Chapter 2: Fundamentals of
Welfare Economics
-In order to evaluate government policies, we
need a general framework
-We can’t evaluate each policy on a case-bycase basis
-ie: Lower interest rates lowers unemployment,
then raising minimum wage increases
unemployment (counter-productive)
-Welfare Economics – the branch of economic theory
concerned with the social desirability of alternate
economic states and policies
Chapter 2: Fundamentals of
Welfare Economics
 Welfare
Economics
 First Fundamental Theorem of
Welfare Economics
 Second Fundamental Theorem of
Welfare Economics
Starting Point:
Pure Exchange Economy

We start with a simple model:
– 2 people
– 2 goods, each of fixed quantity
– Determine good allocation

The important results of this simple, 2person model hold in more real-world
cases of many people and many
commodities
3
Pure Exchange Economy
Example




Two people: Maka and Susan
Two goods: Food (f) & Video Games (V)
We put Maka on the origin, with the y-axis
representing food and the x axis representing
video games
If we connect a “flipped” graph of Susan’s
goods, we get an EDGEWORTH BOX, where y
is all the food available and x is all the video
games:
4
Maka’s Goods Graph
Food
Ou is Maka’s food, and Ox
Is Maka’s Video Games
u
O
Maka
x
Video Games
5
Edgeworth Box
Food
r
y
Susan
O’ O’w is Susan’s food,
and O’y is Susan’s
Video Games
Total food in the
w market is Or(=O’s)
and total Video
Games is Os (=O’r)
u
O
Maka
x
Video Games
s
Each point in the
Edgeworth Box
represents one
possible good
allocation
6
Edgeworth and utility

We can then add INDIFFERENCE curves to
Maka’s graph (each curve indicating all
combinations of goods with the same utility)
– Curves farther from O have a greater utility
– (For a review of indifference curves, refer to
Intermediate Microeconomics)

We can then superimpose Susan’s utility
curves
– Curves farther from O’ have a greater utility
7
Maka’s Utility Curves
Food
Maka’s utility is greatest at M3
M3
M2
M1
O
Maka
Video Games
8
Edgeworth Box and Utility
Susan
O’ Susan has the
highest utility at S3
r
S1
Food
S2
A
At point A, Maka
has utility of M3 and
Susan has Utility of
M3 S2
S3
M2
M1
O
Maka
s
Video Games
9
Edgeworth Box and Utility
Susan
O’ If consumption is at
A, Maka has utility
M1 while Susan has
utility S3
r
Food
A
S3
O
Maka
B
C
Video Games
By moving to point
B and then point C,
M3 Maka’s utility
M2
increases while
M1
Susan’s remains
constant
s
10
Pareto Efficiency
Food
r
S3
O
Maka
C
Susan
O’ Point C, where the
indifference curves
barely touch is
called PARETO
EFFICIENT, as one
person can’t be
made better off
M3
without harming the
M2
other.
M1
s
Video Games
11
Pareto Efficiency

When an allocation is NOT pareto efficient, it
is wasteful (at least one person could be
made better off)
– Pareto efficiency evaluates the desirability of an allocation


A PARETO IMPROVEMENT makes one person better
off without making anyone else worth off (like the
move from A to C)
However, there may be more than one pareto
improvement:
12
Pareto Efficiency
Food
r
S3
S4
S5
A
C
E
D
O
Maka
Video Games
Susan
O’ If we start at point A:
-C is a pareto
improvement that
makes Maka better
off
-D is a pareto
improvement that
M3
makes Susan better
M2
off
M1
-E is a pareto
improvement that
s
makes both better off
13
The Contract Curve



Assuming any possible starting point, we can
find all possible pareto efficient points and join
them to create a CONTRACT CURVE
All along the contract curve, opposing
indifferent curves are TANGENT to each other
Since the slope of the indifference curve is the
willingness to trade, or MARGINAL RATE OF
SUBSTITUTION (x for y) (MRSxy), along this
contract curve:
Maka
Susan
MRSVf
 MRSVf
Pareto Efficiency Condition
14
The Contract Curve
Susan
O’
Food
r
O
Maka
s
Video Games
15
Starting Point:
Economy with production

A production economy can be analyzed using
the PRODUCTION POSSIBILITIES
CURVE/FRONTIER
– The PPC shows all combinations of 2 goods that
can be produced using available inputs
– The slope of the PPC shows how much of one
good must be sacrificed to produce more of the
other good, or MARGINAL RATE OF
TRANSFORMATION (x for y) (MRTSxy)

Note that although the slope is negative, the negative is assumed and rarely shown
in simple calculations
16
Production Possibilities Curve
Here the MRTSpr is equal to (75)/(2-1)=-2, or two robots must be
given up for an extra pizza.
10
9
8
The marginal cost of the 3rd pizza,
or MCp=2 robots
Robots
7
6
The marginal cost of the 6th and 7th
robots, or MCr=1 pizza
5
4
Therefore, MRTSxy=MCx/MCy
3
2
Therefore, MRTSpr=2/1=2
1
1
2
3
4
5
Pizzas
6
7
8
17
Efficiency and Production

If production is possible in an economy, the
Pareto efficiency condition becomes:
MRTxy  MRS


PersonA
xy
 MRS
PersonB
xy
Assume that MRT>MRS. A person could
transform x into y at the rate of MRS and have
x left over, thus increasing his utility
Assume that MRT<MRS. A person could
transform y in x at the rate of MRS and have y
left over, thus increasing utility
Pareto Efficiency cannot occur at inequality
18

Efficiency & Production Example

Assume MRTpr=3/4 and MRSpr=2/4.
– Therefore Maka could get 3 more robots by
transforming 4 pizzas
– BUT Maka only needs to get 2 robots for 4 pizzas
to maintain utility
– Therefore his utility increases from the extra robot,
Pareto efficiency isn’t achieved

We can therefore reinterpret Pareto efficiency
as:
MC x
PersonA
PersonB
 MRS xy
 MRS xy
MC y
19
First Fundamental Theorem Of
Welfare Economics
IF
1) All consumers and producers act as perfect
competitors (no one has market power)
and
2) A market exists for each and every
commodity
Then
Resource allocation is Pareto Efficient
20
First Fundamental Theorem of
Welfare Economics Origins

From microeconomic consumer theory, we
know that:
P
MRS


x
Py
Since this holds true for all people:
MRS

PersonA
xy
PersonA
xy
 MRS
PersonB
xy
Which is the first requirement for Pareto
efficiency, before production is considered
21
First Fundamental Theorem of
Welfare Economics Origins

From basic economic theory, a perfect
competitive firm produces where P=MC,
therefore: MC
P
x
MC y


x
Py
But we know that MRT is the ratio of MC’s,
therefore:
P
MRTxy 
x
Py
22
First Fundamental Theorem of
Welfare Economics Origins


Again from microeconomic consumer theory,
this changes to:
But we know that MRT is the ratio of MC’s,
therefore:
P
MRTxy 
x
Py
23
The Law of Demand

There is an inverse relationship
between the quantity of anything
that people will want to purchase
and the price they must pay to
obtain it:
ceteris



paribus (all else held equal)
This causes demand curves to be
downward sloping
When prices increase, people buy less
When prices decrease, people buy more
24
The Individual’s Demand Schedule
A
B
C
D
E
5.00
4.00
3.00
2.00
1.00
5
Qn/yr
10
20
30
40
50
Price of Songs ($)
Price/Unit
$
A
B
4
C
3
2 Change in Price
Movement along
1 the Demand
0
10
20
30
D
E
40
Number of Songs per Year
50
25
Note:
We always graph P on vertical axis and Q on
horizontal axis, but we write demand as Q as
a function of P… If P is written as function of
Q, it is called the inverse demand:
Normal Form: Qd=100-2P
Inverse form: P =50 - Qd/2
 Markets defined by commodity,
geography, time.
26
Movement Along Demand/
Changes in Quantity Demanded

A change in a good’s own price
change in quantity
demanded
– the same thing as a movement along
– results in a
the same demand curve.
27
Shifts/Changes in
Demand*
 A change in one or more of the nonprice determinants of demand
(income, tastes, etc)
change in demand *
– also called a shift in demand*
– results in a
*The whole demand schedule
28
A Shift in the Demand
Suppose universities
Curve
outlaw the
use of
Suppose the federal
MP3 Players
Decrease
in Demand
Price of Songs ($)
5
government gives
every student a SanDisk
MP3 player
4
3
Increase
in Demand
2
1
0
D3
20
30
40
50 60
D2
D1
70
80
Quantity of Songs Demanded
29
“Everything Else” :
The “Determinants”/ “Shifters”
of “Demand”

Factors other than Price
which affect “Demand” :
1) Income, wealth
 2) Tastes and
preferences
 3) The price of related
goods
– Complements
– Substitutes

4) Expectations
– Future prices
– Income
– Product availability
 5) Population (market size)

What movement would these factors
cause?
30
Review of Demand Terminology
 Demand:
a schedule of quantities that
will be bought/unit of time, at various
prices, ceteris paribus.
 Quantity
Demanded: a specific amount
that will be demanded /unit of time at a
specific price, ceteris paribus.
 There is a difference between between a
change in the Quantity Demanded and
a shift in Demand.
31
A policy to discourage
smoking (no smoking in
public buildings) shifts
the demand curve left
Price of Cigarettes, per pack
Price of Cigarettes, per pack
Shift vrs. Movement
$2
D’
10
A tax raises the price of
cigarettes, resulting in a
movement along the
demand curve
$4
$2
D
D
20
Number of Cigarettes
smoked per day
10
20
Number of Cigarettes
smoked per day
32
Normal vrs. Inferior Goods
For inferior goods,
Demand increases
When income decrease
Price of Kraft Dinner
Price of Chicken
For normal goods,
Demand decreases
With income
$2
D’
10
$2
D’
D
20
Chicken eaten in a month
D
10
20
30
Kraft Dinner eaten
in a month
33
Supply: Profit

The Cost side of the profit
equation depends on the Costs of
Production which depend on
 the kinds of inputs (factors of
production) used
 the amount of each input
used
 prices of inputs used
 technology
34
Supply: Definition

A schedule that shows how
much of a product a firm will
supply at alternative prices for a
given time period “ceteris
paribus”.
35
The Law of Supply
• The price of a product or service and
the quantity supplied are directly
related: “ceteris paribus”
• Causes an upward sloping supply curve
• The higher the price of a good, the more
sellers will make available
• The lower the price of a good, the fewer
sellers will make available
• All else being equal
36
The Individual Producer’s Supply
Schedule
Qnty of
F
$5
550
G
4
400
H
3
350
I
2
250
J
1
200
5
Price of Song ($)
Price /
Song
Songs
Supplied
(thousands /
year)
F
G
4
H
3
I
2
1
J
Change in Price
Movement along
The Supply
0 100 200 300400500 600
Quantity of Songs Supplied
(thousands of constant-quality units
per year)
37
Movement Along Supply/
Changes in Quantity Supplied
– A change in a good’s own price
change in quantity supplied.
 that is, a movement along the supply curve.

leads to a
38
Shifts/Changes in
Supply

A change in one or more of the nonprice determinants of supply leads to a
– change in supply which is the same
thing as a
– shift of the supply curve.
39
A Shift in the Supply Curve
When supply decreases the quantity supplied
will be less at each price:
ie: Singers form a union and successfully negotiate
higher wages
Price of Songs ($)
5
S2
a
b
4
3
b
c
d
S2
S1
d
2
1
0
20
40
60
When supply increases
the quantity supplied
will be greater at each
price:
ie: producer finds that
she can use some
cheaper singers from
Newfoundland
80 100 120 140
Quantity of Songs Supplied
(millions of constant-quality units per year)
40
“Everything Else” : The
“Determinants”/“Shifters” of Supply
 Factors
Supply
other than Price that affect
– 1) Cost of inputs (price in factor markets)
–
–
–
–
2)
3)
4)
5)
Technology and Productivity
Taxes and Subsidies
Price Expectations (in the product market)
Number of firms in the industry
How will these shift
supply?
41
Market Equilibrium Price & Quantity
 Market:
where prices tend toward
equality through the continuous
interaction of buyers and sellers: the
market forces of demand and supply
Single Equilibrium
Price
42
Putting Demand and Supply Together:
Finding Market Equilibrium
(1)
(2)
(3)
Price per
Constant-Quality
Song
Quantity Supplied
(Songs
per year)
Quantity Demanded
(Songs
per year)
(4)
Difference
(2) - (3)
(Songs
per year)
(5)
Condition
$5
100 million
20 million
80 million
Excess quantity
supplied (surplus)
4
80 million
40 million
40 million
Excess quantity
supplied (surplus)
3
60 million
60 million
0
2
40 million
80 million
-40 million
Excess quantity
demanded (shortage)
1
20 million
100 million
-80 million
Excess quantity
demanded (shortage)
43
Market Equilibrium: Definition
The condition in a
S
market when
quantity
supplied equals
quantity
Market clearing, or
Q
=
Q
E
D
S
equilibrium, price
demanded at a
particular price;
a point from
A
B
where there
tends to be no
Excess quantity demanded at price $1 D
20
40
60
80
100
movement
Excess quantity supplied at price $5
Price pef Song ($)
5
4
3
2
1
0
Quantity of Songs
(millions of constant-quality units per year)
44
The Law of Supply &
Demand
The price of any good will adjust until the
price is such that the quantity demanded
is equal to the quantity supplied
 A high price will result in excess supply,
pushing price down, and a low price will
result in excess demand, pushing price up

 the
market clears resulting in a single
market clearing or equilibrium price.
45
Qd = 500 – 4p
S
Q = -100 + 2p
p = price of cranberries (dollars per barrel)
Q = demand or supply in millions of
barrels per year
46
a. The equilibrium price of cranberries is calculated by
equating demand to supply:
Qd = QS … or…
500 – 4p = -100 + 2p
…solving,
500+100=2p+4p
p* = $100
b. plug equilibrium price into either demand or supply
to get equilibrium quantity:
Qd = 500-4d
Qd = 500-4(100)
Qd = 100
47
Example: The Market For Cranberries
Price
125
Market Supply: P = 50 + QS/2
P*=100
50
Market Demand: P = 125 - Qd/4
Quantity
48
Example: The Market For Cranberries
Price
125
P*=100
Market Supply: P = 50 + QS/2
•
50
Market Demand: P = 125 - Qd/4
Q* = 100
Quantity
49
Comparative Statics: Shifts in
Demand &/or Supply
•Suppose something in the demand &/or the
supply “ceteris paribus” assumptions changes.
•How is the MARKET affected?
– 1.) Decide whether Demand &/or Supply is
affected.
– 2.) Decide in which direction the affected
Demand &/or Supply will move.
– 3.) Use a Demand and Supply diagram to
determine the new equilibrium.
– 4.) Calculate the new equilibrium (if
possible)
50
Comparative Statics: Gas Prices
Summer 2009: Gas prices at equilibrium
at $1.07 per liter
 Winter arrives and certain drivers limit or
end their driving for the season (shift in
demand)

–The new market equilibrium is $0.87
per liter

Cold Weather causes a decrease in gas
prices
51
Ford Escape Market

Consider the market
for Ford Escapes.
1. For each event
identify whether
demand or supply
is affected.
P1
2. Determine the
direction of change.
3. Draw a diagram to
illustrate how
equilibrium is
changed.
S
E1
D1
Q1
52
Ford
Escape
Market
Steelworkers Strike Raises
Steel Prices
S2
E2
S1
P2
E1
P1
D
Q2 Q1
53
Ford
Escape
Market
New Automated Machinery
Introduced
S1
E1
S2
P1
P2
E2
D
Q1 Q2
54
Ford Escape
Market
Price of Station Wagons Rises
E2
S
P2
E1
P1
D1
Q1
Q2
D2
55
Ford Escape
Market
Stock Market Crash Lowers Wealth
S
P1
P2
E1
E2
D2
Q2 Q1
D1
56
Simultaneous Shifts
Example of a double shift.
– 2 events
 1.
 2.
 supply
 demand
only  supply P, Q.
 only  demand P, Q.

57
Shifts in Demand and in Supply
S1 S
2
E2
P2
P1
E1
D1
Q1
Q2
D2
58
Simultaneous Shifts
S1
P1
P2
S2
E1
E2
D1
Q1
Q2
D2
59
Simultaneous Shifts
Example of a double shift.

second possibility
– 2 events
 1.
 2.
 supply
 demand
only  supply P, Q.
 only  demand P, Q

60
Shifts in Demand and in Supply
S1
S2
E1
P1
P2
E2
D2 D1
Q1Q2
61
Shifts in Demand and in Supply
S1
S2
E
P1
P
1
E2
2
D1
D2
Q2 Q1
62
Qd = 500 – 4p
QS = -100 + 2p
p = price of cranberries (dollars per barrel)
Q = demand or supply in millions of
barrels per year
Assume that a plague reduced cranberry supply and fear of
inflection likewise reduced cranberry demand so that:
Qd = 400 – 4p
QS = -200 + 2p
63
a. The new equilibrium price of cranberries is
calculated by equating demand to supply:
Qd = QS … or…
400 – 4p = -200 + 2p
…solving,
400+200=2p+4p
p* = $100
b. plug equilibrium price into either demand or supply
to get equilibrium quantity:
Qd = 400-4d
Qd = 400-4(100)
Qd = 0
64
Example: The Market For Cranberries
Price
125
POLD=PNew
New Market Supply: P = 100 + QS/2
Old Market Supply: P = 50 + QS/2
•
50
Old Market Demand: P = 125 - Qd/4
QNew
QOLD
Quantity
New Market Demand: P = 100 - Qd/4
65
Elasticity: Percentage Change
Consider
the following:
– An increase of 50 cents or an increase of
50% in the price of a hamburger
– An increase of $100 or an increase of 1%
in the price of a new car
Percentage
changes are easier to grasp
than the amount of change
– Therefore economists often use elasticities
to examine percentage change or
responsiveness
66
Price Elasticity of Demand

Price Elasticity of Demand (Є Q,p)
– The responsiveness of quantity demanded
of a commodity to changes in its price
– Related to the slope, but concerned with
percentage changes
67
Price (dollars per pizza)
Impact of a Change in Supply &
Therefore Price on the Quantity
Demanded
S0
40.00 … a
30.00
large
fall in
price...
S1
An increase
in supply
brings ...
Large price
change and
small quantity
change
20.00
10.00
… and a small
increase in quantity
5.00
0
5
10 13 15
Da
20
25
Quantity (pizzas per hour)
68
Price (dollars per pizza)
Impact of a Change in
Supply…
An increase
in supply
S0
brings ...
40.00
30.00 … a small
fall in price...
20.00
15.00
Small price
change and
large quantity
change
Db
10.00
0
S1
… and a large
increase in quantity
5
10
25
15 17 20
Quantity (pizzas per hour)
69
Solution: Price Elasticity of Demand
Price Elasticity of Demand
ЄQ,P 
Percentage change in quantity demanded
Percentage change in price
%Qd
Q,P 
%P
The ratio of the two percentages is a
number without units.
70
Price Elasticity

Example
– Price of oil increases 10%
– Quantity demanded decreases 1%
- 1%
Q,P 
 .1
 10%
When calculating the price elasticity of
demand, we often ignore the minus
sign for % change in Q.
71
TYPES OF ELASTICITY -Hypothetical Demand Elasticities
Product
% Change in
price (%P)
% Change in
quantity
demanded
(%QD)
Elasticity
(%QD/%P)
Insulin
+ 10%
0%
0  Perfectly
inelastic
Basic
Telephone
service
+ 10%

-1%
.1  Inelastic
Beef
+ 10%

-10%
1.0  Unitarily
elastic
Bananas
+ 10%

-30%
3.0Elastic
72
Price Elasticity Ranges: Extreme
Price Elasticities
Perfect elasticity,
D
Price
P1
P0
0
8
Quantity Demanded per Year
(millions of units)
30
D
P1
Price
Perfect
inelasticity,
zero elasticity,
no matter how
much Price
changes,
Quantity
stays the
same;
insulin
infinite elasticity,
the slightest
increase
in price will
lead to
zero sales.
P1 is
the
demand
curve
0
Quantity Demanded per Year
(millions of units) 73
Price Elasticity Ranges
Summary from Table
 Elastic Demand
%Q  %P; Q,P  1
 Unit Elastic
%Q  %P; Q,P  1
 Inelastic Demand
%Q  %P; Q,P  1
74
Elasticity of Demand

Calculating elasticity
ЄQ,P 
or
Change in Q
Sum of quantities/2
ЄQ,P 
Change in P
Sum of prices/2
Change in Q
(Q1  Q2 )/2
or
Change in P
(P1  P2 )/2
Q
ЄQ,P 
Avg. Q
P
Avg. P
75
Calculating the Elasticity of Demand
Price (dollars/pizza)
Original
point
20.50
ΔP=1
Q /Qave 2/10
=
Elasticity =
=4
P/Pave 1/20
20.00
New
point
19.50
D
Qave =1/2(11+9)=10
Pave =1/2(20.50+19.50)=20
9
10
ΔQ=2
11
Quantity (pizzas/hour)
76
Elasticity of Demand (mid-point)
Q =2
% Q
=20%
X 100
Q1 + Q2 (9 + 11)
= 10
2
ЄQ,P
=
 P = $1.00
% P
=5%
= ЄQ,P =
20%
4
=
5%
X 100
P1 + P2 ($20.50 + $19.50)
= $20
2
Always use the mid-point formula for calculating elasticity
77
Elasticity: Example







You are the consulting economist to the
Guelph transportation commission,
The current fare is $.95
There are 17,500 riders per day
For each $.10 increase in the fare, rider ship
decreases by 10,000 riders per day.
What is the price elasticity of demand at the
current fare?
Should fares be raised or lowered?
What fare will maximize revenue?
78
Total Revenue and
Elasticity
Total Revenue
=
Price Per Good
X
# of Goods Sold
TR = P X Q
Assumption : Costs are constant
79
Elastic
demand
Price
1.10
.80
Unit
elastic
.55
Inelastic
demand
Quantity
0
55
(dollars)
Total Revenue
3.00
When demand is
elastic, price cut
increases total
revenue
110
Maximum
total revenue
When demand
is inelastic,
price cut decreases
total revenue
Quantity
0
55
110
80
Relationship Between Price
Elasticity of Demand and Total Revenues
Price Elasticity
of Demand
Effect of Price Change
on Total Revenues (TR)
Price
Decrease
Inelastic (ЄQ,P < 1)
Unit-elastic
Elastic
TR 
(ЄQ,P = 1) No change
(ЄQ,P > 1)
TR
Price
Increase
TR
No change
TR 
Note: It is possible to classify elasticity by observing
the change in revenue from a price change
81
Question
•
•
•
•
•
2 drivers - Tom & Jerry each drive to to
a gas station.
Before looking at the price, each places
an order.
Tom says, “I’d like 10 litres of gas”.
Jerry says, “I’d like $10 of gas”.
What is each driver’s price elasticity of
demand?
82
Determinants of
Price Elasticity of Demand

Existence of substitutes
–Goods are more price elastic if substitutes exist

Share of budget
–Goods are more price elastic when a consumer’s
expenditure on the good is large (in dollar terms
or relatively)

Necessity
–Goods are less price elastic when seen as a
necessity
83
Market and Brand Elasticities

Market and Brand Elasticities are not
equal
–Although a water addict is very price inelastic to
the price of bottled water in general, he/she
would quickly switch to another brand if only 1
brand of water increased in price
–GENERALLY, Brand price elasticity of demand is
higher than market price elasticity of demand
84
Qd = a – bp
a,b are positive constants
p is price
-b is the slope
a/b is the choke price (price at which
nothing is sold)
85
the elasticity is
Q,P = (Q/p)(p/Q) …definition…
= -b(P/Q)
Since the slope of the graph is –b.
Therefore…elasticity falls from 0 to - along the
linear demand curve, but slope is constant.
if Qd = 400 – 10p, and p = 30,
Q,P = (-10)(30)/(100) = -3 "elastic"
86
Changes in Elasticity Along a
Linear Demand
1.10
Elastic (ЄQ,P > 1)
1.00
Price per Minute ($)
.90
Unit-elastic (ЄQ,P = 1)
.80
Inelastic (ЄQ,P < 1)
.70
.60
.50
.40
.30
.20
D
.10
0
1
2
3
4
5
6
7
8
9
Quantity per Period (billions of minutes)
10
11
87
The Relationship Between Price Elasticity of
Demand and
Total Revenues for Cellular Phone Service
Price
Quantity
Demanded
Total
Revenue
Elasticity
ЄQ,P
$1.10
0
0
1.00
1
1.0
.90
2
1.8
.80
3
2.4
.70
4
2.8
.60
5
3.0
1.144
.50
6
3.0
1.000 Unit-elastic
.40
7
2.8
.692
.30
8
2.4
.20
9
1.8
.467
.294
.10
10
1.0
.158
21.000
6.333
3.400
Elastic
2.143
Inelastic
88
Qd = Ap
 = elasticity of demand and is
negative
p = price
A = constant
Elasticity is constant, but the slope of demand falls
from 0 to -.
In another form, if
Ln(Qd)=μLN(P),
μ= Price Elasticity of Demand
89
Example: A Constant
Elasticity versus a Linear
Demand Curve
Price
•
P
Observed price and quantity
Constant elasticity demand curve
Linear demand curve
0
Q
Quantity
90
Elasticity of Supply

Calculating elasticity
ЄQs,P
Change in Q
Change in P
Sum of quantities/2
Sum of prices/2
or
Change in Q
ЄQs,P 
(Q1  Q2 )/2
or
ЄQs,P
Change in P
(P1  P2 )/2
Q

Avg. Q
P
Avg. P
91
Price (dollars per pizza)
How a Change in Demand Changes
Price and Quantity
40.00
An increase
in demand
brings ...
Sa
Large price change and
small quantity change
30.00
20.00
10.00
0
… a large
price rise...
… and a small
quantity increase
5
10 13 15
D1
20
25
D0
Quantity (pizzas per hour)
92
Price (dollars per pizza)
How a Change in Demand Changes Price and
Quantity
40.00
Small price
change and
large quantity
change
An increase
in demand
brings ...
30.00
21.00
20.00
Sb
… a small
10.00 price rise...
… and a large
quantity increase
D1
D0
0
5
10
15
20
25
Quantity (pizzas per hour)
93
Elasticity of Supply

Elasticity of supply ranges
– (from) Perfectly Elastic Supply

Quantity supplied falls to 0 when there is any decrease in
price
– (to) Perfectly Inelastic Supply

Quantity supplied is constant no matter what happens to
price
Notice: There is no total revenue test for supply
since price and quantity are directly related
94
supply = 0
Price
Price
Supply Elasticity
SRanges
Elasticity of
Elasticity of
supply =

S
Quantity supplied is
the same for any
price!
0
Quantity
Suppliers will offer
ANY quantity at this
price
0
Quantity
95
Elasticity of Supply: Depends On:
1. Resource substitution possibilities,
-The more unique the resource, the more
inelastic the supply.
2. Time frame for the supply decision,
Momentary supply
Long-run supply
Short-run supply
- Typically, the longer producers have to adjust to
a price change, the more elastic is supply.
96
Long-Run Elasticity of Demand
Elasticities can vary in the short run (when major
changes cannot be made) and the long run.
-For most goods, elasticity of demand is greater in
the long run (curves are “flatter”)
-People are more able to adjust to changes over
time (slowly switch consumption)
-For essential durable goods (ie: Cars), long-run
demand elasticity is less (curves are “steeper”)
-People can change their purchases or suppliers
now, but eventually they have to buy new goods
as old ones break

97
Long-Run Elasticity of Supply
Elasticities can vary in the short run (when major
changes cannot be made) and the long run.
-For most goods, elasticity of supply is greater in the
long run (curves are “flatter”)
-Firms are more able to adjust to changes over time
(slowly switch production)
-For reusable goods (ie: Aluminum), long-run supply
elasticity is less (curves are “steeper”)
-People resell their stock when prices go up, but
eventually their stock runs out

98
Supply Elasticity and the Long Run
(most non-durable,
non-essential goods)
Price per Unit
S1
S2
P1
Pe
As time passes, the
supply curve rotates
to S2 and then to S3
and quantity supplied
rises first to Q1 and
then to Q2
Qe
Q1
Q2
Quantity Supplied per Period
99
How Long is the Long Run?

There is no set amount of time that puts a
market into the long run
– The long run could be a week or a year

The long run is how long a consumer or
firm takes to fully adjust to a price change
– Time required to make major changes
– Ie) Give up Pepsi Vanilla, Build more cost
efficient Pepsi factory, secure a US Pepsi
Vanilla supplier

The short run is anything shorter than the
long run
100
Cross Price Elasticity of Demand

We’ve seen already that demand is affected by
the price of substitutes and compliments
– An increase in the price of a substitute increases
demand
– An increase in the price of a complement decrease
demand
This effect can be measured using cross price
elasticity
 If the cross price elasticity is zero, the good is
neither a complement nor a substitute

101
Cross Price Elasticity of Demand
Є

Qi,Pj
Є Qi,Pj =
Percentage change in quantity demanded of X
Percentage change in price of Y
Change in X
--------------(X1 + X2)/2
/
Change in Price of Y
---------------------------(Py1 + Py2)/2
Substitutes – Positive Cross Price Elasticity
Compliments – Negative Cross Price Elasticity
102
Cross Price Elasticity of Demand Example
“Recent cat attacks have prompted cat
owners to buy guns for self-defense”
Originally,
2 Econ students owned a cat. After the
price of guns went from $100 to $200, only 1 Econ
student owned a cat.
Calculate the cross-price elasticity of demand
103
Cross-Price Elasticity
 Q = -1
% Qi
=-66%
X 100
Q1 + Q2 (2 + 1)
= 1.5
2
ЄQ,P
=
 P = $100
% PJ
=66%
= ЄQi,Pj =
-66%
=
66%
-1
X 100
P1 + P2 ($100 + $200)
= $150
2
Are cats and guns substitutes or compliments?
104
Income Elasticity of Demand
Income Elasticity of demand refers to a
HORIZONTAL SHIFT in the demand
curve resulting from an income change
 Price elasticity of demand refers to a
MOVEMENT ALONG THE DEMAND
CURVE in response to a price change

105
Income Elasticity of Demand
Є Q,I 
Є Q,I=
Percentage change in quantity demanded
Percentage change in income
Change in Q
--------------(Q1 + Q2)/2
/
Change in M
---------------------------(M1 + M2)/2
Normal Good – Positive Shift/Elasticity
Inferior Good – Negative Shift/Elasticity
106
Income Elasticity of Demand Example
In New Zealand, the average family will own 4
Toyotas in their lifetime.
 If average Kiwi family income rose from $140K to
$160K a year, the average Kiwi family would own 2
Toyotas over their lifetime

Calculate Income Elasticity of Demand for Toyotas
in New Zealand.
 Are Toyotas normal or inferior goods in New
Zealand?

107
Income Elasticity of Demand
 Q = -2
% Q
=-66%
X 100
Q1 + Q2 (4 + 2)
=3
2
ЄQ,I
=
 I = $20K
% I
=13.3%
= ЄQi,Pj =
-66%
13.3%
= -5
X 100
I1 + I2 ($140K + $160K)
= $150K
2
In New Zealand, are Toyotas normal or inferior goods?
Guess which brand is the luxury car.
108