Economic Analysis
for Business
Session V: Elasticity and its Application-1
Instructor
Sandeep Basnyat
9841892281
Sandeep_basnyat@yahoo.com
A scenario…
You design websites for local businesses.
You charge $200 per website, and currently sell
12 websites per month.
Your costs are rising (including the opp. cost of
your time), so you’re thinking of raising the
price to $250.
The law of demand says that you won’t sell as
many websites if you raise your price. How
many fewer websites? How much will your
revenue fall, or might it increase?
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Elasticity

Basic idea: Elasticity measures how much
one variable responds to changes in another
variable.
◦ One type of elasticity measures how much demand
for your websites will fall if you raise your price.
Definition:
Elasticity is a numerical measure of the
responsiveness of Qd or Qs to one of its
determinants.
 Elastic and Inelastic demand and supply.

CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Price Elasticity of Demand
Price elasticity
of demand

Percentage change in Qd
=
Percentage change in P
Price elasticity of demand measures how
much Qd responds to a change in P.
 Loosely speaking, it measures the pricesensitivity of buyers’ demand.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Price Elasticity of Demand
Price elasticity
of demand
Percentage change in Qd
=
Percentage change in P
P
Example:
Price
elasticity
of demand
equals
P rises
P2
by 10%
P1
D
Q2
15%
= 1.5
10%
Q falls
by 15%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q1
Q
Price Elasticity of Demand
Price elasticity
of demand
Percentage change in Qd
=
Percentage change in P
P
P2
P1
D
Q2
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q1
Q
Calculating Percentage Changes
Standard method
of computing the
percentage (%) change:
Demand for
your websites
end value – start value
x 100%
start value
P
$250
B
Going from A to B,
the % change in P equals
A
$200
D
8
12
($250–$200)/$200 = 25%
Q
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Calculating Percentage Changes
Problem:
The standard method gives
different answers depending
on where you start.
Demand for
your websites
P
$250
From A to B,
P rises 25%, Q falls 33%,
elasticity = 33/25 = 1.33
B
A
$200
From B to A,
P falls 20%, Q rises 50%,
Q
elasticity = 50/20 = 2.50
D
8
12
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Calculating Percentage Changes

So, we instead use the midpoint method:
end value – start value
x 100%
midpoint
 The midpoint is the number halfway between
the start & end values, also the average of
those values.
 It doesn’t matter which value you use as the
“start” and which as the “end” – you get the
same answer either way!
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Calculating Percentage Changes

Using the midpoint method, the % change
in P equals
$250 – $200
x 100% = 22.2%
$225
 The % change in Q equals
12 – 8
x 100% = 40.0%
10
 The price elasticity of demand equals
40/22.2 = 1.8
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
ACTIVE LEARNING
1:
Calculate an elasticity
Use the following
information to
calculate the
price elasticity
of demand
for hotel rooms:
if P = $70, Qd = 5000
if P = $90, Qd = 3000
11
ACTIVE LEARNING
1:
Answers
Use midpoint method to calculate
% change in Qd
(5000 – 3000)/4000 = 50%
% change in P
($90 – $70)/$80 = 25%
The price elasticity of demand equals
50%
= 2.0
25%
12
Calculating Price Elasticity of Demand
Two Ways: Arc elasticity Calculation and Point
Elasticity Calculation

Arc Elasticity:
DQ
%DQ Q
DQ p
e


%Dp Dp Dp Q
p
◦ where D indicates change.

Important Note:
Along a D curve, P and
Q move in opposite
directions, which would
make price elasticity
negative most of the
cases. (E <0)
Example
◦ If a 1% increase in price results in a 3% decrease in quantity
demanded, the elasticity of demand is e = -3%/1% = -3.
Calculating Price Elasticity of Demand
Point Elasticity: Elasticity at a particular point (price)

Use of derivative: dQ/dP : denotes rate at which quantity
changes with respect to Price: DQ
Dp

For a linear demand equation: dQ/dP is constant.
Eg: Equation of a linear demand curve is: Q  a  bp
 And, the derivative of the equation is: b. Therefore,

DQ
b
Dp Where b is the slope
◦ From the Arc elasticity concept,
the elasticity of demand is:
DQ p
p
e
b
Dp Q
Q
Calculating slopes of the demand and supply curves
Assume the following markets for oranges:
Price (p) in $) Demand(q)
Supply(q)
0.20
14
0
0.40
12
0
0.60
10
4
0.80
8
8
1.00
6
12
1.20
4
16
Calculate the slope of the Demand and Supply curves
Calculating slopes of the demand and supply curves
Assume the following markets for oranges:
Price (p) in $) Demand(q)
Supply(q)
0.20
14
0
0.40
12
0
0.60
10
4
0.80
8
8
1.00
6
12
1.20
4
16
Calculate the slope of the Demand and Supply curves
Answer
• To find the slope of the demand curve, pick any two points (quantity
demanded) on it and their corresponding prices.
• For example, pick points 8 on quantity demanded and it’s corresponding
price $0.80. So, the first coordinate is (8, 0.80).
• Similarly, pick another coordinates as (12, 0.40).
• Using the slope formula, Slope of the demand curve is:
(12-8)/(0.40−0.80) = 4/- 0.40 = -10
Find the slope of the supply curve !!
Calculating Price Elasticity of Demand

The estimated linear demand function for pork is:
Q = 286 -20p
◦ where Q is the quantity of pork demanded in million kg
per year and p is the price of pork in $ per year.
◦ At the equilibrium point of p = $3.30 and Q = 220 Find
the elasticity of demand for pork:
Calculating Price Elasticity of Demand

The estimated linear demand function for pork is:
Q = 286 -20p
◦ where Q is the quantity of pork demanded in million kg
per year and p is the price of pork in $ per year.
◦ At the equilibrium point of p = $3.30 and Q = 220 the
elasticity of demand for pork:
p
3.30
e  b  20
 0.3
Q
220
Numerical example
Consider a competitive market for which the
quantities demanded and supplied (per year) at
various prices are given as follows:
Price($) Demand (millions) Supply (millions)
60
22
14
80
20
16
100
18
18
120
16
20
Calculate the price elasticity of demand when the
price is $80. When the price is $100.

Solution to Numerical example
DQ D
QD
P DQ D
ED 

.
DP
Q D DP
P
From the above question, with each price increase of $20, the quantity
demanded decreases by 2. Therefore,
DQ D  2
 DP   20  0.1.
At P = 80, quantity demanded equals 20 and
80 
ED    0.1  0.40.
20
Similarly, at P = 100, quantity demanded equals 18 and
100 
ED   0.1  0.56.
18
Some more questions

What are the equilibrium price and quantity?

Suppose the government sets a price ceiling
of $80. Will there be a shortage, and, if so,
how large will it be?
Some more questions

What are the equilibrium price and quantity?
Equilibrium price is $100 and the equilibrium
quantity is 18 million.

Suppose the government sets a price ceiling of $80.
Will there be a shortage, and, if so, how large will it
be?
With a price ceiling of $80, consumers would
like to buy 20 million, but producers will supply
only 16 million. This will result in a shortage of
4 million.
Non-linear demand function-Numerical Example
Consider the following non-linear demand function:
Q = Pα
If the value of α = -2, is the demand Price elastic or
inelastic?

Non-linear demand function-Numerical Example
Consider the following non-linear demand function:
Q = Pα
If the value of α = -2, is the demand Price elastic or
inelastic?
Solution:
Differentiating Q = = Pα
dQ/dP = α Pα-1
Therefore, E = α Pα-1 (P /Q) = (α Pα-1+1) / Q = (α Pα) / Q
Since, Q = Pα

E=α
If, α = -2, E = -2. So, the demand is Price Elastic.
What determines the Elasticity of Demand? EXAMPLE 1:
Wai Wai vs. Yogurt or curd

The prices of both of these goods rise by 20%.
For which good does Qd drop the most? Why?
◦ Wai Wai has lots of close substitutes
(e.g., Rum Pum, Mayoz etc.),
so buyers can easily switch if the price rises.
◦ Yogurt has no close substitutes,
so consumers would probably not
buy much less if its price rises.

Lesson: Price elasticity is higher when close
substitutes are available.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
EXAMPLE 2:
“Blue Jeans” vs. “Clothing”

The prices of both goods rise by 20%.
For which good does Qd drop the most? Why?
◦ For a narrowly defined good such as
blue jeans, there are many substitutes
(khakis, shorts, Speedos, or even cotton pant).
◦ There are fewer substitutes available for broadly
defined goods.
(Can you think of a substitute for clothing,
other than living in a nudist colony?)

Lesson: Price elasticity is higher for narrowly
defined goods than broadly defined ones.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
EXAMPLE 3:
Insulin vs. Caribbean Cruises

The prices of both of these goods rise by 20%.
For which good does Qd drop the most? Why?
◦ To millions of diabetics, insulin is a necessity.
A rise in its price would cause little or no
decrease in demand.

◦ A cruise is a luxury. If the price rises,
some people will forego it.
Lesson: Price elasticity is higher for luxuries than
for necessities.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
EXAMPLE 4:
Gasoline in the Short Run vs. Gasoline in the Long
Run

The price of gasoline rises 20%. Does Qd drop more
in the short run or the long run? Why?
◦ There’s not much people can do in the
short run, other than ride the bus or carpool.

◦ In the long run, people can buy smaller cars
or live closer to where they work.
Lesson: Price elasticity is higher in the
long run than the short run.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
The Determinants of Price Elasticity:
A Summary
The price elasticity of demand depends on:
 the extent to which close substitutes are
available
 whether the good is a necessity or a luxury
 how broadly or narrowly the good is defined
 the time horizon: elasticity is higher in the long
run than the short run.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
The Variety of Demand Curves

Economists classify demand curves according to
their elasticity.

The price elasticity of demand is closely related
to the slope of the demand curve.

Rule of thumb:
The flatter the curve, the bigger the elasticity.
The steeper the curve, the smaller the elasticity.

The next 5 slides present the different
classifications, from least to most elastic.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
“Perfectly inelastic demand” (one extreme case)
0%
% change in Q
Price elasticity
=
=
of demand
% change in P 10%
P
D curve:
vertical
D
P1
Consumers’
price sensitivity:
0
Elasticity:
0
=0
P2
P falls
by 10%
Q1
Q changes
by 0%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q
“Inelastic demand”
% change in Q < 10%
Price elasticity
=
=
of demand
% change in P 10%
P
D curve:
relatively steep
P1
Consumers’
price sensitivity:
relatively low
Elasticity:
<1
<1
P2
D
P falls
by 10%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q1 Q2
Q rises less
than 10%
Q
“Unit elastic demand”
10%
% change in Q
Price elasticity
=
=
of demand
10%
% change in P
P
D curve:
intermediate slope
P1
Consumers’
price sensitivity:
intermediate
Elasticity:
1
=1
P2
P falls
by 10%
D
Q1
Q2
Q
Q rises by 10%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
“Elastic demand”
% change in Q > 10%
Price elasticity
=
=
of demand
10%
% change in P
P
D curve:
relatively flat
P1
Consumers’
price sensitivity:
relatively high
Elasticity:
>1
>1
P2
P falls
by 10%
D
Q1
Q2
Q rises more
than 10%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q
“Perfectly elastic demand” (the other extreme)
any %
% change in Q
Price elasticity
=
=
of demand
0%
% change in P
P
D curve:
horizontal
Consumers’
price sensitivity:
extreme
Elasticity:
infinity
= infinity
D
P2 = P1
P changes
by 0%
Q1
Q2
Q changes
by any %
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q
Elasticity of a Linear Demand Curve
P
200%
E =
= 5.0
40%
$30
67%
E =
= 1.0
67%
20
40%
E =
= 0.2
200%
10
$0
0
20
40
60
Q
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
The slope
of a linear
demand
curve is
constant,
but its
elasticity
is not.
Price Elasticity and Total Revenue

Continuing our scenario, if you raise your price
from $200 to $250, would your revenue rise or fall?
Revenue = P x Q

A price increase has two effects on revenue:
◦ Higher P means more revenue on each unit
you sell.
◦ But you sell fewer units (lower Q), due to
Law of Demand.

Which of these two effects is bigger?
It depends on the price elasticity of demand.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Price Elasticity and Total Revenue
Price elasticity
=
of demand
Percentage change in Q
Percentage change in P
Revenue = P x Q

If demand is elastic, then
price elast. of demand > 1
% change in Q > % change in P

The fall in revenue from lower Q is greater
than the increase in revenue from higher P,
so revenue falls.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Price Elasticity and Total Revenue
Elastic demand
(elasticity = 1.8)
If P = $200,
Q = 12 and
revenue = $2400.
If P = $250,
Q = 8 and
revenue = $2000.
P
$250
increased
Demand for
revenue due
your websiteslost
to higher P
revenue
due to
lower Q
$200
D
When D is elastic,
a price increase
causes revenue to fall.
8
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
12
Q
Price Elasticity and Total Revenue
Price elasticity
=
of demand

Percentage change in Q
Percentage change in P
Revenue = P x Q
If demand is inelastic, then
price elast. of demand < 1
% change in Q < % change in P

The fall in revenue from lower Q is smaller
than the increase in revenue from higher P,
so revenue rises.

In our example, suppose that Q only falls to 10
(instead of 8) when you raise your price to $250.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Price Elasticity and Total Revenue
Now, demand is
inelastic:
elasticity = 0.82
If P = $200,
Q = 12 and
revenue = $2400.
If P = $250,
Q = 10 and
revenue = $2500.
P
$250
increased
Demand for
revenue
due
your websites
lost
to higher P
revenue
due to
lower Q
$200
D
When D is inelastic,
a price increase
causes revenue to rise.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
10
12
Q
2:
Elasticity and expenditure/revenue
ACTIVE LEARNING
Pharmacies raise the price of insulin by 10%.
Does total expenditure on insulin rise or fall?
B. As a result of a fare war, the price of a luxury
cruise falls 20%.
Does luxury cruise companies’ total revenue
rise or fall?
A.
42
ACTIVE LEARNING
2:
Answers
A.
Pharmacies raise the price of insulin by 10%.
Does total expenditure on insulin rise or fall?
Expenditure = P x Q
Since demand is inelastic, Q will fall less
than 10%, so expenditure rises.
43
ACTIVE LEARNING
2:
Answers
B. As a result of a fare war, the price of a luxury cruise
falls 20%.
Does luxury cruise companies’ total revenue
rise or fall?
Revenue = P x Q
The fall in P reduces revenue,
but Q increases, which increases revenue. Which
effect is bigger?
Since demand is elastic, Q will increase more than
20%, so revenue rises.
44
Thank you