New Welfare Economics, showing the point of constrained bliss

1. PROF. PRABHA PANTH,
OSMANIA UNIVERSITY,
HYDERABAD

2. Bergson and Samuelson’s Social
Welfare Function
 Hicks and Kaldor’s Compensation principle – does
not show a unique equilibrium point, where
individuals’ and social welfare is maximised.
 If Ps of the two goods change, then equilibrium
point also changes.
 Does the new equilibrium give greater welfare
than the old?
 Also they have indirectly brought in Cardinal
Utility, which is not measureable.
2Prabha Panth

3.  Each economic unit wants to maximise its welfare.
 Consumers’ welfare = maximise utility,
 Producers’ welfare = maximise profits,
 Factors’ welfare = maximise incomes.
Is the sum of maximum individual welfare =
maximum social welfare?
i.e.  Ui = SW (i = 1,2,….. N)
Welfare Economics is based on
 Normative Economics,
 Equity Principles,
 Value Judgments
Prabha Panth 3

4. Pareto Optimality
 Pareto Optimality: Each individual economic unit
maximises its welfare.
 But if X’s welfare increases, and Y’s welfare decreases,
what happens to Social Welfare (SW)?
 Does it increase or decrease?
 In the Pareto system there is no unique equilibrium.
 If relative prices change, leads to new equilibrium.
 Does this new equilibrium denote improvement in
SW?
 See Figure 1.
Prabha Panth 4

5. 5
CommodityB
F
Commodity A
0
E
•Original equilibrium is at
E, on the blue PPC.
•Price ratio is PA/PB.
• Due to change in
economic conditions, PPC
may change to the Red
curve.
•Price ratios have also
changed to P1A/P1B.
•New equilibrium is at F.
•What has happened to
efficiency?
•Equity?
•Social welfare at F
compared to E?
•Is there any
improvement?
•PPC shows only
production efficiency, not
of consumption.
FIGURE 1

6. Social Welfare Function - SWF
 Bergson: SWF is an ordinal index of society’s welfare.
 It is a function of the utility levels of all individuals in
society.
 Brings in optimisation of consumption welfare also.
Pareto optimum reflected only production
optimisation.
 Based on
 Value Judgment of each individual,
 Reflected in consumption,
 Choices are transitive and consistent.
SWF = W(U1, U2, ............... UN)
Prabha Panth 6

7. The Social Indifference Curve
7
N’sutilityindex
M’s utility index0
W1
W2
W3
Q
T
R
S
The Social Indifference Curve: is a locus of various combinations of UM
and UN, which results in equal level of Social Welfare.
In the figure, W1, W2, W3, are Social Indifference Curves.
Each curve shows equal different combinations of utility of the two
consumers M and N, which give the same level of Social Welfare.
The Ws have same properties as ordinary
Indifference Curves.
All combinations on each W, have same level
of Social Welfare.
Higher W has higher level of Social Welfare.
From R on W1 to T on W2  N’s
U, M’s . But on higher W, so
Social Welfare increases.
Same case of movement from T
to Q on W3. M’s U and N’s U.
But Social Welfare  as shift to
higher W.
From T to S, SW constant, as they
are on same W.
FIGURE 2

8. Utility Possibility Curve
In Fig.3, the contract curve of consumers 0A 0B, shows equilibrium points of the two
consumers. Moving from point 1 to 4, as UX , UY
Plotting the contract curve on a diagram, gives the Utility Possibility Curve or Frontier
for a given set of Ps. Figure 4. If Ps change, so will the Utility Possibility curve,
8
IC 1X
IC2 X
IC3 X
IC4X
BY
IC2Y
IC3Y
IC4Y
AX
IC1Y
1
2
3
4
AY
BX
0B
0A
UX3
UX1
UX2
UY4
O
UY
UY1
UY2
UY3
UY4
1
2
3
4
Figure 3 Figure 4
Utility Possibility
Frontier

9. Grand Utility Possibility Frontier
9
O
UY
F1
G1
H1
F1
UX
G1 H1
Figure 5
The Grand Utility Possibility
Frontier
• When Ps change, the contract curve
changes, and the Utility Possibility
Curve also changes.(F1F1, G1G1, and
H1H1).
• The Outer Envelope of the different
Utility Possibility Frontier curves is
called “The Grand Utility Possibility
Frontier.”
• It is the locus of all the possible
contract curves or Utility Possible
curves from changes in the prices of
the two goods.
• Satisfies the marginal conditions:
MRTS = MRS for each commodity mix.
• Satisfies Pareto marginal conditions
of a) efficiency in production, b)
efficiency in distribution, and c)
efficiency in product composition.

10. Point of Constrained Bliss
 But again this does not give a Unique Point of
Social Welfare.
 If the SWF and Grand Utility Possibility Frontier are
combined, then the point of maximum Social and
Individual together can be found’
 This point is called the Point of Constrained Bliss.
 Because a movement away from it will reduce
Social Welfare.
Prabha Panth 10

11. Prabha Panth 11
O
UY
W*
G
H
U*Y
UX
U*X H1
Constrained
Bliss Point
W1
W2
W3
W4
Figure 6
In Fig.6 the Grand Utility Frontier is
combined with a set of social
indifference curves (Ws).
Social welfare is maximised at W*,
where Grand Utility Possibility
Frontier is a tangent to the highest
possible Social Indifference curve
W3.
The two consumers enjoy the
highest levels of welfare of U*Y and
U*X.
Point G on W1 is on the Grand
Utility Frontier, but not unique
equilibrium point.
Similarly H on a higher Social
Welfare curve than G, but not an
equilibrium point.
W* is the maximum social welfare
possible, given factor endowments,
state of technology, and individual’s
preferences. At W*, Social Justice
condition: Slope of Iso welfare curve
= Slope of Utility Frontier