Price Elasticity of Demand

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Price Elasticity of Demand
Overheads
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How much would your roommate pay to watch a live
fight?
How does Showtime decide how much to charge for a
live fight?
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What about Hank and Sons Concrete?
How much should they charge per square foot?
Can ISU raise parking revenue by raising parking
fees?
Or will the increase in price drive demand down
so far that revenue falls?
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All of these pricing issues revolve around the
issue of how responsive the quantity demanded is
to price.
Elasticity is a measure of how responsive one
variable is to changes in another variable?
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The Law of Demand
The law of demand states that when the price of a
good rises, and everything else remains the same,
the quantity of the good demanded will fall.
The real issue is how far it will fall.
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The demand function is given by
QD quantity demanded
P price of the good
ZD other factors that affect demand
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The inverse demand function is given by
To obtain the inverse demand function we just
solve the demand function for P as a function of Q
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Examples
QD 20 - 2P
2P QD 20
2P 20 - QD
P 10 - 1/2 QD
Slope - 1/2
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Examples
QD 60 - 3P
3P QD 60
3P 60 - QD
P 20 - 1/3 QD
Slope - 1/3
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One measure of responsiveness is slope
For demand
The slope of a demand curve is given by
the change in Q divided by the change in P
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For inverse demand
The slope of an inverse demand curve is given
by the change in P divided by the change in Q
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Examples
QD 60 - 3P
Slope - 3
P 20 - 1/3 QD
Slope - 1/3
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Examples
QD 20 - 2P
Slope - 2
P 10 - 1/2 QD
Slope - 1/2
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We can also find slope from tabular data
Q P 0 10 2 9 4 8 6 7 8 6 10 5
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Demand for Handballs
Q P 0 10 1 9.5 2 9 3 8.5 4 8 5 7.5 6 7 7 6
.5 8 6 9 5.5 10 5 11 4.5 12 4 13 3.5 14 3
15 2.5 16 2 17 1.5 18 1 19 0.5 20 0
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Q P 0 10 1 9.5 2 9 3 8.5 4 8 5 7.5 6 7 7 6
.5 8 6 9 5.5 10 5 11 4.5 12 4 13 3.5 14 3
15 2.5 16 2 17 1.5 18 1 19 0.5 20 0
Demand for Handballs
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Price
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Quantity
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Q P 0 10 1 9.5 2 9 3 8.5 4 8 5 7.5 6 7 7 6
.5 8 6 9 5.5 10 5 11 4.5 12 4 13 3.5 14 3
15 2.5 16 2 17 1.5 18 1 19 0.5 20 0
Demand for Handballs
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Price
?Q 2 - 4 -2
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?P 9 - 8 1
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0
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Quantity
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Problems with slope as a measure of responsiveness
Slope depends on the units of measurement
The same slope can be associated with very
different percentage changes
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Examples
QD 200 - 2P
2P QD 200
2P 200 - QD
P 100 - 1/2 QD
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Q P 0 100 1 99.5 2 99 3 98.5 4 98 5 97.5 6
97 7 96.5 8 96 9 95.5 10 95 11 94.5 12 94 1
3 93.5 14 93
Consider data on racquets
Let P change from 95 to 96
? P 96 - 95 1
? Q 8 - 10 -2
A 1.00 price change when P 95.00 is tiny
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Graphically for racquets
Demand for Racquets
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Price
100
98
96
Slope - 1/2
94
92
90
88
0
2
4
6
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10
12
14
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Large change in Q
Quantity
Small change in P
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Graphically for hand balls
Demand for Handballs
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Price
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? P 7 - 6 1
9
8
7
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? Q 6 - 8 -2
P
5
4
3
Slope - 1/2
2
1
0
0
2
4
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10
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Quantity
Large change in Q
Large change in P
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So slope is not such a good measure of
responsiveness
Instead of slope we use percentage changes
The ratio of the percentage change in one
variable to the percentage change in another
variable is called elasticity
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The Own Price Elasticity of Demand is given by
There are a number of ways to compute percentage
changes
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Initial point method for computing The Own Price
Elasticity of Demand
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Price Elasticity of Demand (Initial Point
Method)
P Q 6 8 5.5 9 5 10 4.5 11 4 12
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Final point method for computing The Own Price
Elasticity of Demand
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Price Elasticity of Demand (Final Point
Method)
P Q 6 8 5.5 9 5 10 4.5 11 4 12
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The answer is very different depending on the
choice of the base point
So we usually use
The midpoint method for computing The Own Price
Elasticity of Demand
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Elasticity of Demand Using the Mid-Point
For QD we use the midpoint of the Qs
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Similarly for prices
For P we use the midpoint of the Ps
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Price Elasticity of Demand (Mid-Point Method)
Q P 8 6 9 5.5 10 5 11 4.5 12 4
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Classification of the elasticity of demand
Inelastic demand
When the numerical value of the elasticity of
demand is between 0 and -1.0, we say that demand
is inelastic.
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Classification of the elasticity of demand
Elastic demand
When the numerical value of the elasticity of
demand is less than -1.0, we say that demand is
elastic.
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Classification of the elasticity of demand
Unitary elastic demand
When the numerical value of the elasticity of
demand is equal to -1.0, we say that demand is
unitary elastic.
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Classification of the elasticity of demand
Perfectly elastic - ?D - ?
horizontal
Perfectly inelastic - ?D 0
vertical
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Elasticity of demand with linear demand
Consider a linear inverse demand function
The slope is (-B) for all values of P and Q
For example,
The slope is -0.5 - 1/2
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P Q 12 0 11.5 1 11 2 10.5 3 10 4 9.5 5 9 6
8.5 7 8 8 7.5 9 7 10 6.5 11 6 12 5.5 13 5
14 4.5 15 4 16 3.5 17 3 18
Demand for Diskettes
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Price
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Quantity
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The slope is constant but the elasticity of
demand will vary
P Q 12 0 11.5 1 11 2 10.5 3 10 4 9.5 5 9 6
8.5 7 8 8 7.5 9 7 10 6.5 11 6 12 5.5 13 5
14 4.5 15 4 16 3.5 17 3 18
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The slope is constant but the elasticity of
demand will vary
P Q 12 0 11.5 1 11 2 10.5 3 10 4 9.5 5 9 6
8.5 7 8 8 7.5 9 7 10 6.5 11 6 12 5.5 13 5
14 4.5 15 4 16 3.5 17 3 18
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The slope is constant but the elasticity of
demand will vary
A linear demand curve becomes more inelastic as
we lower price and increase quantity
The elasticity gets closer to zero
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The slope is constant but the elasticity of
demand will vary
Q P Elasticity Expenditure 0 12 0 2 11 -23.0000
22 4 10 -7.0000 40 6 9 -3.8000 54 8 8 -2.4286
64 10 7 -1.6667 70 12 6 -1.1818 72 14 5 -0.8462
70 16 4 -0.6000 64 18 3 -0.4118 54 20 2 -0.263
2 40 22 1 -0.1429 22 24 0 -0.0435 0
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The slope is constant but the elasticity of
demand will vary
Q P Elasticity Expenditure 0 12 0 2 11 -23.0000
22 4 10 -7.0000 40 6 9 -3.8000 54 8 8 -2.4286
64 10 7 -1.6667 70 12 6 -1.1818 72 14 5 -0.8462
70 16 4 -0.6000 64 18 3 -0.4118 54 20 2 -0.263
2 40 22 1 -0.1429 22 24 0 -0.0435 0
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Note
We do not say that demand is elastic or inelastic
..
We say that demand is elastic or inelastic at a
given point
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Example
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The Own Price Elasticity of Demand and Total
Expenditure on an Item
How do changes in an items price
affect expenditure on the item?
If I lower the price of a product, will the
increased sales make up for the lower price per
unit?
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Expenditure for the consumer is equal to revenue
for the firm
Revenue R price x quantity PQ
Expenditure E price x quantity PQ
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Modeling changes in price and quantity
?P change in price
?Q change in quantity
The Law of Demand says that as P increases Q will
decrease
P ?
Q ?
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So
P initial price
?P change in price
P ?P final price
Q initial quantity
?Q change in quantity
Q ?Q final quantity
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So
Initial Revenue PQ
P ?P final price
Q ?Q final quantity
Final Revenue (P ?P) (Q ?Q)
P Q ?P Q P ?Q ?P ?Q
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Now find the change in revenue
?R final revenue - initial revenue
P Q ?P Q P ?Q ?P ?Q - P Q
?P Q P ?Q ?P ?Q
?R ?R / R ?R / P Q
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We can rewrite this expression as follows
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Classification of the elasticity of demand
Inelastic demand
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?Q and ?P are of opposite sign so ?R has the
same sign as ?P
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Classification of the elasticity of demand
Inelastic demand

-
?Q and ?P are of opposite sign so ?R has the
same sign as ?P
Lower price ? lower revenue
Higher price ? higher revenue
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Classification of the elasticity of demand
Elastic demand
-

?Q and ?P are of opposite sign so ?R has the
opposite sign as ?P
Higher price ? lower revenue
Lower price ? higher revenue
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Classification of the elasticity of demand
Unitary elastic demand
-

?Q and ?P are of opposite sign so
their effects will cancel out and ?R 0.
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Tabular data
Q P Elasticity Revenue 0 12 0 2 11 -23.0000 22
4 10 -7.0000 40 6 9 -3.8000 54 8 8 -2.4286 64 1
0 7 -1.6667 70 12 6 -1.1818 72 14 5 -0.8462 70
16 4 -0.6000 64 18 3 -0.4118 54 20 2 -0.2632 40
22 1 -0.1429 22 24 0 -0.0435 0
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Graphical analysis
Q P Elasticity Revenue
Demand for Diskettes
0 12 0 2 11 -23.0000 22 4 10 -7.0000 40
6 9 -3.8000 54 8 8 -2.4286 64 10 7 -1.6667 70 12
6 -1.1818 72 14 5 -0.8462 70 16 4 -0.6000 64 18 3
-0.4118 54 20 2 -0.2632 40 22 1 -0.1429 22 24 0 -0
.0435 0
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Price
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Quantity
Lose B, gain A, revenue rises
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Graphical analysis
Q P Elasticity Revenue
Demand for Diskettes
0 12 0 2 11 -23.0000 22 4 10 -7.0000 40
6 9 -3.8000 54 8 8 -2.4286 64 10 7 -1.6667 70 12
6 -1.1818 72 14 5 -0.8462 70 16 4 -0.6000 64 18 3
-0.4118 54 20 2 -0.2632 40 22 1 -0.1429 22 24 0 -0
.0435 0
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Price
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Quantity
Lose A, gain B, revenue falls
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Factors affecting the elasticity of demand
Availability of substitutes
Importance of item in the buyers budget
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Availability of substitutes
The easier it is to substitute for a good,
the more elastic the demand
With many substitutes, individuals will move away
from a good whose price increases
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Examples of goods with easy substitution
Gasoline at different stores
Soft drinks
Detergent
Airline tickets
Local telephone service
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Narrow definition of product
The more narrowly we define an item,
the more elastic the demand
With a narrow definition, there will lots
of substitutes
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Examples of narrowly defined goods
Lemon-lime drinks
Corn at a specific farmers market
Vanilla ice cream
Food
Transportation
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Necessities tend to have inelastic demand
Necessities tend to have few substitutes
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Examples of necessities
Salt
Insulin
Food
Trips to Hawaii
Sailboats
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Demand is more elastic in the long-run
There is more time to adjust in the long run
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Examples of short and long run elasticity
Postal rates
Gasoline
Sweeteners
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Factors affecting the elasticity of demand
Importance of item in the buyers budget
The more of their total budget consumers spend on
an item,
the more elastic the demand for the good
The elasticity is larger because the item has a
large budget impact
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Big ticket items and elasticity
Housing
Big summer vacations
Table salt
College tuition
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The End