Elasticity...
…is a concept that relates the responsiveness
(or sensitivity) of one variable to a change in another
variable.
• Elasticity of A with respect to B =
%
change in A / % change in B
• Elasticity answers the question of how much one
variable will change when another one changes.
With elasticity we will be able to answer the question:
If the price of a good increases by a certain amount, then
how much will the quantity demanded decrease by
because of this.
Why is elasticity important?
Importance of elasticity
• Many business and economic decisions are not
based on if something will happen, but buy how
much will it change by:
Example: How much should business firms raise or
lower their prices and by?
Will total revenue (this affects profit) go up or down
when price increases? By how much?
• The effects of public policy will be different
depending on the elasticity of the good in question…
…for example: How much will the price of a good
increase if a tax is placed on it?
Price Elasticity of Demand...
...measures the responsiveness of quantity demanded (QD)
of a good to the change in the price of the good (P).
• Price elasticity of demand =
% change in QD / % change in P.
• It is a number(unit free measurement) that represents
the % change in QD for a 1% change in price.
• Example: Suppose the price of a good rises by 5%. We
observe that the quantity demanded declines by 10%.
The price elasticity of demand is -10% / 5% = - 2.
• This means for every 1% change in price, the quantity
demanded of this good will change by - 2%.
Calculating elasticity
Sometimes we must first find the % change in a variable from
some absolute numbers to calculate elasticity
• Example: Suppose the price of a Fore Golf car is
$10,000 and Fore sells 500,000 of them.
• Fore then raises it’s price to $11,000. The next year they
find they have sold 465,000 Golf cars
• What is the price elasticity of demand for Fore Golf
cars?
• Price elasticity of demand =
% change in QD / % change in P
• We can use what is called the mid-point formula to
calculate the % change in QD and P...
…the mid point formula uses the average of the beginning
and ending values to calculate the % change
Calculating elasticity
Price elasticity of demand = % change in QD / % change in P.
% change in QD = change in QD / average of the 2 quantities
% change in QD = Q2 - Q1 / {(Q2 + Q1)/2} x 100%
% change in QD = 465,000 - 500,000 / {(465,000 + 500,000)/2} x 100%
% change in QD = -35,000 / 482,500 x 100%
% change in QD = - 7.25%
% change in P = change in P/ average of the 2 prices
% change in P = P2 - P1 / {(P2 + P1)/2}
x 100%
% change in P = $11,000 - $10,000 / {($11,000 + $10,000) / 2} x 100%
% change in P = 1,000 / 10,500 x 100%
% change in P = 9.52%
Price elasticity of demand = - 7.25 / 9.52 = - 0.76
Interpretation: A 1% increase in Fore Golf Cars will reduce
their quantity demanded by 0.76%
This calculation can be reduced to a more manageable
formula:
Price elasticity Q2 - Q1
of Demand = Q2 + Q1
P2 + P1 465,000 - 500,000 $11,000 +$10,000
x
=
x
P2 - P1 465,000 + 500,000 $11,000 -$10,000
=
=
- 35,000
965,000
- 0.0363
x
x
$21,000
$1,000
21
- 0.76
• Importance: Given any 4 of the above variables you can always
find the 5th.
• Suppose Fore Golf want sell 550,000 (instead of 500,000) cars and
know the elasticity is -0.76. If the original price was $10,000 you
can find the price they must charge to sell 550,000 cars!
• Once a firm estimates it’s price elasticity it can estimate changes
in sales from a price change; or to reach a sales target, estimate
how much to cut prices.
=
Price
Given any two points on a demand curve we
can calculate it’s elasticity between the two points
P1
Q2 - Q1
P2 + P1
Price elasticity
x
=
of Demand (Pd) Q2 + Q1
P2 - P1
P2
Quantity
Q1
Q2
• Since elasticity is unit free it is better than using the slope of a line
for measuring the responsiveness of variables.
• Still, the price elasticity of demand will affect the way we draw the
demand curve.
Types of Elasticity's
• Economists group the numbers that are
calculated into different types of elasticity
depending on which percentage change is
greater: price or quantity
• Depending on the number that is calculated we
put that number into 1 of 5 different types
• We ignore the minus sign (use absolute value)
when doing so.
Price
Price
P1
P1
P2
P2
D
D
Q1
Q2 Quantity
Elastic Demand: 1< Pd <
the % change in QD is greater than
the % change in P that caused it.
Indicates that consumers are very
responsive or sensitive to price
changes and there can be large
changes in QD.
Q1 Q2
Quantity
Inelastic Demand: 0 < Pd < 1
the % change in QD is less than the
% change in P that caused it.
Indicates that consumers are not
very responsive or sensitive to price
changes and there will be small
changes in QD.
Price
Quantity
Perfectly Inelastic demand
Pd = 0
Price
Quantity
Unit Elastic demand
Pd = 1
Quantity
Perfectly Elastic demand
Pd =
8
Price
the % change in QD is
Any change is price will
Quantity demanded does
the same as the %
cause QD to go to zero
not change at all no matter change in P
Practical application:
how much price changes
that caused it.
A firm facing this demand
curve can sell all that it
Example: Prescription drugs
wants at this predetermined
that are needed to live
price, but no higher
…infinite perfect substitutes
…no substitutes available
Total Revenue and Elasticity
• Total Revenue (TR) = Price (P) x Quantity (Q)
• If a business firm raises the price it charges will total
revenue go up?
• It depends, because when price increases, quantity
decreases
• While the price increase will raise revenue per unit,
the firm will sell less units.
• The elasticity of demand will determine whether
total revenue goes up or down when price goes up or
down.
Total Revenue = Price x Quantity
This is shown by the Light Blue
shaded area on the graph
Price
P2
P1
TR =
PxQ
D
Q2
Q1
Quantity
• When price increases, the firm gains the green area in
revenue...
...but will lose the red area because of the decline in sales.
Let’s draw an inelastic demand curve and
compare the areas gained and lost.
Total Revenue = Price
Price
x Quantity
Inelastic Demand: P increase > Q decrease
P2
P1
TR =
PxQ
D
Q2 Q1
Quantity
• The % increase in P is greater than the % decrease in QD
The revenue gained from the P increase > revenue lost from the
QD decrease.
The green area is greater than the red area
Total revenue increases when price rises for an inelastic good!
Total Revenue = Price
Price
x Quantity
Elastic Demand: P increase < Q decrease
P2
P1
TR =
PxQ
D
Q2 Q1
Quantity
• The % increase in P is less than the % decrease in QD
The revenue gained from the P increase < revenue lost from the
QD decrease.
The green area is less than the red area
Total revenue decreases when price rises for an elastic good!
Elasticity and Total Revenue: Summary
Type of
demand
Value of Ed
Change in quantity
versus change in price
Effect of an
Effect of a decrease
increase in price in price on total
on total revenue revenue
Elastic
Greater than Larger percentage
1.0
change in quantity
Total revenue
decreases
Total revenue
increases
Inelastic
Less than 1.0 Smaller percentage
change in quantity
Total revenue
increases
Total revenue
decreases
Unitary
elastic
Equal to 1.0
Same percentage change Total revenue
Total revenue does
in quantity and price
does not change not change
• When demand is inelastic, price and total revenues are
directly related. Price increases generate higher revenues.
• When demand is elastic, price and total revenues are
indirectly related. Price increases generate lower revenues.
What determines price elasticity of demand ?
• Most important is the number of substitute goods.
More substitutes = higher elasticity. Why?
Consumers can easily switch from one good to another.
If there are few or no substitutes then switching is
impossible…
…consumers will find it hard to reduce purchases of the good
when price increases
• How important is the item in a consumers budget?
The price elasticity of salt will be very low because it is
insignificant in a consumers budget
Housing, car payments are a much higher proportion of
a budget and will have a higher elasticity
• Time is also important, because more substitute goods
appear and the consumer can change his behavior.
Some calculated price elasticity of demand.
Item
Short-run elasticity
Gasoline
- 0.4
Housing
- 0.3
Tobacco products - 0.46
Automobiles
-1.87
Movies
-0.87
Furniture
Books, Magazines, Newspapers
Long run elasticity
-1.5
-1.88
-1.89
-2.24
-3.67
-1.26
-0.32
Other measures of Elasticity.
• 1. Income Elasticity of Demand..... measures the
responsiveness of consumer purchases to changes
in consumer income.
• Income elasticity =
% change in consumer demand / % change in income
• Why is it important?
• Determines if a good is a normal good (a positive
number) or an inferior good (a negative number).
• Goods with positive numbers greater than 1
(income elastic) are sometimes referred to as
“luxuries”; goods with positive numbers less
than 1 (income inelastic) are referred to as
“necessities”
Other measures of Elasticity
Firms that produce income elastic goods do very
well in prosperous times...
....but very bad during recessions.
For “necessities” the opposite is true.
• With this knowledge, firms can plan production
according to expectations of consumers income.
Some calculated income elasticity of demand.
Item
Short-run elasticity
Potatoes
Pork
0.27
Beef
0.51
Autos
5.50
Jewelry
1.00
Foreign travel
0.24
Physician Services
0.28
Movies
Restaurant meals
Clothing
Telephone
Long run elasticity
-0.81
0.18
0.45
1.07
1.60
3.09
1.15
3.41
1.61
0.51
0.32
Cross elasticity of demand...
...measures the responsiveness of buyers to the
purchase of one good in response to changes in
the price of another good (substitute or
complementary)
• Cross elasticity=
% change in quantity of good X
% change in price of good Y
• Positive number = goods are substitutes
• Negative number = goods are complements
• Zero = goods are unrelated
Price elasticity of Supply...
…measures the responsiveness of quantity
supplied (QS) by business firms to changes in the
price of a good (P).
• Price elasticity of supply =
% change in QS / % change in P
• This is always a positive number.
Elastic supply...greater than 1 but less than infinity
Inelastic supply...greater than 0 but less than 1
Price
Price
S
P2
P2
P1
P1
Q1
Q2
Quantity
Elastic Supply: 1< Ps <
the % change in QS is greater than
the % change in P that caused it.
Indicates that Firms are very
responsive or sensitive to price
changes and are willing and able to
make a lot more of the product
available with small price increases.
Price Elasticity of Supply
S
Q1 Q2
Quantity
Inelastic Supply: 0 < Ps < 1
the % change in QS is less than the
% change in P that caused it.
Indicates that Firms are not very
responsive or sensitive to price
changes and are either not able or
willing to make more of this product
available without a large price
increase.
Price
Quantity
Perfectly Inelastic Supply
Ps = 0
Quantity supplied does
not change at all no matter
how much price changes
Example: Fixed seating at
a theater or arena.
Price
Quantity
Unit Elastic Supply
PS = 1
Quantity
Perfectly Elastic Supply
Ps=
8
Price
the % change in QS is
Any change is price will
the same as the %
cause QS to go to zero
change in P
Practical application:
that caused it.
A firm is willing to make
as much of this product
available at a constant price
(Could happen if costs do
not change)
Factors influencing the
Price elasticity of supply
1. How much does the cost per unit of output rise
as quantity supplied increases?
The more it (costs /output) increases the more
inelastic supply will be.
If costs don’t rise at all as QS increases then
supply is perfectly elastic.
2. Time is a factor in costs per unit.
Usually, as time increases, costs per unit do not
rise as much and supply is more elastic.
Firms find better and faster ways of production
Application using Elasticity
• Tax Burden (Who pays an excise tax?)
The government places an excise tax on the
suppliers of a good such as tobacco, liquor, and
gasoline.
Do business firms simply pass the entire tax to
consumers in the form of higher prices?
(This is called tax shifting)
It depends on the elasticity of demand and supply.
• Knowing both elasticity allows economists to
determine who pays the greater amount of an
excise tax on sellers of a good.
Price
This graph initially shows a good without the excise tax...
S2
$3.50
S1
S2 is $0.50 cents greater
than S1, reflecting the tax
}
$0.50
$3.25
$3.00
But the equilibrium
price($3.25) occurs where
the new supply curve
intersects the demand curve.
(Surplus at $3.50)
D
Q2
Q1
Quantity of gasoline
Suppose the government then decides to put a $0.50 cent tax per
gallon on gasoline…
…an excise tax will raise the cost of a gallon of gasoline by the
amount of the tax: $0.50, which will cause the supply curve to
shift upward {decrease in supply} by $0.50.
By comparing the price consumers pay and firms receive after the
tax (compared to the before tax price) we can determine how much
of the tax has been paid by consumers and firms.
Price
S2
S1
$3.25
$3.00
Firms receive $3.25 per
gallon from the consumer
Out of that $3.25 they must
pay $0.50 to the government
Firms only receive $2.75 out
of every gallon of gas sold
Tax paid by consumer
$2.75
Tax paid by firms
D
Q2
Q1
Total tax paid to Gov’t
Quantity of gasoline
By comparing the price consumers pay and firms receive after the
tax (compared to the before tax price) we can determine how much
of the tax has been paid by consumers and firms.
•Consumers pay $0.25 of the tax and firms pay $0.25 of the tax
•The Green area represents consumers share, the Light Blue area
represents firms share of the tax
Price
S2
$3.40
$3.00
$2.90
}
S1
What if Demand for gas is
inelastic while Supply is the
same as before (unit elastic)
$0.50
Tax paid by consumer
Tax paid by firms
Total tax paid to Gov’t
D
Q2 Q1
Quantity of gasoline
Consumers pay $0.40 of the tax and firms pay $0.10 of the tax
Why do consumers pay more of the tax when demand is inelastic?
Since consumers don’t respond very much to price changes
firms are able to pass on most of the tax in the form of higher
prices without a large reduction in sales
Price
S2
S1
}
What if while Demand for
gas is elastic Supply is the
same as before (unit elastic)
$0.50
$3.10
$3.00
Tax paid by consumer
Tax paid by firms
D
$2.60
Q2
Q1
Total tax paid to Gov’t
Quantity of gasoline
Consumers pay $0.10 of the tax and firms pay $0.40 of the tax
Why do Firms pay more of the tax when demand is elastic?
Since consumers respond very much to price changes firms are
unable to pass on very much of the tax in the form of higher
prices due to the large loss in sales.
Tax incidence and elasticity
• Government gets more revenue from taxing
goods and services that are inelastic...
…quantity sold does not go down as much
• Rule of Thumb: The more inelastic side of the
market will pay the GREATER PROPORTION
of the tax.
Price
$3.50
S2
}
Example Tax Burden:
Extreme Case
$0.50
$3.00
S1
Tax paid by consumer
Tax paid by firms
D
Q2
Q1
Total tax paid to Gov’t
Quantity of gasoline
If Supply is perfectly elastic, Consumers pay all the tax.
Price
$3.50
S2
}
S1
Example Tax Burden:
Extreme Case
$0.50
$3.00
Tax paid by consumer
Tax paid by firms
Total tax paid to Gov’t
D
Q1
Quantity of gasoline
If Demand is perfectly inelastic, Consumers pay all the tax.
Price
S2
Example Tax Burden:
Extreme Case
S1
}
$0.50
$3.03
$3.00
Tax paid by consumer
Tax paid by firms
Total tax paid to Gov’t
$2.53
D
Q2Q1
Quantity of gasoline
If Supply is almost perfectly inelastic, Firms pay virtually
all of the tax.