The Compensation
Principle and Social
Welfare Function
Chapter 3
Incompleteness of Pareto Criterion

Pareto criterion is useless as a criterion for social
choices in many real-world situations since most
policy changes produce both gainers and losers

We employ two approaches to handle the inability of
Pareto criterion to handle mixed outcomes

Compensation principle

Social welfare function
The Compensation Principle

Hicks (1939) and Kaldor (1939)

Consider a project that moves economy from
state A to state B

This movement produces both gainers and
losers

Incomes can be costlessly redistributed
across individuals
Kaldor Compensation Criterion
The project is desirable according to
Kaldor compensation criterion if gainers
can compensate losers in state B in
such a way that everyone becomes
better off compared to state A
Kaldor Criterion: An Example
State A
John Bill
$100 $100
State B
John
$300
Bill
$0
State B after
redistribution
John Bill
$150 $150
$150
Since both John and Bill are better off in state B after the redistribution
compared to state A, the project that replaces state A with state B is
desirable according to the Kaldor criterion
Hicks Compensation Criterion
The project is desirable according to
Hicks compensation criterion if the
would-be losers are unable to bribe the
would-be winners not to make the
move from state A to state B
Pareto and Compensation Criteria

The compensation principle is stated in terms of potential
compensation rather than actual compensation

If compensation were required, the compensation principle
would be equivalent to Pareto principle (consider example for
Kaldor compensation criterion)

Considering the hypothetical compensation allows one to focus
on the efficiency aspects of the policy change

In other words, a policy change is desirable according to the
compensation criterion if total revenue resulting from the policy
change exceeds total cost
Compensation Principle and
General Equilibrium
We can further illustrate the meaning and
limitations of the compensation
principle by considering redistributions
of income between two households in
the framework of general equilibrium
Utility Possibilities Frontier
V
U = utility of household 1
Utility Possibilities Frontier
V = utility of household 2
AA = budget line in state A
VA
BB = budget line in state B
Good 2
VB
VB
A
UB
UA
UA
VA
A
Good 1
UB
U
Utility Possibilities Frontier:
Properties

All points on the utility possibilities frontier satisfy the
Pareto condition, i.e. you cannot increase both
households’ utilities by moving along this frontier
away from any point on it

Any movement along the frontier involves
redistribution of wealth (any improvement in one
household’s welfare necessarily requires a reduction
in the other household’s welfare)

No two points on the utility possibilities frontier can
be compared by Pareto or the compensation criterion
Compensation Criterion in
General Equilibrium Setting
V
1. Initially economy is at point O, which is Paretoinefficient since it is not on the utility possibilities
frontier
A
B
O
2. A move to point B is a Pareto
improvement for both households
3. A move to point A or C is a Pareto
improvement for at least one of the
households
C
D
Utility Possibilities Frontier
What about movement
to point D?
U
Compensation Criterion in
General Equilibrium Setting
V
1. A movement from O to D is NOT a Pareto-improvement since
utility of household 2 (or V) goes down
A
B
O
2. According to (Kaldor) compensation criterion, a
movement from O to D is an improvement because we
can move along the utility possibilities frontier (by
redistributing wealth among the two households) to point
B, which is a Pareto improvement compared to O
C
3. Remember: those compensations are
hypothetical! The move from O to D is still NOT a
Pareto improvement
D
Utility Possibilities Frontier
U
Compensation Principle: Limitations
V
1. Frontier PP represents the old technology,
while frontier RR represents the new one
R
C
2. B is preferred to A according to the new technology since
a movement along the RR utility possibilities frontier to C will
result in a Pareto improvement relative to A
P
3. However, A is also preferred to B since
a movement along the PP frontier to D will
result in a Pareto improvement as well
A
D
B
R
5. Thus, the compensation
principle cannot
completely order social
states
P
U
Social Welfare Function

Whenever there is a utility conflict among households, we need
more than a Pareto or compensation principle in order to be
able to rank social states

Such a complete and consistent ranking of social states is
called a social welfare ordering

If the social welfare ordering is continuous, it can be translated
into a social welfare function

Social welfare function relates individual utility levels to one
number called social welfare level so that the combinations of
individual utility levels that translate into higher levels of social
welfare are preferred to the combinations that result in lower
levels of social welfare.
Social Welfare Functions:
Properties

Welfarism: social welfare depends only on the utility levels of

Social welfare function is increasing in each household’s
utility level (ceteris paribus), so that an isolated increase of
any household’s utility level increases welfare of the whole
societysocial welfare indifference curves are negatively
sloped

Social welfare indifference curves are convex to the origin

Anonymity: It does not matter who gets a high or low level of
the households
utility
Social Welfare Indifference Curves
V
1. Social welfare increases as we move NorthEast from the origin so that a move from A to B
increases social welfare
2. Note that even if moving from A
to B makes household 2 lose (V
decreases) and no actual or
hypothetical compensation is paid,
the move is still socially desirable
A
B
W1
W2
W3
U
Social Choice using Utility Possibilities Frontier
and Social Welfare Function
V
1. Maximum achievable welfare is attained at the
tangency of the utility possibilities frontier and the
highest attainable social welfare indifference curve
A
2. Using the social welfare function, we
have reduced the infinite number of
possible general equilibria to a single
equilibrium point
Utility possibilities frontier
U