity of
Demand
The Expenditure
I
Measures the change in demand when income
changes in percentage points.
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Base Formula
Income Elasticity ≡ η =
Percentage change in Q
Percentage change in M
∆Q/Q
∆M/M .
I
Other formulae: η =
I
Using the expression of the demand curve: η =
Income Elasticity of Demand
dQ M
dM Q
Unit 7
Economics - 6th
year
Types of goods depending on η
Price Elasticity of
Demand
The Expenditure
Income elasticity and Normal Goods
Inferior
Luxury
Normal
0
1
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Cross-price Elasticity of Demand
Unit 7
Economics - 6th
year
Price Elasticity of
Demand
I
Measures the change in demand when the price of
other goods change, in percentage points.
The Expenditure
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand
Base Formula
Income Elasticity ≡ εXY =
Percentage change in Q
Percentage change inPy
∆Q/Q
∆Py /Py .
I
Other formulae: εXY =
I
Using the expression of the demand curve:
dQ Py
εXY = dP
y Q
Cross-Price Elasticity of Demand
Unit 7
Economics - 6th
year
Types of goods depending on εXY
Price Elasticity of
Demand
The Expenditure
Cross­Price Elasticity and Goods
Independent
Cross­price elastic
­1
0
Substitutes
Cross­price elastic
1
Complementary
Cross­price inelastic
Income Elasticity
of Demand
Cross-price
Elasticity of
Demand