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Chapter 18: Elasticity
• Price elasticity
•
•
– demand
– supply
Cross elasticity
Income elasticity
Basic idea
• We know when P
Qd
Qs
holding other factors constant
but how much?
• if price doubles
•
how much does Qd fall?
– by 10%
– by 50%
– by 300%?
price elasticity tells us
Price
Supply
Demand
1
35
530
2
130
400
4
320
140
4) a- consider theses two points (1,35) and (2,130)
Line equation is Y= M X + b (Y is the price and X is
the quantity)
M= (Y2-Y1)/(X2-X1)
M= 2-1/130-35 , M= 1/95
Y= (1/95)X + b so, 1=(1/95) * 35 + b
B= 60/95
Qs= (1/95)P + 60/95
Price
Supply
Demand
1
35
530
2
130
400
4
320
140
4) b- consider theses two points (1,530) and (2,400)
Line equation is Y= M X + b (Y is the price and X is
the quantity)
M= (Y2-Y1)/(X2-X1)
M= 2-1/400-530 , M= -1/130
Y= (-1/130)X + b so, 1=(-1/130) * 530 + b
B= 660/130
Qd= (-1/130)P + 660/130
4) C, we know that at the equilibrium Qs = Qd,
so
• Qs= (1/95)P + 60/95
• Qd= (-1/130)P + 660/130
• (1/95)P + 60/95 = (-1/130)P + 660/130
• { (1/95) + (1/130)}P = {(660/130)-(60/95)}
• P = 244
Price
Supply
Demand
20
400
500
30
250
400
50
250
400
1- consider theses two points (20,400) and (30,250)
Line equation is Y= M X + b (Y is the price and X is
the quantity)
M= (Y2-Y1)/(X2-X1)
M= 30-20/250-400 , M= 10/-150
Y= (10/-150)X + b so, 20=(10/-150) * 400+ b
B= 7000/150
Qs= (10/-150) P+ 7000/150
Price
Supply
Demand
20
400
500
30
250
400
50
250
400
2)- consider theses two points (20,500) and (30,400)
Line equation is Y= M X + b (Y is the price and X is
the quantity)
M= (Y2-Y1)/(X2-X1)
M= 30-20/400-500 , M= 10/-100
Y= (10/-100)X + b so, 20=(10/-150) * 500+ b
B= 8000/100
Qd= (10/-100) P+ 8000/100
• At equilibrium Qs = Qd
• (10/-150) P+ 7000/150=(10/-100) P+
•
8000/100
??
I. Price Elasticity of Demand
example
• mocha latte at Starbucks
• price rises from $3 to $5 per cup
• Qd falls from 15 to 5 cups per hr.
equation
% change in Qd
% change in P
% change in Qd
new Qd - initial Qd
average Qd
midpoint method
x 100
example
5 cups - 15 cups
(5+15)/2 cups
-10 cups
10 cups
x 100
x 100
= -100%
% change in P
new P - initial P
average P
midpoint method
x 100
example
$5 - $3
($5+$3)/2
$2
$4
x 100
x 100
= 50%
demand elasticity
% change in Qd
% change in P
-100%
50%
= -2
• If price of latte increases 1%,
Qd of latte decreases 2%
demand elasticity
• a unit-free measure
•
– compare all goods & services
changes for different points
on the demand curve
if price elasticity of demand
(absolute value)
•=1
unit elastic
% change Qd = % change P
•>1
elastic
% change Qd > %change P
sensitive to P changes
•<1
inelastic
% change Qd < %change P
not sensitive to P changes
elastic demand
(>1)
• flatter curve
P
small change in P
big change in Qd
D
Q
inelastic demand
(<1)
• steep curve
P
big change in P
small change in Qd
D
Q
perfectly inelastic demand
• vertical line
P
change in P
no change in Qd
D
Q
perfectly elastic demand
• horizontal line
P
any change in P
Qd falls to zero
D
Q
effect on total revenue
• total revenue (TR)
•
•
=PxQ
if demand is elastic,
– TR falls as price rises
if demand is inelastic,
– TR rises as price rises
example: cup of latte
• initial P=$3, Qd = 15.
•
•
TR = $3 x 15 = $45
new P = $5, Qd = 5
TR = $5 x 5 = $25
demand for latte is elastic
TR falls as P rises
what makes demand elastic or
inelastic?
1. is it a luxury or necessity
– if luxury, demand is elastic
– if necessity, demand is inelastic
example
• mocha latte at Starbucks
•
is a luxury
a liver transplant is not
2. definition of good
– latte at Starbucks,
narrow definition= many substitutes
(other brands of coffee, tea)
demand is elastic
– coffee in general,
broad definition = fewer substitutes
demand is less elastic
3. time since price change
– short time
no time to adjust,
demand is inelastic
– long time
time to adjust,
demand is elastic
example
• Price of gas per gallon
• the day price rises
•
– demand inelastic
years later
– demand much more elastic
as carpool or buy smaller car
factors 1-3
all get at same issue:
• can consumers substitute a cheaper
good easily?
– if yes, demand is elastic
– if no, demand is inelastic
4. Is item large part of your budget?
– if yes, then demand elastic
(forced to change behavior)
– if no, then demand inelastic
(no need to change behavior)
example
• soap
•
– if price doubles, will you buy less?
rent
– if rent doubles?
-- stay on campus?
-- more roommates?
II. Price Elasticity of Supply
% change in Qs
% change in P
example
• bunch of roses
• P = $40/bunch, Qs = 6 (million bunches)
• P = $60, Qs = 15
% change Qs
15 - 6
(6+15)/2
x 100
9
10.5
= 86%
x 100
% change P
60 - 40
(60+40)/2
x 100
20
50
= 40%
x 100
supply elasticity
% change in Qs
% change in P
86%
40%
= 2.15
• if price rises 1%,
•
•
Qs rises 2.15%
unit-free measure
depends on points chosen
on the supply curve
if price elasticity of supply
•=1
•
unit elastic
% change Qs = % change P
>1
elastic
% change Qs > %change P
sensitive to P changes
•<1
inelastic
% change Qs < %change P
not sensitive to P changes
inelastic supply
• steep curve
P
big change in P
small change in Qs
S
Q
perfectly inelastic supply
• vertical line
P
change in P
no change in Qs
S
Q
elastic supply
• flatter curve
P
S
Q
small change in P
big change in Qs
perfectly elastic supply
• horizontal line
P
any change in P
Qs falls to zero
S
Q
what makes supply elastic or
inelastic?
1. production possibilities
Can you make more easily?
NO
then supply is inelastic
YES
then supply is elastic
example
• oceanfront property
•
– can’t make more
– inelastic supply
salt
– almost an infinite amount
– elastic supply
2. time since price change
– it takes time to produce
– if a short time,
supply is inelastic
– if a long time
supply is elastic
example
• hotel rooms
– takes time to build
– supply inelastic in short-run,
elastic in long-run
3. Can you store it easily/cheaply?
– if yes, then elastic
– if no, then inelastic
example
• bananas
– storage time limited
– supply inelastic
III. Income Elasticity of Demand
• impact of income changes on
•
demand
size of shift
in the demand curve
when income changes
equation
% change in Qd
% change in income
• > 0 normal good
• < 0 inferior good
example: jewelry
• income increases 10%
• Qd jewelry increases 35%
income elasticity
% change in Qd jewelry
% change in income
35%
10%
= 3.5
IV. Cross Elasticity of Demand
• impact of price change of
•
substitutes or complements
size of shift
in demand curve
when price of a related good
changes
equation
% change in Qd
% change in P of related good
cross elasticity
• > 0 for substitutes
• < 0 for complements
example: Peanut butter
• what happens to Qd of PB,
•
when price of jelly rises?
PB & jelly are complements
price jelly = $3 jar,
Qd PB = 2 jars per month
price jelly = $4 jar,
Qd PB = 1 jar per month
% change in Qd PB
1 jar - 2 jars
1.5 jars
x 100
= - 66.7%
% change in P of jelly
$4 - $3
$3.5
x 100
= 28.6%
cross price elasticity of PB
• with respect to price of jelly
% change in Qd PB
% change in P jelly
- 66.7%
28.6%
= - 2.33
example: Coca-Cola & Pepsi
• what happens to Qd of C-Cola,
•
when price of Pepsi rises?
Coca-Cola & Pepsi are substitutes
P Pepsi= $1,
Qd Coca = 2
P Pepsi= $3 stick,
Qd Coca= 2.2
% change in Qd Coca
2.2 - 2
2.1
x 100
= 9.5%
% change in P of Pepsi
$3 - $1
$2
x 100
= 100%
cross price elasticity of Cola
• with respect to price of Pepsi
% change in Qd Cola
% change in P Pepsi
9.5%
100%
= .095
summary
• law of demand & supply
•
•
– direction of change in Qd/Qs
when P changes
price elasticity
– how large are these Qd/Qs
changes?
cross/income elasticity
– size of shift in demand curve
Elasticity on a Linear
Demand Curve
(1)
Total Quantity of
Tickets Demanded
Per Week, Thousands
1
(2)
Price Per Ticket
8
6
]
7]
6]
]
5
]
4]
3]
7
2
8
1
2
3
4
5
(3)
Elasticity
Coefficient (Ed)
5.00
2.60
1.57
1.00
0.64
0.38
0.20
(4)
Total Revenue
(1) X (2)
$8,000
]
14,000 ]
18,000 ]
]
20,000 ]
20,000 ]
18,000 ]
14,000
8,000
(5)
Total-Revenue
Test
Elastic
Elastic
Elastic
Unit Elastic
Inelastic
Inelastic
Inelastic
Price
Price Elasticity and the
Total-Revenue Curve
$8 a
7
b
6
c
5
d
4
e
3
f
2
g
1
Elastic
Ed > 1
Unit Elastic
Ed = 1
Inelastic
Ed < 1
h D
0 1 2 3 4 5 6 7 8
Total Revenue
(Thousands of Dollars)
Quantity Demanded
$20
18
16
14
12
10
8
6
4
2
Elastic
Ed > 1
Unit Elastic
Ed = 1
TR
0 1 2 3 4 5 6 7 8
Quantity Demanded
Inelastic
Ed < 1
Determinants of Price Elasticity of Demand
Substitutability
•
Substitutes for the product: Generally, the more substitutes,
the more elastic the demand.
Proportion of Income
•
The proportion of price relative to income: Generally, the
larger the expenditure relative to one’s budget, the more
elastic the demand, because buyers notice the change in
price more.
Luxuries versus Necessities
•
Whether the product is a luxury or a necessity: Generally,
the less necessary the item, the more elastic the demand.
Time
•
The amount of time involved: Generally, the longer the time
period involved, the more elastic the demand becomes.
Cross Elasticity of Demand
Exy =
Percentage Change in Quantity
Demanded of Product X
Percentage Change in Price
of Product Y
• Substitute Goods – Positive Sign
• Complementary Goods- Negative
Sign
• Independent Goods – Zero or NearZero Value
Income Elasticity of Demand
Ei =
•
•
Percentage Change in Quantity
Demanded
Percentage Change in Income
Normal Goods – Positive Sign
Inferior Goods- Negative Sign
Insights into the Economy
• Income elasticity of demand helps explain the expansion and
contractions in the economy. As income grows, industries of
products whose income elasticity is high expand rapidly,
while those of low or negative tend to grow slowly.
What you will learn in this chapter:
How much benefit do producers and
consumers receive from the existence of a
market?
How is the welfare of consumers and
producers affected by changes in market
prices?
How are these concepts related to demand
and supply curve?
Consumer Surplus
Producer Surplus
Cost
Market Failure
Consumer Surplus and the Demand Curve
Individual consumer surplus is the net gain to
an individual buyer from the purchase of a
good. It is equal to the difference between the
buyer’s willingness to pay and the price paid.
Total producer surplus in a market is the sum of
the individual producer surpluses of all the
sellers of a good.
New ipod
How much you
willing to pay for
this new ipod?
Student
A
B
C
D
How much you
willing to pay
Selling price
Your surplus
Used textbook
Used Text Books
Market
Amna
59
Bader
45
MAryam
35
Willingness to
pay
Amna
$59
Bader
$45
Maryam
$35
Nawaf
$25
Reem
$10
Nawaf
25
10
Potential
buyers
Reem
1
2
3
4
5
6
A consumer’s willingness to pay for a good is the maximum price
at which he or she would buy that good.
Used Text Books
Market
Amna
59
Bader
45
MAryam
35
Willingness to
pay
Amna
$59
Bader
$45
Maryam
$35
Nawaf
$25
Reem
$10
Nawaf
25
10
Potential
buyers
Reem
1
2
3
4
5
6
A consumer’s willingness to pay for a good is the maximum price
at which he or she would buy that good.
Used Text Books
Potential
Market
buyers
Amna
59
Willingnes
s to pay
Price paid
Individual
consumer
surplus
Amna
$59
Bader
$45
Maryam
$35
Nawaf
$25
---
---
Reem
$10
---
---
$30
$29
$30
$15
$30
$5
Bader
45
MAryam
$30
35
Nawaf
25
Reem
ICS = Willingness to pay –
Price paid
10
1
2
3
4
5
6
Willingness to Pay and Consumer
Surplus
Total consumer surplus is the sum of the
individual consumer surpluses of all the
buyers of a good.
The term consumer surplus is often used to
refer to both individual and to total
consumer surplus.
Amna
Willingnes
s to pay
Bader
$59
Maryam
$45
Nawaf
$35
Reem
$25
---
---
Amna
$10
---
---
Amna’sAmna
CS= $59 - $30 = $29
59
Bader CS= $45 - $30 = $15
Bader
MAryam
45
$3
035
Nawaf
Maryam’s CS= $35 - $30 = $5
Reem
25
10
1
2
3
4 5
Price paid
Individual
consumer
surplus
$30
$29
$30
$15
$30
$5
Demand curve for computers
The demand for computers is
smooth because there many
potential buyers of consumers.
Consumer Surplus
equal to the shaded
area: the are below the
demand curve but
above the price
Consumer Surplus
• difference between what you pay for
a good,
and what you are WILLING to pay for
a good
example
• market price pizza = $10
• my marginal value of 3rd pizza this
week = $12
• my consumer surplus = $2
my demand curve
P
$12
my consumer surplus
$10
D
Q
3
P
total consumer surplus
$10
area between D
and price of pizza
D
Q
10,000
How Changing Prices Affect Consumer
Surplus
A fall in the price of a good increases consumer
surplus through two channels:
A gain to consumers who would have
bought at the original price and
A gain to consumers who are
persuaded to buy by the lower price.
Let’s see these two channels in the following
graph…
Amna’s CS= $59 - $20 = $39
59
$2
9
45
$3
035
$2
025
10
Bader’s CS= $45 - $20 = $25
$1
5
Maryam’s CS= $35 - $20 = $15
$5
Nawaf’s CS= $25 - $20 = $5
Price of
Computers
Consumer surplus
Increase in Consumer surplus to original buyers
$5000
$1500
Consumer surplus gained by new buyers
200,000
1 million
Quantity of computers
Producer Surplus and the Supply Curve
A potential seller’s cost is the lowest price at
which he or she is willing to sell a good.
Individual producer surplus is the net gain to
a seller from selling a good. It is equal to the
difference between the price received and the
seller’s cost.
Total producer surplus in a market is the sum
of the individual producer surpluses of all the
sellers of a good.
The Supply Curve for Used Textbooks
Producer Surplus in the Used-Textbook
Market
Producer Surplus
The total producer
surplus from sales of
a good at a given
price is the area
above the supply
curve but below that
price.
Changes in Producer Surplus
When the price of a good rises, producer
surplus increases through two channels:
The gains of those who would have
supplied the good even at the original,
lower price and
The gains of those who are induced to
supply the good by the higher price.
Let’s consider the impact of a rise in the
market price on the producer surplus in the
following graph…
A Rise in the
Price Increases
Producer
Surplus
Putting it together: Total Surplus
The total surplus generated in a market is
the total net gain to consumers and
producers from trading in the market. It is
the sum of the producer and the consumer
surplus.
The concepts of consumer surplus and
producer surplus can help us understand
why markets are an effective way to
organize economic activity.
Total Surplus
1. If the price is set at $600:
CS = A
PS = B + C + E
TR = B + C + E +G
2. If the price is set at $400:
CS = A + B + C + D
PS = E + F
TR = E + F + G + H
3. If the price is set at $600,
then dropped to $400:
CS = A+ D
PS = B + C + E + F
TR = B + C + E + G + F + H
Consumer Surplus
Calculating from the graph
We can calculate the
consumer surplus in this
example using the
information provided on
the graph along with the
formula for
a triangle: (BASE x
HEIGHT)/2
Base = 40 – 0 = 40
Height = 3600 – 2000 = 1600
CS = (40 X 1600)/2 = 32000
Producer Surplus
Calculating from the graph
As with consumer
surplus, we can calculate
the producer surplus in
this example using the
information provided on
the graph along with the
formula for
Base = 40 – 0 = 40
a triangle: (BASE x
HEIGHT)/2
Height = 2000 – 400 = 1600
CS = (40 X 1600)/2 = 32000
Ann, Betty, and Carol are three buyers of shoes. Their
demand curves are shown below in terms of their
willingness to pay.
willingness to pay of:
a) If the price of shoes is $15, how many pairs will Ann buy?
a) If the price of shoes is $15, how many pairs will Betty buy?
c) If the price of shoes is $15, how many pairs will Carol buy?
Number of
Pairs
Ann
Betty
Carol
First
$100
$80
$90
Second
20
40
30
Third
10
30
10
Fourth
5
10
2
Fifth
2
5
1
2
3
2
d) If the price of shoes is $15, how many pairs of shoes will be bought in total?
e) What will Ann's consumer surplus be at this price? $
f) What will the total consumers' surplus be? $
7
= 100- 15 +20 – 15 = 90
= 90 + 105 + 90 = 285
Consumer Surplus
•
•
The benefit (utility) surplus received by the consumer in a market
is called consumer surplus )the difference between the maximum
price the consumer is willing to pay and the actual price he pays).
The utility surplus arises because all consumers pay the
equilibrium price even though many would be willing to pay more
than that price to obtain the product. Consider this example
Consumer
A
B
C
D
E
F
max price
13
12
11
10
9
8
actual price
8
8
8
8
8
8
consumer surplus
5
4
3
2
1
0
Consumer Surplus
O 18.3
Price (Per Bag)
Consumer
Surplus
Equilibrium
Price = $8
P1
D
Q1
Quantity (Bags)
Producer Surplus
• Producers also receive a benefit surplus which is the
difference between the actual price a producer receives and
the minimum acceptable price (determined at the supply
curve). Most sellers are willing to accept a lower than the
market price to sell the product.
• There is a direct relationship between equilibrium price and
producer surplus. Consider this example
Producer
•
G
H
I
J
K
L
max price
3
4
5
6
7
8
actual price
8
8
8
8
8
8
producer surplus
5
4
3
2
1
0
Producer Surplus
Price (Per Bag)
S
Equilibrium
Price = $8
P1
Producer
Surplus
Q1
Quantity (Bags)
Efficiency Revisited
• All markets that have downward slopping demand and upward
slopping supply curves yield consumer and producer surplus.
•
•
The equilibrium quantity in these markets reflect economic
efficiency.
Productive efficiency is achieved because competition forces
producers to minimize their costs.
•
•
1.
2.
3.
Allocative efficiency is also achieved because the correct
quantity at which MB (points on the demand curve or the
maximum willingness to pay) equals MC (points on the
supply curve or the minimum acceptable price). At
equilibrium consumer surplus and producer surplus are
maximized.
Allocative efficiency occurs at quantity levels where three
conditions exit:
MB = MC
Maximum willingness to pay = minimum acceptable price
Combined consumer and producer surplus is at a
maximum
Consumer and Producer Surplus
Efficiency Revisited
S
Price (Per Bag)
Consumer
Surplus
Equilibrium
Price = $8
P1
Producer
Surplus
D
Q1
Quantity (Bags)
Efficiency losses (deadweight loss)
• Efficiency losses are reductions of combined consumer and
producer surplus associated with underproduction (produce
less than equilibrium quantity) or overproduction (produce
more than equilibrium quantity).
•
•
•
Underproduction: at Q2 there is a deadweight loss equals
dec.
Overproduction: at Q3 there is a deadweight loss equals
cfg.
Since both consumers and producers are members of the
society, these losses are efficiency loss or a deadweight
loss
Consumer and Producer
Surplus
Efficiency Revisited
Efficiency Losses (Deadweight Losses)
Price (Per Bag)
a
S
d Efficiency
Losses
f
P1
c
g
e
b
D
Q2
Q1
Q3
Quantity (Bags)