Demand and Supply:
Elasticity
Principles Microeconomics
Professor Dalton
ECON 202 – Spring 2013
Boise State University
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Elasticity
 Elasticity - measure of responsiveness
 Measures how much a dependent variable
changes due to a change in an
independent variable
 Elasticity = %Δ X / %Δ Y
• Elasticity can be computed for any two
related variables
2
Elasticity Measures
 Elasticities economists are interested in:
• a change in price on the quantity demanded
• a change in income on the demand function
for a good
• a change in the price of a related good on the
demand function for a good
• a change in the price on the quantity supplied
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Price Elasticity of Demand
 The “law of demand” tells us that as the price of
a good increases the quantity that will be
bought decreases but does not tell us by how
much.
 The price elasticity of demand, ε, is a measure
of that information
 “If you change price by 5%, by what percent
will the quantity purchased change?
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Price Elasticity of Demand
ε 
% DQ
% DP
At a point on a demand
function this can be
calculated by:
Q2 Q
- 2Q
=1 DQ
-1 Q
ε=
Q1
P2 -PP2 1- =P1DP
P1
=
DQ
Q1
DP
P1
5
+2
DQ
[2/3 = .66667]
31
Q
ε=
=
DP
-2
P71
% DQ = 67%
% DP = -28.5%
[-2/7=-.28571]
Price decreases from $7 to $5
Px
P1 = $7
P2 = $5
A
DP = -2
[rounded]
The “own” price elasticity of demand
at a price of $7 is -2.3
P2- P1 = 5 - 7 = DP = -2
DQ = +2
.
-2.3
This is “point” price elasticity. It is calculated at a point
on a demand function. It is not influenced by the direction
or magnitude of the price change.
B
Q1 = 3
=
Q2 = 5
Q2 - Q1 = 5 - 3 = DQ = +2
D
There is a problem! If the
price changes from $5 to
$7 the coefficient of
elasticity is different!
Qx/t
6
ε=
DQ
-2
5Q1
+2
DP
=
% DQ = -40%
% DP = 40%
= -1
[this is called “unitary elasticity]
P51
When the price increases from $5 to $7, the ε = -1 [“unitary”]
In the previous slide, when the price decreased from $7 to $5,
The point price elasticity is
different at every point!
There is an
easier way!
Px
P2 = $7
P1 = $5
A
ep = -2.3
DP = +2
B
DQ = -2
Q2= 3
ε = -2.3
Q1= 5
ep = -1
D
Qx/t
7
By rearranging terms
An easier way!
DQ
Q1
Q1
DP
ε=
DQ
=
Q1
*
P1
D P
P1
ε
Q2= 5
P2- P1 = 5 - 7 = DP = -2
Q2 - Q1 = 5 - 3 = DQ = +2
Then,
DQ
DP
=
+2
-2
DP
*
P1
Q1
this is the
slope of the
demand function
Given that when:
P1 = $7,
Q1 = 3
P2 = $5,
=
DQ
this is a point on
the demand
function
= -1
DQ
= -1
DP
P71
* Q
31
P1 = $7,
= -2.33
Q1 = 3
On linear demand functions the
slope remains constant so you
just put in P and Q
This is the slope of the demand Q = f(P)
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Use of Price Elasticity
 Ruffin and Gregory [Principles of Economics,
Addison-Wesley, 1997, p 101] report that:
|ε|of gasoline is = .15 (inelastic)
long run |ε|of gasoline is = .78 (inelastic)
short run |ε|of electricity is = . 13 (inelastic)
long run |ε|of electricity is = 1.89 (elastic)
• short run
•
•
•
 Why is the long run elasticity greater than short
run?
 What are the determinants of elasticity?
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Determinants of Price Elasticity
 Availability of substitutes
• greater availability of substitutes makes a good more
elastic
 Proportion of budget expended on good
• higher proportion – more elastic
 Time to adjust to the price changes
• longer time period means more adjustments possible
and increases elasticity
 Price elasticity for “brands” tends to be
more elastic than for the category
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D1 is a “perfectly elastic”
D2
P
perfectly
inelastic
demand function.
For an infinitesimally small
change in price, Q changes
by infinity.
Buyers are very
responsive to price changes. An
infinitely small change in price
changes Q by infinity.
ε
0
%
DQ
% DP
P
0
ε=0
perfectly elastic
|ε| = undefined
==undefined
0
D1
Q/t
D2 is a “perfectly inelastic” demand function, no matter how
much the price changes the same amount is bought. Buyers
are not responsive to price changes! |ε| = 0, perfectly inelastic.
.
.
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Income Elasticity
 Income elasticity [ey] is a measure of the effect
of an income change on demand.
 When ey > 0, the good is a normal or superior
good an increase in income increases demand, a
decrease in income decreases demand.
ey < 1 is a normal good
 1 < ey is a superior good
0<
 When ey < 0, the good is an inferior good
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Examples of Income Elasticity
 normal goods, [0 <
ey < 1 ], (between 0 and
1)
• coffee, beef, Coca-Cola, food, Physicians’
services, hamburgers, . . .
 Superior goods, [
ey > 1], (greater than 1)
• movie tickets, foreign travel, wine, new cars, . .
 Inferior goods, [ey < 0],
(negative)
• “top ramen,” flour, lard, beans, . . .
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Cross-Price Elasticity
 Cross-price elasticity [exy] is a measure of how
responsive the demand for a good is to changes
in the prices of related goods.
 Given a change in the price of good Y, what is
the effect on the demand for good X?
 exy is defined as:
e xy
%DQ
x
%D P y
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Cross-Price Elasticity
 In the case of beef and pork
• the ebp is not the same as epb
• ebp is the % change in the demand for beef
with respect to a % change in the price of
pork
• epb is the % change in the demand for pork
with respect to a % change in the price of
beef
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Cross-Price Elasticity
The cross elasticity of the demand for beef with respect to the
price of pork,
+ebp
ebp =
positive
ebeef-pork or ebp can be calculated:
+Q
DQ
%D
ofb beef
%DP+of
DPpork
p
cross elasticity is positive
+eebpbp =
positive
Qbeef
b
%D -Q Dof
%DP of pork
- DPp
An increase in the price of pork,
“causes” an increase in the demand
for beef.
A decrease in the price of pork,
“causes” a decrease in the demand
for beef.
If goods are substitutes, exy will be positive. The greater the
coefficient, the more likely they are good substitutes.
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Cross-Price Elasticity
• exy > 0 suggests substitutes, the higher the
coefficient the better the substitute
• exy < 0 suggests the goods are
complements, the greater the absolute value
the more complimentary the goods are
• exy = 0 suggests the goods are not related
• exy can be used to define markets in legal
proceedings
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Elasticity of Supply
 Elasticity of supply is a measure of how
responsive sellers are to changes in the
price of the good.
 Elasticity of supply [es] is defined:
e
s
% D Quantity Supplied

% D price
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Elasticity of supply
es =
%DQsupplied
%DP
Given a supply function, at a price [P1], Q1 is produced and offered
for sale.
P
At a higher price [P2], a larger
quantity, Q2, will be produced
and offered for sale.
P2
P1
The increase in price [ DP ], induces
a larger quantity goods [ DQ]for
sale.
+DP
The more responsive sellers are to
+DQ
Q1
Q2
DP, the greater the absolute value of
Q /t
es.
[The supply function is “flatter”or
more elastic]
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The supply function is a
model of sellers behavior.
P
Si a perfectly inelastic
supply, es = 0
Sellers behavior is influenced by:
1. technology
2. prices of inputs
3. time for adjustment
market period
short run
long run
very long run
4. expectations
5. anything that influences costs of production
Se
a perfectly
elastic supply
[es is undefined.]
Q /ut
taxes
regulations, . . .
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Elasticity
 Price elasticity of demand
• elastic, inelastic or unitary elasticity
 Income elasticity
• superior, normal, and inferior
 Cross-Price elasticity
• complements/substitutes
 Price elasticity of supply
• Elastic, inelastic
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