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Chapter 2: Fundamentals of
Welfare Economics
-In order to evaluate government policies, we
need a starting point
-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
Theory - 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
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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
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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
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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:
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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
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The Contract Curve



Assuming all possible starting points, 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
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The Contract Curve
Susan
O’
Food
r
O
Maka
s
Video Games
15
MATH – House and Chase
Assume that house and Chase have the following
utilities and MRS for books and coffee:
U
House
MRS
 B C ,U
House
BC
H
H
Chase
 B C
 C / B , MRS
H
H
C
Chase
BC
C
C /B ,
C
C
The Pareto Efficiency Condition therefore becomes:
MRS
House
BC
 MRS
Chase
BC
C /B C /B
H
H
C
,
C
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MATH – House and Chase
If there are 10 books, and 4 cups of coffee, then the
contract curve is expressed as:
MRS
House
BC
 MRS
Chase
BC
,
C / B  (4  C ) /(10  B )
H
H
H
H
If House has 6 books, a pareto efficient allocation
would be:
H
H
C / 6  (4  C ) /(10  6)
4C  6(4  C )
H
H
10C  24
H
C  2.4
H
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MATH – House and Chase
Therefore, House would have 6 books and 2.4 cups
of coffee, and Chase would have 4 (10-6) books
and 1.6 (4-2.4) cups of coffee, for utilities of:
U
House
 B C
U
Chase
 B C  4(1.6)  2.52
H
C
H
 6(2.4)  3.79
C
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Theory - 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) (MRTxy)

Note that although the slope is negative, the negative is assumed and rarely shown
in simple calculations
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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, MRTxy=MCx/MCy
3
2
Therefore, MRTpr=2/1=2
1
1
2
3
4
5
Pizzas
6
7
8
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Efficiency and Production

If production is possible in an economy, the
Pareto efficiency condition becomes:
MRTxy  MRS
PersonA
xy
 MRS
PersonB
xy
 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
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Efficiency & Production Example

From the PPC, we know that:
MC x
 MRT xy
MC y

We can therefore reinterpret Pareto efficiency
as:
MC x
PersonA
PersonB
 MRS xy
 MRS xy
MC y
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Theory - 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
23
First Fundamental Theorem of
Welfare Economics Origins

From microeconomic consumer theory, we
know that:
P
MRS


x
Py
Since prices are the same for all people:
MRS

PersonA
xy
PersonA
xy
 MRS
PersonB
xy
Therefore economic theory gives us the first
part of Pareto efficiency
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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
25
First Fundamental Theorem of
Welfare Economics Origins

Again from microeconomic consumer theory,
this changes to:
MRT xy  MRS xy


Which satisfies the second requirement of
Pareto Efficiency
Therefore, we can expand Pareto Efficiency to
imply that
MC x
Px
PersonA
PersonB
MRTxy 
 MRS xy
 MRS xy

MC y
Py
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Efficiency≠Fairness

If Pareto Efficiency was the only concern,
competitive markets automatically achieve it
and there would be very little need for
government:
– Government would exist to protect
property rights
 Laws,

Courts, and National Defense
But Pareto Efficiency doesn’t consider
distribution. One person could get all
society’s resources while everyone else
starves. This isn’t typically socially optimal.
27
Fairness
Susan
O’
r
Food
B
O
Maka
C
Points A and B are
Pareto efficient, but
either Susan or Maka
get almost all society’s
resources
A
Many would argue C is
better for society, even
though it is not Pareto
s efficient
Video Games
28
Fairness

For each utility level of one person, there is
a maximum utility of the other
– Graphing each utility against the other gives us
the UTILITY POSSIBILITIES CURVE

Just as typical utility is a function of goods
consumed: U=f(x,y), societal utility can be
seen as a function of individual utilities:
W=f(U1,U2)
– This is referred to as the SOCIAL
WELFARE FUNCTION, and can produce
SOCIAL INDIFFERENCE CURVES:
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Utility Possibilities Curve
All points on the curve are
Pareto efficient, while all
points below the curve are
not.
Any point above the curve
is unobtainable
Maka’s Utility
B
O
Maka
C
A
Susan’s Utility
30
Typical Social Indifference
Curves
Maka’s Utility
An indifference curve
farther from the origin
represents a higher level of
social welfare.
O
Maka
Susan’s Utility
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Fairness

If we superimpose social indifference
curves on top of the utilities possibilities
curve, we can find the Pareto efficient point
that maximizes social welfare

This leads us to the SECOND
FUNDAMENTAL THEOREM OF WELFARE
ECONOMICS
32
Maximizing Social Welfare
ii is preferred to i, even
though ii is not Pareto
efficient
Maka’s Utility
i
O
Maka
ii
iii
Susan’s Utility
The highest possible social
welfare, iii, is Pareto
efficient
33
Second Fundamental Theorem
of Welfare Economics
The SECOND FUNDAMENTAL THEOREM OF
WELFARE ECONOMICS states that society
can attain any Pareto efficient allocation of
resources by making a suitable
assignments of original endowments, and
then letting people trade
-Roughly, by redistributing income, society
can pick the starting point in the Edgeworth
box, therefore obtaining a desired point on
the Utility Possibility Frontier:
34
Second Fundamental Theorem
of Welfare Economics Susan
Food
r
O
Maka
O’
Starting
Point
Goal
s
Video Games
35
Why Income Redistribution?
Why achieve equity through income
redistribution instead of taxes/penalties and
subsidies/incentives?
Taxes and penalties punish incomeenhancing behavior, encouraging people to
work less.
Subsidies and incentives give an incentive to
stay in a negative state to keep receiving
subsidies and incentives.
Lump sum transfers have the least distortion.
36
Why Is Government so Big?
1)
Government has to ensure property laws
are protected. (1st Theorem)
2)
Government has to redistribute income to
achieve equity. (2nd Theorem)
3)
Often the assumptions of the First Welfare
Theorem do not hold (Chapter 3)
37
Welfare Economics Limitations
We Assume: Government exists to maximize the
utility of its citizens.
Government could aim to: Be a global power,
achieve cultural goals, achieve religious goals, etc.
Plus…what if people want to sit on the couch all day,
watching the Biggest Loser?
Should the government support this activity?
38
Merit Goods
Merit Good – commodities that should be
provided even if society
a) doesn’t want them
ie: police/fluorine in water
And/Or
b) is unwilling to cover their cost in the free
market
ie: Canadian Broadcast Corporation
(CBC)
39
Welfare Economics Evaluation
-Welfare Economics is concerned with
RESULTS, not PROCESS
-is the HOW important?
-contract law?
-Old Testament law?
-Lottery?
-Free-for-all wrestling match?
40
Welfare Economics Evaluation
Welfare Economics asks 3 questions of every
government action:
1)
2)
3)
Will it have desirable distributional
consequences?
Will it enhance efficiency?
Is the cost reasonable?
-Although these questions may be difficult to
answer, they provide direction, and if they are all
“no”, the government shouldn’t interfere
41