Transcript Percentages and Elasticity

Percentages and Elasticity
percentage: “for each hundred”
one per cent: one for each hundred
ex: "I spend ten percent of my income on
movies and other forms of entertainment"
means that "I spend ten dollars of each
hundred dollars of my income on
entertainment."
Converting from decimal to percentage notation:
Just move the decimal to the right two places.
.65
65%
What percentages are equivalent to the
following numbers?
(a) .01
1%
(b) .94
94%
(c) 1.705
170.5%
(d) .2386
23.86%
(e) .8
80%
Converting from fractions to percentages:
Convert from fraction to decimal by dividing,
and then move the decimal to the right two
places.
1/4
.25
25%
Questions
What percent of 50 is 10?
20%
4 is what percent of 8?
50%
What percent of 60 is 15?
25%
Percentage Change:
absolute change =
before
after - before
before
If spending increased from $50 to $60, by
what percent did spending increase?
percentage change
=
= 60 - 50
50
= 10 / 50
= .20
= 20 %
after - before
before
Suppose your financial aid increased by $50.
You used to spend $10 per week on
entertainment. You now spend $11. By what
percentage did your entertainment spending
increase?
percentage change = after - before
before
= 11 - 10
10
= 1/10
= .10 = 10 %
Your financial aid is cut back by $50 to its
original level. You reduce your entertainment
spending from $11.00 back to $10.00. By what
percent did your spending decrease?
percentage change
=
=
10 - 11
11
= - 1 / 11
= - .0909
= - 9.09 %
after - before
before
A negative change indicates a decrease.
A positive change indicates an increase.
It would be nice to be able to say the following:
In response to a $50 increase, you increased
your spending by some percent x. In response
to a $50 decrease, you decreased your spending
by that same x percent. When we get to the
concept of elasticity, in particular, we will want
to be able to do that.
So we will define percentage changes a little
differently. Instead of using our "before"
value as our denominator, we will use the
average (or midpoint) of our "before" and
"after" values as the denominator.
average = (before + after) / 2
Our percentage change formula becomes
percentage change = after - before
average
Suppose your financial aid increased by $50.
You increase your spending on entertainment
from $10 per week to $11. By what percentage
did your entertainment spending increase?
(Use the midpoint formula.)
First we need to determine the average of the
before and after spending.
average = (before + after) / 2
= (10 + 11) / 2
= (21) / 2 = 10.5
percentage change
=
=
=
=
=
after - before
average
11 - 10
10.5
1 / 10.5
.0952
9.52 %
Financial aid is cut back by $50. You reduce
your spending on entertainment from $11 per
week to $10. Using the midpoint formula,
determine by what percentage your spending
decreases.
percentage change =
after - before
average
=
10 - 11
10.5
=
- 1 / 10.5
=
- .0952 =
- 9.52 %
Suppose that financial aid for the semester
increased from $995 to $1005. Using the
midpoint formula, determine by what percent
financial aid increased.
percentage change
=
=
=
=
=
1005 - 995
1000
10 / 1000
.01
1%
after - before
average
Suppose the 1% increase in financial aid led
you to increase your entertainment budget from
$297 to $303. By what percent did you
increase your entertainment budget?
percentage change
=
=
=
=
=
303 - 297
300
6 / 300
.02
2%
after - before
average
fin. aid
1%
ent. budget
2%
In other words, the percentage increase in
your entertainment budget was 2 times as
large as the percentage increase in financial
aid.
This value (2) is the elasticity of your
entertainment budget with respect to your
financial aid.
The elasticity of X with respect to Y
tells you by what percent X changes when
Y changes by 1%.
The elasticity of X with respect to Y
can be calculated as
the percentage change in X
the percentage change in Y.
If in response to a 20% increase in financial aid,
you increased your entertainment budget by 40%,
what is the elasticity of your entertainment
budget with respect to your financial aid?
2
By how much would you expect your entertainment budget to increase in response to a 1%
increase in financial aid?
2%
Suppose financial aid increased from $1050 to
$1100. In response, you increased your
entertainment budget from $300 to $320.
Calculate the following:
 the
percentage change in financial aid,
 the percentage change in your entertainment
budget, and
 the elasticity of your entertainment budget
with respect to financial aid.
percentage change in financial aid
fin. aid: 1050, 1100
change in fin. aid = 1100 - 1050 = 50
avg. fin. aid = (1050 + 1100)/2 = 2150/2 = 1075
percentage change in financial aid
= (change in fin. aid) / (avg fin. aid)
=
50 / 1075
=
.0465
=
4.65%
percentage change in ent. budget
ent. budget: 300, 320
change in ent. budget = 320 - 300 = 20
avg ent. budget = (300 + 320) / 2 = 620/2 = 310
percentage change in entertainment budget
= (change in ent. budget) / (avg ent. budget)
=
20 / 310
=
.0645
=
6.45%
elasticity
of entertainment budget
with respect to financial aid
percentage change in entertainment budget
percentage change in financial aid
= 6.45/4.65 = 1.387.
So when financial aid increases by
1 percent, your entertainment budget
increases by 1.387 percent.
In the elasticity formula, how do you remember
which variable goes on top and which goes
underneath?
 The
cause goes under the line.
CAUSE and UNDER both have a U.
 The
effect goes on top.
EFFECT and TOP both have a T.
elasticity =
% change in effect
% change in cause
for our financial aid & entertainment example:
elasticity = % change in
% change in
.
Unit Elastic:
|elasticity| = 1
% change in effect
% change in cause
= 1
% change in the effect = % change in the cause
.
fin. aid
5%
ent. budget
5%
Your entertainment budget is unit elastic with
respect to financial aid.
Elastic:
|elasticity| > 1
% change in effect
% change in cause
> 1
% change in the effect > % change in the cause
fin. aid
5%
ent. budget
Your entertainment budget is elastic with
respect to financial aid.
6%
Inelastic:
|elasticity| < 1
% change in effect
% change in cause
< 1
% change in the effect < % change in the cause
fin. aid
5%
ent. budget
4%
Your entertainment budget is inelastic with
respect to financial aid.
Price Elasticity of Demand
(or Elasticity of Quantity Demanded with
Respect to Price)
measures the responsiveness of consumers'
purchases to a change in the price of a
commodity.
Notation
means “change”
and
% means “percentage change”
examples:
 Price or  P means “change in price”
%  P means “percentage change in price”
Suppose the price of personal
computers increased from $1600 to
$1700. As a result, the number of PCs
purchased per week by area consumers dropped
from 500 to 400. Calculate the following:
 the
percentage change in the quantity
demanded of PCs,
 the percentage change in the price of PCs, and
 the elasticity of demand for PCs with respect
to the price of PCs.
percentage change in quantity demanded of PCs
quantity: 500, 400
 qty demanded of PCs = 400 - 500 = -100
avg qty demanded of PCs = (500 + 400) / 2
= 900 / 2 = 450
%  qty demanded of PCs
= ( qty demanded of PCs) / (avg qty demanded)
= -100/450 = -.2222 = - 22.22 %
[The negative indicates a decrease in PCs.]
percentage change in price of PCs
price: 1600, 1700
 Price of PCs = 1700 - 1600 = 100
avg price = (1600 + 1700) / 2 = 3300 / 2 = $1650
%  price of PCs = ( price of PCs) / (avg price)
= 100 / 1650 = .0606 = 6.06 %
price elasticity of demand for PCs
%  qty demanded of PCs
%  price of PCs
= - 22.22 / 6.06 = - 3.667
The negative indicates that there is an inverse
relation between the qty demanded of PCs and
the price of PCs.
When the price of PCs increases by one
percent, the quantity demanded of PCs
decreases by 3.667 percent.
|-3.667| = 3.667 > 1
So, the demand for PCs is elastic
with respect to the price of PCs.
Because it is almost always the case that the
qty demanded of a good is inversely related to
its price, the negative sign is frequently
dropped.
ex: The price elasticity of demand for PCs
would be reported as 3.667 instead of
-3.667. The negative is understood.
Suppose you have an ailment, for
which you must take a particular
medication. (Call it Medex.) Every
Medex
thirty days you purchase one thirtycapsule bottle of Medex. The price
of Medex increases from $4 to $5
per bottle. You still purchase one bottle every
thirty days. Calculate the elasticity of your
quantity demanded of Medex with respect to
the price of Medex.
percentage change in price of Medex
price: 4, 5
 Price of Medex = 5 - 4 = 1
avg price = (4 + 5)/2 = 9/2 = 4.5
%  price of Medex = ( price) / (avg price)
= 1 / 4.5 = .2222
So the price of Medex changed by 22.22 %.
percentage change in qty demanded of Medex
quantity: 1, 1
 qty demanded of Medex = 1 - 1 = 0
avg qty demanded of Medex
= (1 + 1) / 2 = 2 / 2 = 1
%  qty demanded of Medex
= ( qty demanded) / (avg qty demanded)
=0/1=0
So the quantity demanded of Medex changed
by 0 %. (It didn’t change at all.)
price elasticity of demand for Medex
%  qty demanded of Medex
%  price of Medex
= 0 / 22.22 = 0
Perfectly Inelastic
elasticity = 0
It is a special case of inelastic.
Suppose the price of personal
computers increases from $1500 to
$1700. As a result, the number of
PCs purchased per week by consumers in the
area dropped from 850 to 750. Calculate the
elasticity of demand for PCs with respect to
the price of PCs.
percentage change in qty demanded of PCs
quantity: 850, 750
 qty demanded of PCs = 750 - 850 = -100
avg qty demanded of PCs
= (850 + 750) / 2 = 1600 / 2 = 800
%  qty demanded of PCs
= ( qty demanded) / (avg qty demanded)
= -100 / 800 = - .125 = - 12.5 %
percentage change in price of PCs
price: 1500, 1700
 Price of PCs = 1700 - 1500 = 200
avg price = (1500 +1700) / 2 = 3200 / 2 = 1600
%  price of PCs = ( price) / (avg price)
= 200 / 1600 = .125 = 12.5%
price elasticity of demand for PCs
%  qty demanded of PCs
%  price of PCs
= -12.5 / 12.5 = -1
Since the absolute value of the elasticity is 1,
the quantity demanded of PCs is unit elastic
with respect to price.
Suppose you are in the pizza
business. As a very small
company, you take the area
price of pizza ($8) as given.
That is, you always charge the
same price. The
quantity demanded of your pizza fluctuates.
Last week, the quantity demanded of your
pizza increased from 750 to 800 pizzas.
Calculate the price elasticity of demand for
your pizza.
percentage change in qty demanded of pizza
quantity: 750, 800
 qty demanded of pizza = 800 - 750 = 50
avg qty demanded of pizza
= (750 + 800) / 2 = 1550 / 2 = 775
%  qty demanded of pizza
= ( qty demanded) / (avg qty demanded)
= 50 / 775 = .0645 = 6.45 %
percentage change in price of pizza
price: 8, 8
 Price of pizza = 8 - 8 = 0
avg price = (8 + 8) / 2 = 16 / 2 = 8
%  price of pizza = ( price) / (avg price)
= 0/8 =0 =0%
The price changed by 0 %. (It didn't change at all.)
price elasticity of demand for pizza
%  qty demanded of pizza
%  price of pizza
= 6.45 / 0 = infinity or undefined
Perfectly Elastic or Infinitely Elastic
elasticity = infinity
It is a special case of elastic.
Determinants of Price Elasticity of Demand
1. Elasticity of demand is greater if
there are good substitutes available.
Example: The elasticity of demand for a
particular brand of gas would be quite
high because there are lots of other brands
of gas available.
Determinants of Price Elasticity of Demand
2. Elasticity of demand is greater if the price
of the good is high relative to one’s
budget.
Example: The elasticity of demand for a salt
is low because salt is a very small part of
one’s budget.
Determinants of Price Elasticity of Demand
3. Elasticity of demand is greater if the
product is a luxury rather than a
necessity.
Example: The elasticity of demand for
insulin by a diabetic is extremely low
because insulin is a necessity.
Determinants of Price Elasticity of Demand
4. Elasticity of demand is greater if the buyer has
more time to adjust to a change in price.
Example: The elasticity of demand for gas is more
elastic when you allow people more time to
adjust. If the price of gas goes up today, you can
adjust your consumption only a little bit
tomorrow. But if you have a few years, you can
replace your car with one that consumes less gas
and you can move closer to where you work.
Elasticity Graphs
Zero Elasticity or Perfectly Inelastic
P
Q
Low Elasticity (Inelastic)
P
Q
High Elasticity (Elastic)
P
Q
Infinite Elasticity or Perfectly Elastic
P
Q
Elasticity of a Straight Line
P
at midpoint,
|elasticity| = 1
Q
Elasticity of a Straight Line
P
above the midpoint,
|elasticity| > 1
Q
Elasticity of a Straight Line
P
below the midpoint,
|elasticity| < 1
Q
Elasticity of a Straight Line
P
|elasticity| > 1
|elasticity| = 1
|elasticity| < 1
Q
Constant Elasticity
P
Q
Relationship Between
Price Elasticity of Demand
and Total Revenue
Note:
Total Revenue (TR) = Total Expenditure.
Total revenue is from the firm’s perspective;
total expenditure is from the consumer’s
perspective.
Both are computed by multiplying price by
quantity. Thus,
TR = P Q
Consider the product of two numbers,
Z = XY.
Clearly, if both X and Y increase, then the
product Z must increase too.
Also, if both X and Y decrease, then the
product Z must decrease too.
However, if X increases and Y decreases, or
vice versa, then whether the product Z
increases or decreases depends on the relative
magnitude of the changes in X and Y.
That is, if X increases a lot and Y decreases a
little, then Z will increase.
If X increases a little and Y decreases a lot,
then Z will decrease.
If Y decreases by the same percentage that X
increased, then Z will remain unchanged.
The same idea carries over to the concept of
total revenue, which is the product of price
and quantity: TR = PQ.
Generally, when the price of a product
increases, the quantity demanded will
decrease and vice versa.
So, whether TR increases, decreases, or
remains the same when the price of a
product changes depends on the relative
magnitudes of the changes in price and
quantity.
When Demand is Elastic:
P
Q
TR
P
Q
TR
Price and TR move in opposite directions.
Example: Elastic Demand
When the price of PCs increased from $1600 to
$1700, the number of PCs decreased from 500
to 400. The elasticity was -3.667.
Initially, TR = (1600)(500) = 800,000.
Later, TR = (1700)(400) = 680,000.
So TR fell when price increased.
When Demand is Inelastic:
P
Q
TR
P
Q
TR
Price and TR move in the same direction.
Example: Inelastic Demand
Suppose when the price of a good increased
from $90 to $110, the quantity demanded
decreased from 210 to 190. The elasticity can
be computed to be -0.5.
Initially, TR = (90)(210) = 18,900.
Later, TR = (110)(190) = 20,900.
So TR increased when price increased.
When Demand is Unit Elastic:
P
Q
TR unchanged
P
Q
TR unchanged
TR is constant.
Example: Unit Elastic Demand
Suppose when the price of personal computers
increases from $1500 to $1700, the quantity
demanded decreases from 850 to 750. Then the
elasticity is -1.
Initially, TR = (1500)(850) = 1,275,000.
Later, TR = (1700)(750) = 1,275,000.
So TR is unchanged when price changes.
Price Elasticity of Supply
(or Elasticity of Quantity Supplied with
Respect to Price)
measures the responsiveness of producers
to a change in the price of a commodity.
Suppose the price of personal
computers increased from
$1550 to $1650. As a result,
the number of PCs that area
manufacturers were willing to
produce per week
rose from 490 to 510. Calculate the elasticity
of quantity supplied of PCs with respect to
the price of PCs.
percentage change in qty supplied of PCs
quantity: 490, 510
 qty supplied of PCs = 510 - 490 = 20
avg qty supplied of PCs
= (490 + 510) / 2 = 1000 / 2 = 500
%  qty supplied of PCs
= ( qty supplied) / (avg qty supplied)
= 20 / 500 = .04 = 4 %
percentage change in price of PCs
price: 1550, 1650
 Price of PCs = 1650 - 1550 = 100
avg price = (1550 +1650) / 2 = 3200 / 2 = $1600
%  price of PCs = ( price) / (avg price)
= 100 / 1600 = .0625 = 6.25%
price elasticity of supply of PCs
%  qty supplied of PCs
%  price of PCs
= 4 / 6.25 = .64
When the price of PCs increases by one percent,
the quantity supplied of PCs increases by .64
percent.
Since the elasticity is less than one, the quantity
supplied of PCs is inelastic with respect to price.
The Income Elasticity of Demand
or Elasticity of Quantity Demanded with
Respect to Income
measures the responsiveness of consumers'
purchases to a change in consumer income.
Suppose your income
increased from $1000 to
$1150 per month. As a result,
the number of pounds of
potatoes you purchase per
month decreased from 10 to 9. Calculate the
elasticity of demand for potatoes with respect
to income.
percentage change in qty demanded of potatoes
quantity: 10, 9
 qty demanded of potatoes = 9 - 10 = - 1
avg qty demanded of potatoes
= (10 + 9) / 2 = 19 / 2 = 9.5
%  qty demanded of potatoes
= ( qty demanded) / (avg qty demanded)
= - 1 / 9.5 = - .1053 = - 10.53 %
percentage change in income
income: 1000, 1150
 income = 1150 - 1000 = 150
avg income = (1000 +1150)/2 = 2150 / 2 = $1075
%  income = ( income) / (avg income)
= 150 / 1075 = .1395 = 13.95 %
income elasticity of demand for potatoes
%  qty demanded of potatoes
%  income
= - 10.53 / 13.95 = - .75
When the income increases by one percent,
the quantity demanded of potatoes decreases
by 0.75 percent.
Inferior Good
a good with a negative income elasticity of
demand.
The negative sign indicates that income and
quantity demanded of the good (potatoes)
move in opposite directions. When income
rises, people buy less. When income falls,
people buy more.
Normal Good
a good with a positive income elasticity of
demand.
For normal goods, when income rises,
people buy more. When income falls,
people buy less. Most goods are normal
goods.
Suppose your income increased from
$2000 to $2080 per month. As a
result, the number of movies you see
per month rose from 4 to 5.
Calculate the elasticity of demand for movies
with respect to income.
percentage change in qty demanded of movies
quantity: 4, 5
 qty demanded of movies = 5 - 4 = 1
avg qty demanded of movies
= (4 + 5) / 2 = 9 / 2 = 4.5
%  qty demanded of movies
= ( qty demanded) / (avg qty demanded)
= 1 / 4.5 = .2222 = 22.22 %
percentage change in income
income: 2000, 2080
 income = 2080 - 2000 = 80
avg income = (2000 +2080) / 2 = 4080 / 2 = 2040
%  income = ( income) / (avg income)
= 80 / 2040 = .0392 = 3.92 %
income elasticity of demand for movies
%  qty demanded of movies
%  income
= 22.22 / 3.92 = 5.668
When the income increases by one percent,
the quantity demanded of movies increases by
5.668 percent.
Since the income elasticity of movies is
positive, movies are a normal good.
Cross Elasticity of Demand
measures the responsiveness of the quantity
demanded of one good to changes in the
price of another good.
Suppose the price of
compact diskettes falls
from $18 to $14. In
response, the quantity
demanded of cassettes
per week by area consumers falls from 1100
to 900. Calculate the elasticity of the quantity
demanded of cassettes
with respect to the price
of CDs.
percentage change in qty demanded of cassettes
qty of cassettes: 1100, 900
 qty demanded of cassettes = 900-1100 = - 200
avg qty demanded of cassettes
= (1100 + 900) / 2 = 2000 / 2 = 1000
%  qty demanded of cassettes
= ( qty demanded) / (avg qty demanded)
= - 200 / 1000 = - .20 = - 20 %
percentage change in price of CDs
CD price: 18, 14
 price of CDs = 14 -18 = - 4
avg price of CDs = (18 + 14) / 2 = 32 / 2 = 16
%  price of CDs
= ( price of CDs) / (avg price of CDs)
= - 4 /16 = - .25 = - 25 %
cross elasticity of demand for cassettes
with respect to the price of CDs
%  qty demanded of cassettes
%  price of CDs
= -20 / -25 = .80
When the price of CDs falls by one percent,
the quantity demanded of cassettes falls by
.80 percent.
Substitutes
When the cross elasticity between two goods is
positive, the two goods are called substitutes.
A substitute is a good that can be used instead
of another good.
The price of one good and the quantity
demanded of the substitute good move in
the same direction.
When the price of CDs decreases, the
quantity demanded of cassettes decreases.
When the price of CDs increases, the
quantity demanded of the cassettes
increases.
Complements
When the cross elasticity between two goods
is negative, the two goods are called
complements.
A complement is a good that is used along
with another good.
Complements
The price of one good and the quantity demanded
of the complementary good move in opposite
directions.
When the price of coffee decreases, the quantity
demanded of cream increases.
When the price of coffee increases, the quantity
demanded of cream decreases.
Suppose the price of CD
players increases from
$140 to $160. In
response, the quantity
demanded of CDs per
week by area consumers
decreases from 1150 to
850. Calculate the cross
elasticity of demand for
CDs with respect to the
price of CD players.
percentage change in qty demanded of CDs
qty of CDs: 1150, 850
 qty demanded of CDs = 850 - 1150 = - 300
avg qty demanded of CDs
= (1150 + 850) / 2 = 2000 / 2 = 1000
%  qty demanded of CDs
= ( qty demanded) / (avg qty demanded)
= - 300 / 1000 = - .30 = - 30 %
percentage change in price of CD players
CD player price: 140, 160
 price of CD players = 160 -140 = 20
avg price of CD players = (140 + 160) / 2
= 300 / 2 = 150
%  price of CD players = ( price) / (avg price)
= 20 / 150 = .1333 = 13.33 %
cross elasticity of demand for CDs
with respect to the price of CD players
%  qty demanded of CDs
%  price of CD players
= - 30 / 13.33 = - 2.25
Since the cross elasticity of demand for CDs
with respect to the price of CD players is
negative, CDs and CD players are
complements.
The Effect of Elasticity
on the Burden of a Tax
Example:
Suppose supply and
demand are as shown
here. Without a tax,
equilibrium price is $1
and equilibrium
quantity is 60 units.
price
QD
QS
1.09
45
75
1.06
50
70
1.03
55
65
1.00
60
60
.97
65
55
.94
70
50
.91
75
45
Price
Example:
no tax
quantity is 60
price is $1
$1
Supply (without tax)
Demand
60
Quantity
Now suppose a tax of six cents per unit is
imposed.
Then, from the buyer’s view, for each
quantity supplied, the total price per unit
is six cents higher than before.
(Equivalently, for a given total price per
unit, suppliers are willing to provide
fewer units than before.)
So the buyers see a new supply curve.
Price
Supply (with tax)
.06
Supply (without tax)
Demand
Quantity
Old Supply (no tax):
price
QS
1.09
75
1.06
70
1.03
65
1.00
60
.97
55
.94
50
.91
45
Put in the tax.
price
QS
price (with tax)
1.09
75
1.15
1.06
70
1.12
1.03
65
1.09
1.00
60
1.06
.97
55
1.03
.94
50
1.00
.91
45
.97
new supply as viewed by the buyers:
price
QS
price (with tax)
1.09
75
1.15
1.06
70
1.12
1.03
65
1.09
1.00
60
1.06
.97
55
1.03
.94
50
1.00
.91
45
.97
If we line up the demand
column and our new
supply column so that the
price columns match, the
table looks like this.
price
QD
QS
1.15
75
1.12
70
1.09
45
65
1.06
50
60
1.03
55
55
1.00
60
50
.97
65
45
.94
70
.91
75
If we line up the demand
column and our new
supply column so that the
price columns match, the
table looks like this.
Equilibrium quantity is
now 55. Equilibrium price
(from the buyer’s view) is
1.03.
price
QD
QS
1.15
75
1.12
70
1.09
45
65
1.06
50
60
1.03
55
55
1.00
60
50
.97
65
45
.94
70
.91
75
Price
Supply (with tax)
tax = .06
Quantity is 55
Buyer pays 1.03
.06
1.03
Supply (without tax)
55
Demand
Quantity
But the government gets .06.
So the seller gets 1.03 - .06 = .97.
Price
Supply (with tax)
.06
1.03
tax = .06
Quantity is 55
Buyer pays 1.03
Seller gets
1.03 -.06=.97
.97
Supply (without tax)
55
Demand
Quantity
The burden of the tax is shared evenly in this
example. The buyer pays three cents more
per unit than before the tax and the seller gets
three cents less per unit.
Let’s go through the graphs again for the
general case of a tax of amount t.
Price
Supply (without tax)
Demand
Quantity
Price
Before tax:
quantity is Q0
price is P0
Supply (without tax)
P0
Demand
Q0
Quantity
Price
Supply (with tax)
t
Supply (without tax)
P0
Demand
Q0
Quantity
Price
Supply (with tax)
t
Pb
P0
With tax:
quantity is Q1
buyer pays Pb
Supply (without tax)
Demand
Q1 Q0
Quantity
Price
Supply (with tax)
t
Pb
P0
Ps
With tax:
seller gets
Ps = Pb - t
Supply (without tax)
Demand
Q1 Q0
Quantity
With the tax, the buyer pays more
and the seller receives less than
without the tax. The burden of the
tax is shared.
Suppose the elasticity of demand is smaller.
The demand curve is steeper.
How does this affect how the tax burden is
divided?
Price
Supply (without tax)
P0
Demand
Q0
Quantity
Price
Demand
Supply (with tax)
.06
1.04
1.00
.98
tax = .06
Quantity is 59
Buyer pays 1.04
Seller gets
1.04 -.06=.98
Consumer bears
greater share of
tax burden.
Supply (without tax)
59 60
Quantity
When demand is less elastic and consumers
are less responsive to price changes,
consumers will bear a larger share of the tax
burden, and sellers will bear a smaller share.
In the extreme case where demand is perfectly
inelastic (vertical demand curve), consumers
will bear the entire burden of the tax.
The price paid by consumers is t dollars more
than before the tax. The price received by the
seller is the same as before the tax.
Price
Supply (with tax)
Demand
.06
1.06
1.00
tax = .06
Quantity is 60
Buyer pays 1.06
Seller gets
1.06 -.06=1.00
Consumer bears
entire tax
burden.
Supply (without tax)
60
Quantity
When supply is less elastic and sellers are
less responsive to price changes, sellers will
bear a larger share of the tax burden, and
buyers will bear a smaller share.
Price
Supply (with tax)
Demand
.06
1.02
1.00
.96
tax = .06
Quantity is 59
Buyer pays 1.02
Seller gets
1.02 -.06=.96
Seller bears
greater share of
tax burden.
Supply (without tax)
59 60
Quantity
In the extreme case where supply is perfectly
inelastic (vertical supply curve), sellers will
bear the entire burden of the tax.
The price received by sellers is t dollars less
than before the tax. The price paid by
consumers is the same as before the tax.
To show this effect on a graph, we need to
shift the demand curve instead of the supply
curve. From the supplier’s perspective, it
seems as if the demand curve has shifted
down vertically by the amount of the tax.
Price
Supply
1.00
.94
tax = .06
Quantity is 60
Seller gets .94
Buyer pays
.94 + .06 = 1.00
Seller bears entire
tax burden.
.06
Demand (without tax)
Demand (with tax)
60
Quantity