Topic 03 Elasticity(4)

Topic 3
Elasticity and Demand
Estimate
(Chapter 3)
Ratna K. Shrestha
2
Overview
From the time Apple launched iTunes in 2003
through 2009, it charged $0.99 for each song.
Music producers wanted Apple to increase
price.
How can Apple determine what would happen
to its revenue if they increase the price?
It depends on how the number of iTunes
downloads would decrease in response to
price hike (price elasticity of demand)?
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3.1 Price Elasticity of Demand
It measures the percentage change in the
quantity demanded of a good that results
from a one percent change in price.


It is usually a negative number
As price increases, quantity decreases
As price decreases, quantity increases
dP
dQ
Q
P
P dP
Q dQ
P
Q
E
D
P
 



%
%
4
Price Elasticity of Demand
When E
P
 > 1, the good is price elastic
%Q > % P
When E
P
 < 1, the good is price inelastic
%Q < % P
When E
P
 = 1, the good is unit elastic
%Q = % P


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Price Elasticity of Demand
The primary determinant of price elasticity of
demand is the availability of substitutes.
If many substitute goods are available, then
demand is price elastic. For example, if the
price of Pepsi increases, we can easily
switch to Coke.
On the other hand, if the price of food
increase, one has to buy food to survive.
Thus the demand for food is inelastic.
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Price Elasticity of Demand
The availability of substitutes also depends
on how we define the market.
Ex: Demand for a car (broad market) vs.
Toyota Corolla (narrowly market).
Obviously demand for a Toyota car is
more elastic than the demand for a car.
The more inelastic the good, the steeper the
demand curve. If the demand is completely
elastic, the curve is horizontal.
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Completely Elastic Demand
D P
*
Quantity
Price
E
P
= - 
A small increase in price
will cause demand to drop
off completely.
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Completely Inelastic Demand
Quantity
Price
Q
*
D
E
P
= 0
Even if price
increases a lot
quantity demanded
stays the same at Q*.
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Price Elasticity of Demand: A Case
of a Linear Curve
In the case of a linear demand curve, will
the price elasticity of demand be same at all
points along the curve?
The answer is NO. This is because E =
dQ/dP * P/Q and so even if (dQ/dP) is the
same at all points, P/Q is not.
As you move downwards along the demand
curve, P/Q becomes smaller and hence the
demand becomes more inelastic.
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Price Elasticity of Demand: A Case
of a Linear Curve
Q
Price
4
8
2
4
E
p
= -1
E
p
= 0
E
P
= -
Elastic
Inelastic
Computing Point Elasticity
 Consider a demand curve: Q = 8 – 2P.
 At the center of a liner line,
E = dQ/dP * P/Q = - 2* (2/4) = - 1
 At P = 0 and Q = 8, E = - 2 * 0/8 = 0 --
demand is completely inelastic. At this point
the consumer has already consumed the
maximum possible. So the consumer will not
buy any extra for an infinitesimal change in P.
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Computing Elasticity
Price Elasticity
of Demand, E
D

 Elasticity may be computed for a change
from one point on the D curve to another point
on the same curve (Arc Elasticity).
% Q
=
% P
=
(Q
2
– Q
1
)/Q
1

(P
2
– P
1
)/P
1

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 Another approach is to divide the change
by the average of two points—(Q
1
+ Q
2
)/2
instead of Q
1
and (P
1
+ P
2
)/2 instead of P
1
.
Computing Arc Elasticity
Demand for
Ice Cream
2.20
2.00
10 8
E
D
=
(8 - 10) / 9
($2.2 - $2.0)/$2.1
=
- 2.33
Demand is Elastic as
E
D
 > 1. With this
midpoint method, the
elasticity value will be the
same regardless of the
direction of the movement
from A to B or B to A.
13
A
B
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Other Demand Elasticities
Income Elasticity of Demand
Measures how much quantity demanded
changes with a change in income.


If it is positive, the good is normal.
 Suppose Q = 20 – 3P +0.03Y. What is
E
Y
of this good? Is this good a normal or
inferior good?
dY
Q d
Q
Y
Y/Y d
Q/Q d
EY  
Other Demand Elasticities
 Goods consumers regard as ―necessities‖
tend to be income inelastic...
Examples include: food, fuel, clothing,
utilities, & medical services.
Goods consumers regard as ―luxuries‖
tend to be income elastic...
Examples include: Sports cars, furs,
and expensive foods.
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16
Other Demand Elasticities
Cross-Price Elasticity of Demand
Measures the percentage change in the
quantity demanded of one good that
results from a one percent change in the
price of another good.



m
b
b
m
m m
b b
P Q
dP
dQ
Q
P
P dP
Q dQ
E
m b
 
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Other Demand Elasticities
Complements:
Cross-price elasticity of
demand is negative for
complement goods.
 For example: when the
price of cars (P
C
)
increases, quantity
demanded of tires
decreases.
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Other Demand Elasticities
Substitutes: Butter and
Margarine
Cross-price elasticity of
demand is positive for
substitute goods.
When price of butter
increases, quantity of
margarine demand rises.
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Other Demand Elasticities
In the wake of an increasing price of
gasoline, the demand for fuel efficient cars
has been increasing recently. Why?
Consider demand for tires
Q = 50 - 4P
T
– 2P
C
.
Find the cross price elasticity of tire demand.


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Price Elasticity of Supply
Measures the percentage change in quantity
supplied resulting from a 1 percent change in
price.
P
Q
E
S
S
P



%
%
21
Demand Elasticity Over time
In general, demand is much more price
elastic in the long run
Consumers take time to adjust
consumption habits.
Demand might be linked to another good
that changes slowly.
More substitutes are usually available in
the long run.
22
Demand Elasticity over Time: Gasoline
D
SR
D
LR
In the long run, people tend to
drive smaller and more fuel
efficient cars. Alternative energy
cars (e.g., battery operated)
may also be available.
Quantity of Gas
Price
3.2 Regression Analysis
Table 3.1 Data Used to Estimate Cod Demand at the
Portland Fish Exchange

Price in $ per lb. Thousands of lbs
1.90 1.5
1.35 2.2
1.25 4.4
1.20 5.9
0.95 6.5
0.85 7.0
0.73 8.8
0.25 10.1
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Cod Data in a Diagram
We can
estimate a
demand
curve by
drawing a
line or curve
through
these points.
24
Using Regression to Estimate
Demand
We want to find the ―best possible‖ line or
curve that represents this data.
 We think of price as the explanatory variable
and quantity as the dependent variable.
Fishing boats catch as much as they can and
bring that to market. Price adjusts to clear the
market.
25
Inverse Demand
If we start with a standard demand curve of
the form Q = a + bp (where b is negative), we
can rearrange this expression to obtain p = -
a/b + Q/b.
We can rewrite this as p = g + hQ where g = -
a/b and h = 1/b.
This (p = -a/b + Q/b) is the inverse demand
curve. It expresses the same information as
the standard demand curve.
26
Random Error
When we observe actual data it would not
normally lie on straight line. However, we can
write: p = g + hQ + e
where e is an ―error‖. The ―error‖ shows the
difference between the proposed linear
relationship and the actual observation.
The error might be due to non-price factors
that we cannot hold fixed (such as random
variations in the number of buyers who show
up on a particular day) .
27
An Estimated Demand Curve
The
observed
points do not
lie on the
estimated
line precisely,
because of
the random
error.
28
Ordinary Least Squares
The ―residual‖ is the vertical distance
between the actual price and the ―predicted‖
price obtained from the regression line. We
get our estimate of the demand curve by
making the residuals small.
An ―ordinary least squares (OLS)‖ method
makes the sum of squared residuals as
small as possible. This is normally done
using computer programs such as Excel.
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Regression Using Excel
Carry out the following steps.
1. Put the Cod data in an Excel spreadsheet.
Put Quantity in column A and Price in
Column B.
2. Select the two columns of data.
3. Click on <Insert>, <Scatter>, and select the
first type of scatter plot. You should see a
scatter plot like Figure 3.3.
30
Regression Using Excel
4. Click on Layout, then Trendline and select
Linear Trendline. The estimated demand
curve will appear.
5. Right Click on the line and then Format
Trendline. Select Display Equation, and
Display R-squared.
6. Click on and then delete the legend that
appears at the right.
7. Excel uses Ordinary Least Squares
Regression to get this line.
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Trendline
32
y = -6.0542x + 11.967
R² = 0.8491
0
2
4
6
8
10
12
0 0.5 1 1.5 2
Question: Effect of Changing Price
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The R
2
number shows how well the estimated
regression line fits the data. Thus the R
2

statistic measures the goodness of fit.
If R
2
= 1, then all the observed points lie on
the estimated line and hence the estimated
regression line perfectly fits the data.
On the other hand if the regression explains
none of the variation in the dependent
variable, then R
2
=0.
Goodness of Fit and R
2
Statistics
0
5
10
15
0 10 20 30 40
Q, Pies per day
p
,

$

p
e
r

p
i
e
0
5
10
15
0 10 20 30 40
Quantity of Pies Sold
P
r
i
c
e
(a) R
2
= 0.98 (b) R
2
= 0.54



R
2
= 0.54 on the right panel shows that 46% of
the variation in demand is due to random
errors.
34
Do We Have the Right Functional
Form? – Advertising and Demand
(a) Linear (b) Quadratic

Using a linear regression would be a mistake
in this case. The actual relationship is more like
a quadratic function.
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