Econ 1000 lecture 4:
Elasticity
C.L. Mattoli
(C) Red Hill Capital Corp, Delaware USA
2008
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This week


Mod 2, part 3
Chapter 5: Elasticity
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2008
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Learning objectives: Mod 2
On successful completion of this module
(lecture 3 of the module), you should be able
to:



Explain the concept of elasticity
Calculate and interpret price, income and
cross-price elasticity of demand
Calculate and interpret price elasticity of
supply .
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Introduction


1.
2.

We have talked, in general terms, about
demand and supply schedules and curves.
We have discussed opportunity costs:
When a consumer buys one thing, he will
not have money for others.
When a producer decides to produce one
thing, he will forego the opportunity to
produce other things.
The real question is how important is one
thing versus the other opportunities.
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Producer motivations



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Producers (suppliers) are in business to
make a profit.
In that regard, they would like to get as high a
price as they can for a good or service.
On the other hand, they know what minimum
price they can offer goods in certain
quantities and still make a profit.
They need to understand how consumers will
react to different prices, in order to arrive at
proper prices for marketing their wares.
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Psychology & Logic of Econ




Think about how things affect each other,
how they interact.
Think about how people are.
For example, if the price of coca cola goes
up, some people will just switch to Pepsi, if
it’s price didn’t change … it’s just human
nature.
Thus, the availability of substitutes will affect
how demand will change as prices go up and
down.
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Psychology & Logic of Econ



You don’t have much of a choice about who
will supply your electricity, if you live in a city
… you can’t get by on batteries.
If there are barriers to entry for an industry,
high prices will be charged, until other people
break into the market and compete and lower
the excess profits.
A change in the price of one vegetable will
affect the supply of other vegetables. There
is only so much farming land, and farmers will
allocate according to their profit expectations.
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Psychology & Logic of Econ
With a lot of things, the more you do
it, the less pleasure you get out of it.
You eat out, and you eventually get
saturated with eating out. But if the
price was lowered, you might go back
for more.
 You only have so much money, and
you have to allocate it according to
your needs and desires.

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Revenue and how is it shown in the
market model
Price
What happens to revenue
when demand changes?
S0
Revenue goes up when demand goes up
P0
P1
D0
D1
Q1
Q0
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Quantity
9
Revenue and how is it shown in the
market model?
Price
What happens to revenue
when supply changes?
S0
S1
Not as clear
P0
P1
D0
Q0
Q1
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Quantity
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The importance of percentages
Often, in finance and economics, we
are more concerned with percentages
and percentage changes than with
raw numbers or absolute number
changes.
 That is because percentages give us
a better basis for comparison, in
many cases.

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The importance of percentages

For example, it is not so important that
someone made $100 on an
investment. What is more important is
to ask how much did she invest to
earn the $100. If she invested $100 to
earn $100, then the return on
investment was Income/investment =
$100/$100 = 100%. If the investment
was $10,000, the return on investment
was $100/$10,000 = 1%. The
percentage number was much more
interesting.
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The importance of percentages

The same is true about growth in GDP
(gross domestic product). If one country’s
GDP growth was $100 million last year
and another country's growth $1 trillion,
the next question to ask is how much total
did the countries have in GDP. Then, we
can compute a percentage growth rate,
and we will better be able to compare the
growth rates in GDP of the two
economies.
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The importance of percentages
 We
looked at the general concepts
of supply and demand: quantity
demanded should be a
decreasing function of price,
while quantity supplied should be
an increasing function of price.

But how will those quantities vary
exactly with price: that is an important
question.
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The importance of percentages
To begin our next stage of economic
analysis, elasticity, we will look, more
precisely, at how quantities vary with.
To do that, in a meaningful way, we
will …. You guessed it…. Use
percentages.
 Elasticities look at percentage
change of one variable with respect
to percentage change of another.

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Elasticity of Demand
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Price Elasticity of demand


The law of demand says that the quantity
demanded, QD(P), is a function of price,
P, and QD(P) is decreasing with increasing
price.
The question is: how much will QD change
when price changes. That will be a
valuable piece of information for suppliers to
know. Then, they can pick up their own
pencils, and figure out whether or not
production should be done, at what price,
quantity, and what cost.
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Price Elasticity of demand

Instead of using the ordinary variation of QD
with P, i.e., ΔQD/Δ P, consider the
percentage change of quantity, ΔQD/ QD,
versus the percentage change in price, Δ
P/P.
ED = Elasticity of demand
= [percentage change in quantity
demanded ]/ [percentage change in
price]
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Price Elasticity of demand
= [ΔQD/ QD ]/[Δ P/P]

In that regard, we are looking at
percentage change in the number of
units purchased caused by a one
percent change in price.
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Elasticity of demand exampled


Suppose that we made observations that
found that Kangda college’s enrollment will
drop by 20%, if the price of tuition
increases by 10%.
Then, we could calculate the elasticity
coefficient of demand =[percentage change
in quantity demanded ]/ [percentage change
in price] = [ΔQD/ QD ]/[Δ P/P] =
%ΔQD/%ΔP = (-20%)/(10%) = -2.
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Elasticity of demand exampled
It will always be a negative number
since, if price goes up, quantity
demanded goes down, and vice
versa.
 That’s just human nature.
 So, we usually just say that the
elasticity coefficient is equal to 2.

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What it means to a supplier



What that means to the supplier is that, if
he increases or decreases the price by
1%, he will experience a an opposite
change of 2% in the number of units that
he will be able to sell.
That will affect his total revenues, which
are equal to QxP = Total Revenue = RT.
For example, assume that the price for
tuition at Kangda is currently $50,000 per
year = P0, and that there are 5,000
students = Q0. Then, RT0= Q0xP0 =
$50,000x5,000 = $250 million.
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What it means to a supplier



Next, suppose that we try to increase the
price by 1% = $50,000 x 0.01 = $500 to P1
= $50,500.
Then, according to the elasticity coefficient
of 2, enrollment will decrease by 2% = 100
to 4,900.
In that case total revenue will be RT =
$50,500x4,900 = $247,450,000, which
means that the supplier has lost revenue
of about $2.5 million, which is no small
amount of money.
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What it means to a supplier


What that means is that, in order to be
ahead of the game by raising prices, he
will also have to raise his profit margin
enough to more than compensate for his
loss in revenue.
For example, assume that he had a profit
margin of 10%, originally. Profit margin =
PM = profit/revenue = 10%. Then, his
original profit would be profit = E0 = RTxPM
= $250,000,000x10% = $25,000,000.
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What it means to a supplier



For the supplier to break even on profits,
his new profit margin needs to be
$25,000,000/$247,450,000 = 10.1%.
Therefore, the supplier will have to look at
his pro-forma profit margin before he can
make a decision to raise or lower prices.
In the end, it will be his own internal
costs and marginal cost considerations
that will allow him to make a decision
about what price he should charge to
maximize his profits
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Mathematically: total revenue change


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Total revenue equals price time quantity
demanded: RT0 = Q0xP0
Q1 = Q0 + ΔQ ; P1 = P0 – ΔP since price and
quantity demanded will have opposite signs.
The variation of total revenues with respect to
price is given by: Δ RT /ΔP = P x[ΔQ/ΔP] +
QxΔP/ΔP = P x[ΔQ/ΔP]
And Δ RT /ΔP = [Q0xP0 – Q0xΔP – ΔQxΔP +
ΔQxP0 – Q0xP0]/ΔP = – Q0 – ΔQ + ΔQxP0/ΔP =
– Q1 + P0x ED. So what?...
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Mathematically: total revenue & elasticity
If we want to find the condition for
increasing total revenue, that means that
the change in revenue should always be a
positive number. In algebra, we require:
Δ RT /ΔP > 0.
 So, Δ RT /ΔP = P x[ΔQ/ΔP] + Q >0
 Rearranging the symbols in the equation,
we get ΔQ/(ΔP/P) > – Q

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Mathematically: total revenue
Or, (ΔQ/Q)/(ΔP/P) = %ΔQ/%ΔP = ED >
–1
 Thus, in order for R to increase with
increasing P, E must be less than 1 in
size.
 Demand must be price inelastic.
 We shall take a closer look at revenues,
in the next module.

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The problem with elasticity calculations


When we actually do calculations, we are
not dealing in abstract equations or perfect
continuous curves. We will usually deal
with a finite number of pairs of quantity
and price, (Qi,Pi), in a demand schedule or
a table.
Suppose we know two points in the
demand schedule between which we want
to calculate elasticity: (Q1,P1) = (400,$10)
and (Q2,P2) = (440,$9.50).
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The problem with elasticity calculations


Then, we can calculate the percentages
two different ways.
If we assume that prices fall and we want
to know how much demand will rise, we
quite naturally choose the starting
points as (Q1,P1) = (400, $10) and
calculate the percentages changes from
those starting points of price and quantity,
so elasticity = ED = [(440 –
400)/400]/[($9.50 – $10)/$10] = 2.
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The problem with elasticity calculations


If, on the other hand, we want to look at
what would happen to a price increase
from $9.50 to $10, we would naturally use
starting point of (Q2,P2) = (440,$9.50).
Elasticity is, then, [(400 – 440)/440]/[($10
– 9.50)/$9.50] = 1.72.
So, we get two different answers,
depending on how we calculate: which
point we start at.
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Elasticity: Mid-point approximation


The simple cure to this problem, in
economics, is to use an average of some
sort,
After all, right now we are imagining
that we do not care if price goes up or if
price goes down by 1%, we want one
number for the percentage quantity that
will either be retracted from or added to
demand, as a general result.
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Elasticity: Mid-point approximation


Moreover, since we are using 2 discrete,
separate points, not even in a real curve,
what we are really doing in our actual
calculation of elasticity is to measure an
approximate value at the mid-point on
the actual curve that would exist, if we had
mounds of minutely-detailed data for
quantity and price.
Thus, economics, as done in this course,
will use a mid-point average value that is
calculated in the following manner:…….
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Elasticity: Mid-point approximation
1.
2.

Take the mid points for both quantity and for
price, which are simple averages ΔQD/ [(Q1D
+ Q2D)/2] and ΔP/ [(P1 + P2)/2].
Then, use percentages based on the mid-point
as: mid-point elasticity approximation:
%ΔQD/%ΔP = {ΔQD/ [(Q1D + Q2D)/2]}/{ ΔP/
[(P1 + P2)/2]} ={ΔQD/ (Q1D + Q2D)}/{ ΔP/ (P1
+ P2)} because the 2’s on top and bottom
cancel.
We demonstrate some of these concepts,
pictorially, in the next slide
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Graphical Approximations


First, look at elasticity along the dashed line.
That is actually what we are using to calculate
the approximate elasticity.
It is approximately the
Demand Curve
P
same line as the dotted line
that is tangent to the actual $10.50
curve at the mid-point, more $10
or less, so we use the mid$9.50
point to calculate it.
Notice, also, that on a real $9
demand curve the elasticity
will change at different
points o the line. (C) Red Hill Capital Corp, Delaware USA
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400
QD
440 480 520
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Graphical Approximations
 For example, if we calculate mid-point
Elasticities between $9.50 and $10, we get E =
[(440-400)/ ((440+400)/2)]/[($9.5-$10)/
((9.5+10)/2)] = 1.86
If we calculate between $9
P
and $9.5, we get E = [(520$10.50
440)/((530+440)/2)]/ [(9$10
9.5)/((9.5+9)/2)] = 3.08.
$9.50
So, demand is more
responsive to changes in
$9
price as price decreases, in
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this case.
2008
Demand Curve
QD
400
440 480 520 36
Elasticity classifications

1.

We classify elasticity into 3 basic categories:
Elastic demand, ED > 1, means that the
percentage change in quantity demanded
changes more than the percentage change in
price. Thus, a reduction in price will cause
total revenues to increase; a rise in price will
cause total revenues to fall.
So, if elasticity of demand for Kangda college is
1.5, enrollment is 5000, and the price increases
by 10% from $50,000/year to $55,000, then,
enrollment will decrease by 1.5x10% = 15%.
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Elasticity classifications

2.

Enrollment will fall to 5000x85% = 4250, and
total revenues will fall to from 5,000x$50,000 =
$250 million to 4250x%55,000 = $233,750,000.
Unitary elasticity, ED = 1, is a special case in
which the percentage change in quantity
exactly equals the percentage change in price.
In this special case, total revenues are completely
insensitive to changes in price.
Total revenue for Kangda will remain at $250
million, no matter what price is charged for
tuition.
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Elasticity classifications
3.


Inelastic demand, ED < 1, means that the percentage
change in quantity demanded will be less than the
percentage change in price. That means that total
revenues will increase when price increases but will
decrease when price decreases.
In this case, if Kangda has an elasticity of 0.75, and it
decides to raise its tuition from $50,000 to $60,000, a
20% price hike, it will only lose 15% (=0,75x20%) in
enrollment, from 5000 to 4250, and total revenues will
rise to $255 million.
We show graphical examples of the three cases in the
next 2 slides.
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How does the relative elasticity affect
changes in producer revenue?
Price
($)
Inelastic = revenue increase with price
increase & vice versa
90
70
D0
1000
1400
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Quantity/wk
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3 Types of elasticity

The general shapes of elasticity graphs (see page
120 of the textbook) and their causal chains.
Price
decrease
Elastic
Total
Revenues
Increase
Price
decrease
Total
Revenues
unchanged
Unitary Elastic
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Price
decrease
Total
Revenues
decrease
Inelastic
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Elasticity extremes



There are also extreme cases for elasticity:
perfectly inelastic, ED = 0, and perfectly elastic,
ED = ∞. These are limiting cases for the index.
Perfectly elastic demand corresponds to a
demand curve that is perfectly horizontal (slope
of Q(P) = ∞). So, if tuition is $50,000 and is
perfectly inelastic, a change in tuition to
$50,000.01 will result in zero enrollment.
Perfectly elastic is the limiting case in which an
infinitesimally small change in price will result
in an infinite change in quantity demanded.
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Elasticity extremes



Perfect inelasticity is the opposite
extreme. In that case a change in price
results in no change in quantity demanded.
The demand curve is totally vertical (slope
of Q(P) = 0), and demand is limited to an
exact quantity.
Perfect inelasticity is the limiting case in
which a change in price causes no change
at all in quantity demanded.
We show example graphical representations
of these extremes, in the next slide.
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Graphical Perfect elasticity



Perfect elasticity
P
can be represented
by a flat demand
curve. Then,
change in price
results in an
infinite change in
demand.
There is only one
price
ED = ∞
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Q
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Graphical Perfect inelasticity



Perfect inelasticity P
can be represented
by a vertical
demand curve.
Then, change in
price results in no
change in demand.
There is only one
quantity
ED = 0
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Q
45
Elasticity variations on a line


Since elasticity is percentage change versus
percentage change, it is different from the
slope of a line, and elasticity may vary along
demand curves.
Thinking at the extremes, when price is very
high and quantity demanded is small.
Then, a change of one unit of quantity
demanded is a large percentage change,
while a change of price by $1 will be a small
percentage change, so that demand is very
elastic.
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Elasticity variations on a line

When price is low and the quantity
demanded is already large numbers of
units, a $1 change in price is a large
percentage change, while a unit change in
quantity demanded is a small percentage
change. Thus, demand at that end of the
curve will be very inelastic.

In between those extremes will come a
turning point at which elasticity of demand will
be unitary.
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Elasticity variations on a line
Actually, it will, in particular, vary
along a straight-line demand curve.
 We show this varying type of elasticity
for a line, in the next slide.
 In the slide we show demand for
DVD’s from a street vendor.
 In the upper region, it is elastic; in the
lower, inelastic

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Elasticity variations on a line
Demand Schedule
Demand for DVD’s
40
MidQuantity
Total
point
Price demanded Revenues Elasticity
Elastic: E>1
35
30
25
Unitary elastic: E=1
20
15
$40
0
$0
Inelastic: E<1
10
5
35
5
175
15.00
0
0
30
10
300
4.33
25
15
375
2.20
10
20
30
40
50
Total Revenues
450
400
20
20
400
1.29
350
300
15
25
375
0.78
250
200
10
30
300
0.45
150
100
50
5
35
175
0.23
0
0
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10
20
30
40
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Break time


Please take a 10 minute break.
Come up and ask questions, if you have any.
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Determinants of Price
Elasticity of Demand
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Elasticities for goods and services


In truth, at least because of inflation, prices
of most things change over time. Thus,
we can expect that most things will have
long-term and short-term elasticities that
might be very different.
Elasticities are one thing that economists
like to keep track of, so we can look at
elasticities of some common goods and
services to see some real examples (see,
also, page 126 of the textbook).
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Elasticities for goods and services

1.
2.
3.
4.
5.
6.
According to some estimates, we have the
following approximate elasticities of demand:
Automobiles: 2, elastic
Gas for automobiles: 0.5, inelastic
Automobile tires and tubes: 1, unitary elastic
Jewelry and watches: 0.5, inelastic
Movies: 0.9, short-term inelastic; 3.7, longterm elastic
Medical care: 0.3–0.9, inelastic
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ED: availability of substitutes




The most important element of electricity
of demand is the availability of
substitutes.
Demand, quite naturally, will be more
elastic for goods and services for which
there are close substitutes.
Then, if the price of the good or service
changes, people can and will switch to
the substitute.
Again, it is simple human nature, logic &
psychology.
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ED: availability of substitutes



For example, if the price of cars goes up,
people can switch to riding buses, trains,
bicycles, or they can walk.
Indeed, the more public transportation
that is available, the more elastic will be
the demand for automobiles.
If you live in the middle of nowhere, and
you have no car, your opportunity cost
will involve all of the time that you spend
walking from one place to another.
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ED: availability of substitutes


Of course, the question of available
substitutes depends on how broadly or
narrowly we define the market.
For example, the elasticity of demand is
different for Ford automobiles than for
some other automobile makers and
automobiles, in general, because all of the
other automobiles by other manufacturers
are additional substitutes for Fords.
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ED: percentage of consumer budgets



On the other hand, if there are no close
substitutes, then, demand will be more
inelastic.
For example, there are no close substitutes
for gasoline for automobiles. Thus, the
demand for gasoline is fairly inelastic.
For an item, like salt, which represents a very
minor item in a person’s budget, the price
could double, and most consumers would not
bat an eye: it is so inexpensive and will
remain so, in comparison to an overall
consumer budget.
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ED: percentage of consumer budgets




Thus demand for small percentage items
will be inelastic.
On the other hand, if the price of home
purchase or meals at expensive restaurants
were to double, demand for those items
would drop substantially.
They have very elastic demand because
they represent a larger portion of a person’s
budget.
In general, the elasticity coefficient varies
directly with the percentage that an item
represents in the budget.
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Response to price changes over time
As we have seen in examples in the
lecture and can see on page 126 of
the text, there are short-term and
long-term elasticities.
 Elasticity can even change character
between the short run and the long
run, going from, e.g., inelastic in the
short-run and elastic in the long-run.

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Response to price changes over time



The explanation of this can be looked at in
terms of people’s mentalities and the
availability of substitutes.
In some cases, people cannot accept change,
immediately, but over time they can adjust,
mentally.
Because they are used to driving back and
forth to work, alone, the immediate response to
a hike in gasoline prices is to keep going the
way they have been.
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Response to price changes over time
As the high price persists, they will begin
to cut back on little trips to the store.
 They will slow speed to save gasoline.
 They may form car pools and drive
together.
 They might stop being so stubborn and
decide that a bus or a train is not such a
bad alternative to driving.

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Response to price changes over time



The next time they buy a car, they will
seek one that is more fuel efficient.
Thus, their demand elasticity while fairly
inelastic in the short-run, becomes less
inelastic in the long-run.
Demand for movies is inelastic in the
short-run (0.87) because everyone wants
to see the new movie when it previews.
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Response to price changes over time



Over time, however, the excitement
diminishes. Friends tell you about their
experience at the movie. You keep thinking
that someday, maybe you should see it, but it
becomes less important, and demand
becomes very elastic (3.67).
Indeed, as a price change persists, there
might be greater efforts to find substitutes or
to invent them.
In general, the price elasticity of demand
increases with time the longer a price
change persists.
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Opportunities




You have a certain amount of earnings each
month.
You allocate that among choices. The choices
that you give up to take others are your
opportunity costs.
For a particular good, a substitute that you gave
up to get that good is your opportunity cost.
As the price of a good goes up relative to
substitutes, the opportunity cost of continuing to
buy that good increases in terms of the others.
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Airline ticket pricing: an example of
complicated elasticity of demand to price


Airline ticket pricing can seem particularly
complicated and convoluted, but, if we think in
terms of price elasticity of demand, people’s
convenience, and inflexibility, we will understand
that the designers of the pricing scheme are very
crafty.
Most people might not like the idea of getting up
early in the morning to ride on a plane, so unit
demand at those hours is very flexible to changes in
price.
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Airline ticket pricing: an example of
complicated elasticity of demand to price



Thus, demand is elastic, and the airlines make
prices cheap at such slow times of the day to
induce people to fly.
At busy times of the day, demand is inelastic, so
airlines can charge higher prices.
Similar pricing patterns can be observed on longer
time scales. For example a trip from GZ to Xi’an
was 40% of the normal price in early January, but
as the Chinese New Year approached, the price
went up to 90%. If you book ahead three months
before the May holiday, you can get 40%.
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Airline ticket pricing: an example of
complicated elasticity of demand to price

Those longer term pricing policies reflect
inelastic demand for urgent, lastminute travel and more elastic demand
for longer term travel planning. The
airline induces people to book early and
penalizes those that it can: those who
have no choice but to travel on lastminute plans.
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Other Elasticities
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Elasticity, in general


As we discussed, earlier, elasticity is
simply a specialized measure of change in
one variable with respect to another.
Sometimes, the ordinary slope, ΔY(X)/ΔX,
the change in Y, a function of X [Y(X)],
with respect to a change in X is an
appropriate measure.
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Elasticity, in general


In other case, however, especially in
economics and finance, percentages and
percentage changes are more appropriate
measures to analyze a problem.
Thus, the general concept of elasticity,
percentage change of a variable with
respect to percentage change of another
variable, can arise as an appropriate
measure in other circumstances.
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Income elasticity of demand
An important non-price financial factor
in demand is income.
 Indeed, we have discussed that there are
even two separate categories of goods,
normal and inferior, that respond in
opposite manners to changes in income.

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Income elasticity of demand


Thus, in order to examine how consumption
responds to changes in income, economists
look at income elasticity of demand.
Income elasticity of demand is defined as the
percentage change in quantity demanded with
respect to percentage changes in income, Y
(the standard symbol for income in econ), EY
= %ΔQD/%ΔY ={ΔQD/ (Q1D + Q2D)}/{ ΔY/
(Y1 + Y2)}.
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Positive and negative income elasticity



Unlike the case of price elasticity of demand, which was
always a negative number, income elasticity of demand
will be positive for normal goods, EY>0, and negative
for inferior goods, EY<0.
In that regard, we could classify normal goods as those
whose income elasticities of demand are positive and
inferior goods as those whose income elasticities are
negative.
In any event, it will be useful to know what will happen
to demand for any good or service when income changes
since income changes all the time, and it can particularly
change in times of general economic downturns:
recessions.
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Income demand elasticity exampled


Suppose that it is found that the quantity demanded of
illegal DVD’s in Guangzhou increases from 10,000 per
month to 15,000 per month when monthly income
increases from $1,000 to $1,250 or inferior.
Then, we can find both the income elasticity and its sign
to discover the good’s true nature: normal or inferior…
EY = %ΔQD/%ΔY ={ΔQD/ (Q1D + Q2D)}/{ ΔY/ (Y1 + Y2)}
= [(15000–10000)/(15000+10000)]/[(1250-1000)/(1250+1000)]
= +1.8
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Income demand elasticity exampled




Thus, in this mid-point approximation, an 11%
average change in income results in a positive
20% average change in quantity of DVD’s sold.
Thus, illegal DVD’s are a normal good with
fairly responsive demand versus income changes
in a positive manner.
In the end-point calculation, the elasticity is 2,
which is fairly positively elastic, and elastic, in
the case of a positive elasticity is a good thing.
Income elasticity can be different in the long and
short runs, becoming either more or less elastic.
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Recessions: not necessarily a bad thing.




Although the bite of a recession, a downturn in
economic activity, causes many people to suffer
decreases in income, others prosper.
While sellers of luxury automobiles, expensive
jewelry, and ritzy restaurants will see lower
income in recessions, sellers of so-called inferior
goods, like cheap used cars or generic brands of
food and drugs, will see a rise in their unit sales.
Normal goods have a negative income elasticity
of demand: when income falls, unit demand rises.
At least recessions can be good for sellers of
inferior goods.
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Normal or inferior



In the table on page 129 of the textbook, only one good,
potatoes, showed a negative elasticity of income for the
long-term.
For most of the other limited items on page 129, elasticity
is positive, and, except for automobiles and furniture,
most of the elasticities are larger in the long-run than in
the short-run.
Other goods and services that we might imagine as
having negative income elasticity are bus rides, used
cars, cheap restaurant meals, retread tires, hamburger
helper, and other things that people buy because they
cannot afford to buy a better substitute.
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Children: normal or inferior



It has been observed, especially over the last
century, that two trends have emerged in the
world.
As the world entered the industrial age, people’s
incomes have grown substantially, on the one
hand, and the number of children in families has
decreased.
As economists, we would conclude, ceteris
paribus, that the demand for children seems to
react opposite to change in income.
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Children: normal or inferior


If that is truly the case, then, children would seem
to be inferior goods.
Some economists might argue that there are so
many other factors that affect family size, others
would point out that there might be a connection
to the prices of complementary goods for
children, like clothing, food and education, have
also risen, and that these price changes have also
contributed to the decrease in demand for
children.
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Children: normal or inferior


You might also think of other factors that can affect
demand for children. Children provide satisfaction for
parents, but with rising income, there are many other
choices of satisfying goods available for parents to
purchase, like expensive vacations and luxury
automobiles. In the past, children were also a free source
of labor to, for example, help with farming, but with
farms gone, and better jobs supplied by other people,
again, the demand for children is diminished.
In any event, we might conclude that children are inferior
goods.
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Cross-elasticity of demand



Another factor that we learned can affect
demand for one good or service is prices of
other goods or services.
Again, in this case, we have two different
categories of goods: substitutes and
complements.
Thus, we can apply the elasticity concept to
examine responsiveness of quantity demanded
of one good based on price changes of other
related goods.
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Cross-elasticity of demand


Given those circumstances, we can define the
cross-elasticity of demand as the percentage
change in quantity demanded of one good
corresponding to a percentage change in the
price of a related good or service:
EC = %ΔQX/%ΔPY ={ΔQX/ (QX1 + QX2)}/{
ΔPY/ (PY1 + PY2)} is the cross-elasticity of
demand for good X versus change in price of
good Y (mid-point formula).
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Complement or substitute: what’s your
sign?


Thus, the general rule is that cross elasticity
for substitutes is a positive number.
As in the case of income elasticity, cross
elasticity can be positive or negative: the sign
will distinguish between the two categories of
goods whose prices can affect the quantity
demanded of the good in question.
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Complement or substitute: what’s your
sign?


Consider that if Coke raises its price by 10%
and as a result, ceteris paribus, consumers buy
5% more Pepsi. Then, the cross elasticity of
demand for Pepsi with the price of Coke is EC
= +0.5.
Next, suppose that the price of motor oil to
lubricate automobile engines rises by 50%, and
as a result the quantity demanded for gasoline
declines by 1%.
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Complement or substitute: what’s your
sign?



Motor oil and gasoline are complements. You
need to keep your engine lubricated, if you are
going to drive your car. The more you drive,
the more motor oil you need.
The characteristic of complement is also
displayed in the cross-elasticity result as a
negative sign.
Thus, the cross elasticity of demand for gas
with respect to price of motor oil is EC = (–
1%)/(50%) = – 0.02, a negative number.
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Elasticity of Supply
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Elasticity of supply
In studying elasticity of demand we
already discovered some useful
information for suppliers: how total
revenues will vary with price.
 Just as price affects consumer sentiment
about purchasing goods and services,
price is an important factor to a
supplier.

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Elasticity of supply


Indeed, in the case of supply, the price will
determine whether or not the supplier can
make a profit on his sales. That is why he has
chosen to be in business, and if he cannot
make profits, he will exit the business, and
supply will decrease definitely.
In the next chapter, we will begin to study the
cost side of production and supply and see how
cost interacts with price and profits.
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Elasticity of supply


For now, we can look at things from the
outside by defining the elasticity of supply
as the percentage change in quantity supplied
resulting from a certain percentage change in
price: ES ={ΔQS/ (Q1S + Q2S)}/{ ΔP/ (P1 +
P2)}.
Intuitively, elasticity of supply should
always be a positive number. If price
increases, a supplier should be willing to
supply more, not less. The same for a price
decrease: if the price is cut, a supplier should
be willing to supply less, not more.
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Elasticity of supply
Supply is elastic when ES>1, unit elastic
when ES=1, and inelastic when ES<1.
 As in the case of elasticity of demand,
supply elasticities will be different in the
sort-run and in the long run. Price
elasticity of supply will, in general, be
more elastic in the long run, so the longrun supply curve will be flatter.

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Elasticity of supply
 In
chapter 7, we discuss how the time
factor is a major determinant in the
shape of the supply curve.
 Here, we will look at one cost in
supply, taxation, how it affects
supply, and how governments use
elasticity to design taxation
schemes that will bring them a lot of
revenues.
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Graphical supply elasticity

We show the 3 general cases of price elasticity of
supply, in the extremes.
Perfect Elastic
Unit Elastic
Perfect Inelastic
P
10%
10%
QS
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Taxation and supply elasticity



Governments get the bulk of their income from
taxes.
Comprehensive coverage taxes, like the GST, the
goods and services sales tax, are generally a small
percentage, like 5% so as not to be too large a
factor in discouraging demand. They usually
also exempt necessities, like food, clotting, and
shelter, to name a few, so as not to affect demand
for things that people need to live.
Thus, governments consider welfare and other
economic factors when designing tax systems.
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Taxation and supply elasticity



Excise taxes are taxes imposed on sellers of
certain goods and services, and they are usually
substantially higher than sales tax on regular
goods.
These taxes are on items that the government has
deemed as harmful or in some way bad for
society, anyway, like alcohol, cigarettes, and
gasoline, but they also display inelastic demand.
So demand will be little affected by the additional
tax on the item, and tax revenues can be fairly
certain.
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Excise tax: who really pays?



You could say that the seller pays since he
is the one who pays the tax.
Economists use the elasticity concept in
this problem to analyze the question of
who really pays: the consumer or
supplier?
Tax incidence is the portion of tax paid by
consumer or seller.
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Who pays example




Tax incidence will depend on both
elasticities of supply and demand.
The more inelastic supply, the more is
paid by seller.
The more inelastic demand, the more is
paid by the buyer.
Suppose that there is initially no excise tax
on gasoline, and the equilibrium price is
$1.00/liter.
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Who pays example




Next, suppose that the government installs
an excise tax of $0.50/liter.
Elasticity of demand with respect to price will
tell part of the tale.
If demand is completely inelastic, then, all
of the cost will be born by the buyer, even
though the tax was imposed on the seller
If demand has elasticity, the tax burden will
be shared between consumer and the seller.
(see next slide)
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Who pays example


Who pays excise tax?
Supplier adds excise tax to his price and shifts the
supply curve up $0.50 at every price
More Inelastic demand
Total inelastic demand
More paid by buyer
All paid by buyer
Less paid by seller
None paid by seller
Buyer
Seller
Buyer
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Who pays Example

As elasticity of supply becomes more vertical
(inelastic) and elasticity of demand becomes
more horizontal (elastic), the tax burden is
shifted to seller
12
10
8
Paid by
buyer
6
Paid by
seller
4
2
0
0
25
50
75
100
125
150
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200
99
Who pays example



Thus, if demand is completely inelastic, the buyer
will bear all of the tax burden.
If the demand curve is upward sloping, the new
supply curve will intersect the old demand curve
at a quantity that would have been supplied at a
price, $0.50 lower than where the new
equilibrium is.
In that sense, the final equilibrium price will be
below $1.50, and the cost of the tax will be split
between consumer and seller.
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Taxes and markets



In general, taxes will distort market outcomes and
result in prices that are too high and output that is
too low.
Thus, imposing taxes can lead to inefficient
markets when the object is tax revenue and
disincentive for consumers to engage in bad
things.
However, we have also seen the case, in the last
section, whereby taxes are used as a disincentive
for suppliers to stop doing bad things or at least
pay for the damage that they are inflicting on
others, like in the case of pollution.
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Tax, Equilibrium P&Q, and Revenues
Price
S1
Tax Revenues
S0
Initial producer revenue
PT
P0
Revenues after tax
P-T
D0
QT
Q0
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Quantity
102
Summary of Elasticities
%ΔQD/%ΔP
%ΔQA/%ΔPB
%ΔQD/%ΔY
%ΔQS/ %ΔP
Price
elasticity of
demand
Crosselasticity
Income
elasticity of
demand
Elasticity of
supply
Profit
Substitute/ Normal/
change with Complement Inferior
price
change
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Greater in
Long Run
103
In the end



In the end, economics is about wants
being fulfilled by businesses.
The price charged for something will
cause less people to want it, as price
increases, while a higher price will be
viewed favorably by business.
The market, left to its own devices, will find
an agreeable price at which sellers are
willing to supply exactly the amount that
buyers wants. Then, the market will clear.
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In the end


Although we might think that as price
increased, indefinitely, suppliers would be
better and better off, in this lecture, we
learned that there will be a maximum
price, after which total revenues begin to,
again, decrease.
That is a result of the demand equation.
The limit to total revenue is strictly a result
of demand, and is out of the immediate
control of the seller, although he might try
to create more demand.
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In the end
That maximum revenue means that
profit margins must be able to be
increased, enough, by the unit price
rise, to overcome the decrease in
total revenues since RT = Price x
Quantity , profit margin = PM =
profits/revenues , profits = profit
margin x revenues.
 Our next step will be to examine the
cost side of the supplier’s equation.

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In the end



Then, we will have to find out if there is
a maximum point for profits, beyond
which a supplier will not increase
supply.
We will have to see how costs, on the
supply side, interact with revenues
generated by the demand side.
Then, we will have a more clear picture
of economics, through the operation of
the businesses at its base.
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Exam-caliber questions
1.
2.
For excise taxes, If supply is vertical, all tax
is paid by consumer; if demand is horizontal,
all tax is paid by the producer. Can you
describe, in words, and show, in pictures,
how tax incidence varies with changing
elasticities of supply and demand?
Governments tend to impose excise taxes
on social or economic “evils”, like smoking,
alcohol, and traffic violations. Discuss at
least 3 general reasons that a government
would want to tax such things.
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How Smart are You
3.
We said that it is a concave curved demand
line that can display unit elasticity
everywhere. Can you show that any
straight-line supply curve that passes
through the origin (P=Q=0) is everywhere
unit-elastic?
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Homework

Chapter 5
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End
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