WELFARE ECONOMICS
Topic 5. Overcoming the limitations
of the Pareto principle:
(i) the compensation criteria
(ii) social welfare functions
1. Summary of last week’s lecture
3 requirements for Pareto Optimality in
general equilibrium:
1. MRS of any one household = MRS of
any other household
2. MRTS of any one firm = MRTS of any
other firm.
3. MRT between two goods = MRS
between those two goods
 The first fundamental theorem of
welfare economics is that a
competitive market equilibrium will
satisfy each requirement for Pareto
optimality
Good Y
Slope = MRT
Slope = PX/PY
Good X
 MRT = MRS
2. What conclusions can be drawn?
 Competitive markets generate an
equilibrium which is optimal in the
Pareto sense i.e. it is impossible to
make a change (in the mix of
goods produced, the inputs used
to produce them, or their allocation
between consumers) without
making at least one person worse
off.
 But may not be optimal in any
other sense e.g. may be very
unfair. The outcome depends
entirely on the initial distribution
of endowments
 There are an infinitely large
number of potential equilibria that
satisfy each of the 3 criteria. Each
is Pareto-non-comparable.
Choosing between them requires a
further criterion i.e. to invoke a
value judgement stronger than
Pareto.
3.
The Pareto principle:
limitations
The Pareto principle…
 is neutral to distributional
concerns
 is unable to rank every Pareto
optimal allocation superior to
every non-optimal allocation
 is unable to rank different
Pareto optimal allocations
relative to one another.
→ Cannot rank states that involve a
tradeoff in utility between
households.
→ a ‘stronger’ value judgement is
required to achieve a complete social
ordering of states.
4. Deriving the utility possibility
frontier and the grand utility
possibility frontier.
[diagrams to be drawn on the whiteboard]
Again, to reiterate the limitations of
Pareto, use the UPF to demonstrate
that:
 not all Pareto non-optimal points
can be ranked against all Pareto
optimal points.
 We cannot rank the Pareto optimal
points.
5.
The compensation criterion
→ is a shift from state x to state y (a
‘measure’) an improvement?
→ extend the notion of a Pareto
improvement to create a potential
Pareto Improvement.
Kaldor: If those who gain from the
measure can compensate those who
lose from the measure, such that the
losers are no worse off and the gainers
better off.
Hicks: If those who lose from the
measure are not able to bribe the
gainers not to take the measure.
6. Critiques of the
compensation criterion.
(a) Payments not actually carried out, so
the Pareto improvement remains potential
(not actual).
(b) The Scitovsky paradox.
The criterion may lead to intransitivity: a
measure as well the reversion of the
measure may be recommended under the
Kaldor Hicks criterion.
U1
c
a
d
b
UPF’
UPF
U2
7. Social welfare functions:
choosing the ‘optimum optimorum’
 SWF: a function of the utility levels
f(U1, U2) of all (both) households
such that a higher value of the
function is preferred to a lower one.
[‘Bergsonion’ or ‘BergsonSamuelson’]
 Bergsonian SWF a general
expression. Simply says social
welfare = ‘some function of’
individual utilities.
 General properties: welfarism;
welfare increasing in each
individual’s utility; negativelysloped; convexity; anonymity.
 slope = marginal rate of social
substitution (MRSS)
U1
W3
W2
W1
Grand
UPF
U2
8.
Specific functional forms
(i) Simple utilitarian SWF: equalweighted sum of utilities.
(ii) Generalised utilitarian: weighted
sum of utilities.
i.e. society ‘should’ be prepared to
prepared to accept a decrease in the
utility of the poor as long as there is
a much larger increase in the utility
of the rich.
(iii) Rawlsian (maximin)
The welfare of society depends only
on the utility of the poorest (worst-off)
household.
9. Requirements: measurability
and comparability.
Where do SWF ‘come from’?
What limits our ability to establish a
SWF?
 Measurability: refers to the sense
in which the real numbers attached
to a household’s utility levels are
meaningful (convey information)
 Comparability: refers to the sense
in which the real numbers attached
to different households’ utility levels
can be meaningfully compared.
 Measurability possibilities: Absolute
scale, cardinal scale, ratio scale,
ordinal scale.
“The more information that is
available (or the higher the degree of
measurability and comparability the
planner is faced with…) the larger
the set of SWOs to choose from. The
choice of a specific form for the SWO
then involves a further ethical
judgement about how to aggregate
the individual utilities.”
[Boadway and Bruce, p. 169]