Lecture 4
Elasticity
Elasticity
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Readings: Chapter 4
Elasticity
4. Consideration of elasticity
 Our model tells us that when demand increases
both price and quantity will increase. It does
not tell us whether the price or quantity increase
will be relatively big or small.
 To make these sorts of predictions we need
information on the price sensitivity of the
demand and supply relationships.
Elasticity
Q: How should price sensitivity be measured?
 The Demand and Supply equations have slope
parameters that measure price sensitivity.
 Recall: Qd = a - b•P
and Qs = c +d•P
 b = ∆Qd / ∆P = (Qd2 - Qd1) / (P2 - P1)
 d = ∆Qs/ ∆P = (Qs2 - Qs1) / (P2 - P1)
Elasticity
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Problem: The slope parameters depend on the
units used to measure price and quantity.
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If there is inflation, the slope parameter will change
every year. Comparisons of price sensitivity will be
meaningless.
Comparisons of the slope parameters in different
countries are meaningless because of different national
currencies.
Comparisons of the price sensitivity of different
commodities will also be impossible because of the
differing units used to measure different commodities.
Elasticity
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Solution: Elasticity provides a universal measure
that is immune to inflation and is comparable
across national borders and across different
commodities.
Q: What is elasticity?
Elasticity = % Δ (dependent variable)
% Δ (independent variable)
It is a unit free measure because it is a ratio of %.
Elasticity
Q: What are the important elasticities?
 We will use four:
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ηd = │(%ΔQd) / (%ΔP)│ = Price Elasticity of Demand
ηs = (%ΔQs) / (%ΔP) = Price Elasticity of Supply
ηm = (%ΔQd) / (%ΔIncome) = Income Elasticity of D
ηxy = (%ΔQxd) / (%ΔPy) = Cross-price Elasticity of D
High elasticity  dependent variable highly
responsive to changes in the independent variable
Low elasticity  dependent variable unresponsive
to changes in the independent variable
Elasticity
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The price elasticity of demand tells us the
price sensitivity of the quantity demanded.
P
P
Elastic Demand
D
Inelastic Demand
D
Q
Q
Elasticity
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The price elasticity of supply tells the price
sensitivity of the quantity supplied.
P
P
S
Elastic Supply
Inelastic Supply
S
Q
Q
Elasticity
Q: How do we use data to calculate the
d
elasticity of demand?
%Q
 The arc elasticity of demand:  
d
%P
 Where:
d
Q

Q

Q
2
1
%Q d 

(Q2  Q1 ) / 2 Qavg
P2  P1
P
%P 

( P2  P1 ) / 2 Pavg
Elasticity
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Example: Consider the demand for pop (Dpop) when P falls from
$1.50 to $1.00
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ηd = │(∆Qd/ Qaverage)/(∆P / Paverage)│
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ηd =│ 5 / 7.5 │ = │ +66.6% │ = │ -1.67 │= 1.67
│-0.5/1.25│ │ - 40% │
P
1.50
Dpop
1.00
5
10
Q
Elasticity
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This is an approximation of the elasticity on the region
of the demand curve between
P = $1.50 and $1.00.
It is most accurate at the midpoint of this region.
P
1.50
1.00
Dpop
5
10
Q
Elasticity
Q: What about the other elasticities?
 They have similar arc elasticity formulas:
Q d / Qavg
%Q d
d 

%P
P / Pavg
Q s / Qavg
%Q
S 

%P
P / Pavg
d
d

Q
/ Qavg
%Q
m 

%m
m / mavg
s
Qxd / Qx,avg
%Q
 xy 

%Py
Py / Py ,avg
d
x
Elasticity
Q: How does knowledge of the elasticity of
demand help us understand the market?
 Knowing the elasticity of demand we can:
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1. Predict the relative movements of price and quantity
to changes in supply.
2. Predict what will happen to industry revenue if price
changes.
Elasticity
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Predicting the relative movements of P and Q.
S
S
S’
S’
ηd > 1
D
d > 1

0<η
d <d1< 1
D
Elasticity
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Predicting the relative movements of P and Q.
S
S
S’
S’
D
ηdd > 11

0<η
1
d <1

d <
D
Elasticity
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Predictions:
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Elastic (ηd >1) Increasing Supply causes small decline
in P and large increase in Q.
Inelastic (ηd <1) Increasing Supply causes large decline
in P and small increase in Q.
Elastic (ηd > 1) Decreasing P causes increase in
Industry Revenue.
Inelastic (ηd <1) Decreasing P causes decline in
Industry Revenue.
Exercise: If supply is elastic how will P and Q
respond to demand changes? What if supply is
inelastic?
Elasticity
Q: Does a straight line demand curve have a constant
elasticity?
 A straight-line demand curve has a constant slope, but
elasticity declines with P.
P
ηd > 1
ηd = 1
ηd < 1
Q
Elasticity
Q: How is the slope of a straight line demand
curve related to the elasticity?
 b = ∆Q / ∆P
 ηd = │∆Q / Qavg│ = │(∆Q /∆P)•(Pavg/Qavg) │ =b•(Pavg /Qavg)
│ ∆P / Pavg│
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This is an approximation of the elasticity on a
region of the demand curve.
At a particular point (Q,P) on the demand curve,
the point elasticity of demand will be
ηd = b•(P/Q)
Elasticity
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With a little thought, you can see why the mid-point has
unit elasticity.
2P
P
● ηd = b•(P/Q) = 1
Q
2Q
Elasticity
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Q: How is the straight-line demand curve
related to revenue?
P
ηd > 1
ηd = 1
ηd < 1
Q
R
Revenue: R = P•Q
Q
Elasticity
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Q: Is there a point elasticity of supply equation?
Yes. If the supply equation is Qs = c + dP then the point
elasticity of supply is ηs = d•(P/Q).
Supply: Qs = c + d•P
ηs = d•(P/Q)
P
Q
Elasticity
Q: What about the income elasticity of
demand?
 Recall:
ηm = ∆Qd/ Qavg ,
∆m / mavg
 If ηm > 0 then the good is a normal good and a
rise in income will cause the demand curve to
shift right (demand increases).
 If ηm < 0 then the good is an inferior good and a
rise in income will cause the demand curve to
shift left (demand declines).
Elasticity
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Q: What about the cross-price elasticity of
demand?
Recall:
ηxy = ∆Qdx/ Qx,avg
∆Py / Py,avg
If ηxy > 0 , then and increase in the price of y
causes the quantity of x demanded to increase,
and hence x and y are substitutes.
If ηxy < 0 , then x and y are complements.
Elasticity
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