Managerial Economics
Lecture 3:
Quantitative Demand Analysis
Elasticity and its Applications
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Overview
 The Elasticity Concept
– Own Price Elasticity
– Elasticity and Total Revenue
– Cross-Price Elasticity
– Income Elasticity
 Demand Functions
– Linear
– Log-Linear
 Regression Analysis
1-2
Elasticity Concept
1-3
Elasticity Concept
Quantitative Questions
 Our previous two lectures addressed qualitative method of tackling
managerial issues. This lecture will look at ‘detailed’ quantitative answers to
questions like:
 How much do we have to cut our price to achieve 3.2 percent sales growth?
 If we cut prices by 6.5 percent, how many more units will we sell?
 How much will our sales change if rivals cut their prices by 2 percent or a
recession hits and household incomes decline by 2.5 percent?
1-4
Elasticity Concept
Scenario
 Suppose some variable, such as the price of a product,
reduced by 10 percent. What would happen to the quantity
demanded of the good?
– Based on our previous lecture and the law of demand, a fall in price will
lead to a rise in quantity demanded.
– However, it will be useful for a manager to know the magnitude of the
rise in quantity demanded, whether it will be 5% 10% or any amount rise.
– We primarily use the concept of elasticity to establish such a magnitude.
1-5
The Elasticity Concept
 How responsive is variable “G” to a change in variable “S”
– For instance: the elasticity of your grade with respect to studying is
the percentage change in your grade that will result from a given
percentage change in the time you spend studying. In other words.
EG , S
% G

% S
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.
1-6
The Elasticity Concept
The Elasticity Concept Using Calculus
BEAR IN MIND: If the absolute value of the elasticity is greater than
1, the numerator is larger than the denominator in the elasticity
formula, and we know that a small percentage change in S will lead
to a relatively large percentage change in G and the reverse is true.
 An alternative way to measure the elasticity of a function G =
f(S) is
EG , S
dG S

dS G
1-7
The Elasticity Concept
The Elasticity Concept Using Calculus
NOTE: Two aspects of an elasticity are important: (1) its sign and (2)
whether it is greater or less than 1 in absolute value.
1-8
Types of Elasticity
1-9
Types of Elasticity of Demand

There are three main types of elasticity:
– Point/Own Price Elasticity of Demand
– Cross-Elasticity of Demand
– Income Elasticity of demand
1-10
Point/Own Price Elasticity of Demand
1-11
Point/Own Price Elasticity of Demand

Businesses cannot directly control demand.

They can seek to influence demand by utilizing a variety of strategies and
tactics but ultimately the consumer decides whether to buy a product or not.

One important way in which consumer behavior can be influenced is
through a firm changing the price of its good.

Thus, an understanding of the price elasticity of demand is important in
anticipating the likely effects of changes in price on demand.

Price elasticity of demand measures how much the quantity demanded
responds to change in price.

This means that an elasticity of 0.7 means that a 1 percent change in price
leads to 0.7 percent change in quantity demanded.
1-12
Point/Own Price Elasticity of Demand
Computing the Price Elasticity of Demand
 The price elasticity of demand is computed as the percentage change in the
quantity demanded divided by the percentage change in the price. That is,
EQX , PX

% Q X

%PX
d
It can also be expressed as
EQx, Px
dQx Px

dPx Qx
 It is always Negative because of the ‘law of demand’.
Elastic: EQ X , PX  1
Inelastic: EQ X , PX  1
Unitary: EQ X , PX  1
1-13
Demand Curves according to their Elasticity
Fairly elastic demand
Demand is described as fairly elastic when a small percentage change in
price leads to larger percentage in quantity demanded.
P
P1
E
B
Po
D
Q1
Q0
Qty
In the figure, price increases from Po to P1 (a relatively small margin)
and quantity demanded decreases from Qo to Q1 (a bigger margin).
Here the absolute value of the elasticity is greater than 1. An example of
such a good is a good that has close substitutes. For instance, Milo, Ideal
Milk, Uncle Sam, Geisha Mackerel and so on.
1-14
Demand Curves according to their Elasticity
Fairly Inelastic demand
Demand is described as fairly inelastic when a large percentage change in
price leads to a small percentage in quantity demanded.
P
E
P1
Po
B
D
Q1
Q0
Qty
In the figure, price increases from Po to P1 (a relatively large margin) and
quantity demanded decreases from Qo to Q1 (a smaller margin). Here
the absolute value of the elasticity is less than 1 but greater than zero. An
example of such a good is a good that has no close substitutes. For
instance, Petrol, Diesel, Alcohol and so on.
1-15
Demand Curves according to their Elasticity
Unitary elastic demand
With unitary elastic demand, quantity demanded changes by exactly the
same percentage change in price. The demand curve is rectangular
hyperbola.
P
P1
Po
Q1 Qo
Qty
In the figure, price increases from Po to P1 (a relatively small or
large margin) and quantity demanded decreases from Qo to Q1 (a
same margin). Here the absolute value of the elasticity is equal to
1.
1-16
Demand Curves according to their Elasticity
Perfectly Elastic & Inelastic Demand
Price
Price
D
D
Quantity
Perfectly Elastic ( EQX , PX  )
When demand is perfectly elastic,
a manager who raises price even
slightly will find that none of the
good is purchased.
Quantity
Perfectly Inelastic ( EQX , PX  0)
when demand is perfectly inelastic,
consumers do not respond at all to
changes in price.
1-17
Demand Curves according to their Elasticity
Problem:
 Suppose that the own price elasticity of demand for a product is
-2. If the price of this product fell by 5%, by what percentage
would the quantity demanded for a product change?
 The demand equation for a product is Qd = 500-225P.
Calculate the own-price elasticity of demand if P= 2. Interpret
the result.
1-18
Price Elasticity of Demand: the Midpoint/Arc
Formula
1-19
Price Elasticity of Demand: the Midpoint/Arc Formula
1-20
Price Elasticity of Demand: the Midpoint/Arc Formula
Problem
 Suppose that the price and quantity demanded for a good are GHC 5.00 and
20 units respectively. Suppose further that the price of the product increases
to GHC20.00 and the quantity demanded falls to 5 units. Calculate the price
elasticity of demand.
 At a price of GHC25.00, the quantity demanded of good X is 500 units.
Suppose that the price elasticity of demand is -1.85. if the price of the good
increases to GHC26.00, what will be the new quantity demanded of this
good?
1-21
Factors Influencing Price Elasticity
1-22
Factors that Influence Price Elasticity of Demand
 Availability of close substitutes
– The more substitutes available to a good, the more elastic the demand
and vise versa. For instance, ideal milk, pork, Toyota cars, Geisha
mackerel
 Time
– Demand tends to be more inelastic in the short term than in the long
term.
– Time allows consumers to seek out available substitutes.
 Expenditure Share
– Goods that attract a small share of consumer’s budgets tend to be more
inelastic than goods for which consumers spend a large portion of their
incomes. For example, spending on salt, pepper, matches (inelastic) and
Cars (elastic).
1-23
Factors that Influence Price Elasticity of Demand
 Number of uses of the Good
– The greater the number of possible uses of a product, the greater the
elasticity of demand.
– This is because a price reduction in price will lead to a greater proportionate
change in quantity demanded for the various uses.
– For instance, palm oil, which can be used for soap making, margarine,
cooking and so on will tend to have higher elasticity than butter.

Number of New Buyers
– Goods that a person normally requires only one at a time (for instance,
television), it is new buyers instead of additional demand by existing users
that has a major effect on the market demand curve.
– Thus when the prices of such goods fall within the reach of numerous lower
income groups, demand will increase, and demand will tend to be elastic.
1-24
Factors that Influence Price Elasticity of Demand
 Addictiveness of a product
– When a product is addictive, its elasticity is inelastic
 Necessities verses Luxury
– Necessities tend to have relatively inelastic demands
• For instance if the price of gas and electricity rose together, people will not
demand grammatically less of them.
• They might try and be more energy efficient and reduce their demand a little.
– Luxuries such as pizza are highly elastic in nature in that, when their prices
rise the quantities demanded fall substantially.
1-25
Price Elasticity and Total Revenue
1-26
Price elasticity and Total Revenue
 Suppose a firm sells ideal milk at Ȼ3.00 and it is able to sell 100 tins,
what will be its total revenue?
 Do you know why?
 What will happen to total revenue if price reduces to Ȼ2.50 and sales
increase to 150 tins?
 What did you get?
 What will happen to total revenue if price increases to Ȼ4.00 and sales
fall to 50 tins?
1-27
Price elasticity and Total Revenue
 What do these scenarios inform you?
It means the extent to which quantity demanded changes
as a result of price changes (elasticity of demand)
influence revenue.
1-28
Own-Price Elasticity and Total Revenue
 Elastic
– Increase (a decrease) in price leads to a decrease (an increase)
in total revenue.
 Inelastic
– Increase (a decrease) in price leads to an increase (a decrease)
in total revenue.
 Unitary
– Total revenue is maximized at the point where demand is unitary
elastic.
1-29
The Relationship between Price Changes and
Changes in Total Revenue
/Ep/
Absolute terms
ΔP
ΔQ
ΔTR
˃1
-
+
+
˃1
+
-
-
˂1
-
+
_
˂1
+
-
+
1-30
Elasticity, Total Revenue
and Linear Demand
P
100
TR
0
10
20
30
40
50
Q
0
Q
1-31
Elasticity, Total Revenue
and Linear Demand
P
100
TR
80
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
1-32
Elasticity, Total Revenue
and Linear Demand
P
100
TR
80
1200
60
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
1-33
Elasticity, Total Revenue
and Linear Demand
P
100
TR
80
1200
60
40
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
1-34
Elasticity, Total Revenue
and Linear Demand
P
100
TR
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
1-35
Elasticity, Total Revenue
and Linear Demand
P
100
TR
Elastic
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
Elastic
1-36
Elasticity, Total Revenue
and Linear Demand
P
100
TR
Elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
50
Q
Inelastic
1-37
Elasticity, Total Revenue
and Linear Demand
P
100
TR
Unit elastic
Elastic
Unit elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
50
Q
Inelastic
1-38
Demand, Marginal Revenue (MR) and
Elasticity
1 E
MR  P
E
P
100
Elastic
Unit elastic
80
60
 When
Inelastic
40
20
0
10
20
40
50

Q
– MR > 0, demand is
elastic;
– MR = 0, demand is
unit elastic;
– MR < 0, demand is
inelastic.
MR
1-39
Cross-Price Elasticity of Demand
1-40
Cross-Price Elasticity of Demand
• It reveals the responsiveness of the demand for a good to changes
in the price of a related good. This elasticity helps managers
ascertain how much its demand will rise or fall due to a change in the
price of another firm’s product.
EQ X , PY
% QX

% PY
d
EQx, Py
dQx Py

dPy Qx
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.
1-41
Cross-Price Elasticity of Demand
Scenario:
Cross-price elasticities play an important role in the pricing
decisions of firms that sell multiple products. Indeed, many
drinking bars offer lime for under Ȼ1.00 because their
managers realize that Herb Afrik and lime are complements:
When consumers buy Herb Afrik, lime typically accompanies
the purchase. Thus, by lowering the price of Herb Afrik, a
drinking bar affects its revenues from both Herb Afrik sales and
lime sales. The precise impact on these revenues depends on
the own price and cross-price elasticities of demand.
1-42
Predicting Revenue Changes
from Two Products
Suppose that a firm sells two related goods.
If the price of X (Herb Afrik) changes, then
total revenue will change by:
 


R  RX 1  EQX , PX  RY EQY , PX  %PX
1-43
Cross-Price Elasticity of Demand
Example:
Suppose a drinking bar earns Ȼ4,000 per week in revenues from Herb Afrik
sales ( product X) and Ȼ2,000 per week from lime sales (product Y). Thus,
Rx = Ȼ4,000 and Ry = Ȼ2,000. If the own price elasticity of demand for Herb
Afrik is -1.5 and the cross-price elasticity of demand between lime and Herb
Afrik is -4.0, what would happen to the firm’s total revenues if it reduced the
price of Herb Afrik by 1 percent?
1-44
Income Elasticity of Demand
1-45
Income Elasticity of Demand
It is a measure of the responsiveness of consumer
demand to changes in income.
EQX , M
%QX

%M
d
EQx, M
dQx M

dM Qx
If EQX,M > 0, then X is a normal good.
If EQX,M < 0, then X is an inferior good.
1-46
Income Elasticity of Demand
Problem
Your firm’s research department has estimated the income elasticity of
demand for electric heater to be -1.94. You have just read in the papers that
due to an upturn in the economy, consumer incomes are expected to rise by
10 percent over the next three years. As a manager of an electrical shop,
how will this forecast affect your purchases of electric heater?
1-47
Income Elasticity of Demand
Solution
Since electric heater has an income elasticity of
-1.94 and consumer
income is expected to rise by 10 percent, you can expect to sell 19.4 percent
less electric heater over the next three years. Therefore, you should
decrease your purchases of electric heater by 19.4 percent, unless
something else changes.
1-48
Linear Demand Function and Elasticities
1-49
Linear Demand Function and Elasticities
 General Linear Demand Function and
Elasticities:
QX  0   X PX  Y PY   M M   H H
d
P
EQX , PX   X X
QX
Own Price
Elasticity
EQ X , PY
PY
 Y
QX
Cross Price
Elasticity
M
EQX , M   M
QX
Income
Elasticity
1-50
Linear Demand Function and Elasticities
Problem:
The daily demand for ODIKE Ventures shoes is estimated to
be
QX  100  3PX  4 PY  0.01M  2 AX
d
Where Ax represents the amount of advertising spent on shoes (X),
Px is the price of good X, Py is the price of good Y, and M is average income.
Suppose good X sells at Ȼ25 a pair, good Y sells at Ȼ35, the company utilizes
50 units of advertising, and average consumer income is Ȼ20,000. Calculate
and interpret the own price, cross-price, and income elasticities of
demand.
1-51
Uses of Elasticities
 Pricing
 Managing cash flows
 Impact of changes in competitors’ prices
 Wage negotiations by Trade Unions
 Impact of advertising campaigns.
1-52
Example 1: Pricing and Cash Flows
 According to an IEA Report by Mrs. Mensah,
Vodafone’s own price elasticity of demand for long
distance services is -8.64.
 Vodafone needs to boost revenues in order to meet
it’s marketing goals.
 To accomplish this goal, should Vodafone raise or
lower it’s price?
1-53
Answer: Lower price!
Since demand for Vodafone services is elastic, a
reduction in price will increase quantity demanded by
a greater percentage than the price decline, resulting
in more revenues for Vodafone.
1-54
Example 2: Quantifying the Change
 If Vodafone lowered price by 3 percent, what would
happen to the volume of long distance telephone
calls routed through Vodafone?
1-55
Answer: Calls Increase!
Calls would increase by 25.92 percent!
EQX , PX
%QX
 8.64 
%PX
d
%QX
 8.64 
 3%
d
 3%   8.64   %QX
d
%QX  25.92%
d
1-56
Example 3: Impact of a Change in a Competitor’s
Price
 According to an IEA Report by Mrs. Mensah, Vodafone’s
cross price elasticity of demand for long distance
services is 9.06.
 If competitors (MTN, Airtel, Glo and so on) reduced their
prices by 4 percent, what would happen to the demand
for Vodafone’s services?
1-57
Answer: Vodafone’s Demand Falls!
Vodafone’s demand would fall by 36.24 percent!
1-58
How does elasticity influence wage negotiation and
advertising?
When the demand for a good or service produced by labor has
inelastic demand, unions could negotiate for high wages.
1-59
How does elasticity influence wage negotiation and
advertising?
 When the demand for a good or service produced by labor has inelastic
demand, unions could negotiate for high wages.
 Firms will try to make their products more inelastic using advertisements for
instance, so that they are ensured a decent quantity demanded regardless
of their set price. For instance, Alomo bitters
1-60
Interpreting Demand Functions
 Mathematical representations of demand curves.
 Example:
QX  10  2 PX  3PY  2M
d
– Law of demand holds (coefficient of PX is negative).
– X and Y are substitutes (coefficient of PY is positive).
– X is an inferior good (coefficient of M is negative).
1-61
Example of Linear Demand
 Qd = 10 - 2P.
 Own-Price Elasticity: (-2)P/Q.
 If P=1, Q=8 (since 10 - 2 = 8).
 Own price elasticity at P=1, Q=8:
(-2)(1)/8= - 0.25.
1-62
Regression Analysis
 One use is for estimating demand functions.
 Important terminology and concepts:
– Least Squares Regression model: Y = a + bX + e.
– Least Squares Regression line: Yˆ  aˆ  bˆX
– Confidence Intervals.
– t-statistic.
– R-square or Coefficient of Determination.
– F-statistic.
1-63
An Example
 Use a spreadsheet to estimate the following log-linear
demand function.
ln Qx  0   x ln Px  e
1-64
Summary Output
Regression Statistics
Multiple R
0.41
R Square
0.17
Adjusted R Square
0.15
Standard Error
0.68
Observations
41.00
ANOVA
df
Regression
Residual
Total
Intercept
ln(P)
SS
1.00
39.00
40.00
MS
F
3.65
18.13
21.78
Coefficients Standard Error
7.58
1.43
-0.84
0.30
3.65
0.46
t Stat
5.29
-2.80
Significance F
7.85
0.01
P-value
0.000005
0.007868
Lower 95%
Upper 95%
4.68
10.48
-1.44
-0.23
1-65
Interpreting the Regression Output
 The estimated log-linear demand function is:
– ln(Qx) = 7.58 - 0.84 ln(Px)
– Own price elasticity: -0.84 (inelastic)
 How good is our estimate?
– t-statistics of 5.29 and -2.80 indicate that the estimated coefficients are
statistically different from zero.
– R-square of 0.17 indicates the ln(PX) variable explains only 17 percent of
the variation in ln(Qx).
– F-statistic significant at the 1 percent level.
1-66
Conclusion
 Elasticities are tools you can use to quantify the impact of changes in prices,
income, and advertising on sales and revenues.
 Given market or survey data, regression analysis can be used to estimate:
– Demand functions
– Elasticities
– A host of other things, including cost functions
 Managers can quantify the impact of changes in prices, income, advertising,
etc.
1-67