Economics of Agents with Social
Preferences: The Third
Fundamental Theorem of Welfare
Economics!
Hayat Khan
Lecturer
School of Economics and Finance,
La Trobe University
Australia
“Economic Agent” Vs “Social
Agent”
– Economic Agent: An agent with SELFISH
preferences (self-centered)
• Studied by mainstream economics
– Social Agent: an Agent with Social
Preferences (i.e. whose preferences are
sensitive to social outcomes)
• Other-regarding behaviour
• Endogenous preferences
Why (Motivation)?
• Longstanding concern about the
SELFISHNESS assumption
• Growing area of interest and research
– Behavioral & Experimental Economics
– Economics of agents with with religious
Affiliations
• Islamic Economics
• Christian Economics
• Economic teachings/concepts of other religions
Why (Motivation)?...Cont.
• The good human nature argument
– Too strong an assumption to approximate humane nature
– Voluntary Organization (NGOs etc)
– International Aid programs/Humanitarian aid programs
• Response to calamities (Tsunami, Earth Quake etc)
• Charities etc
• Theoretical Importance
– No standard results to refer to for an economy populated by
“social agents”
– Theoretical properties of such an economy relative to selfcentered economies unknown.
– Missing policy dimension
This paper
• Replaces the “economic agent” in
standard welfare economics with a
“social agent”
– Traces the SR and LR dynamics in GE
Style of the presentation
• Bench-Mark Approach
• The idea is to explore the potential role
normative affiliations play
Main Result
• Multidimensional in nature
• Emphasis here is on “The Third
Fundamental Theorem of Welfare
economics”
– When an economy is populated by agents
with social preferences, market-perfectly
competitive or with some degree of
imperfection-outcomes are Pareto Optimal,
equitable, and Unique
Economics of Agents with Selfish
Preferences
• Main Results
– The First Fundamental Theorem of Welfare
Economics (FFTWE)
– The Second Fundamental Theorem of
Welfare Economics (SFTWE)
Economics of Agents with Selfish
Preferences
• Fisher (1983) asserts that the two fundamental
theorems are the single most important set of
ideas that economists have to convey to lay
people.
• “The most remarkable achievements of modern
microeconomic theory are the proof of the
existence of an equilibrium and the First and
Second Theorems of Welfare Economics …”
Luenberger (1994)
• Franklin Fisher ((2003) claims these theorems to
be the foundation of western capitalism
Problems with the Two Fundamental
Theorems of Welfare Economics
• FFTWE: outcomes may not be equitable
– Solution: the SFTWE
• SFTWE
– Requires Judgment on equitability
• Requires Interpersonal Comparison of utility (ICU)
• ICU based on personal characteristic unobservable by fiscal
authority
– Gains to the poor comes at welfare loss to the rich.
• market failure (e.g. externalities, public good or
information asymmetry)
• non-uniqueness of equilibria
• non-convexities
• Imperfect competition in the real world
Question
What happens to these results when we
have an economy populated by agents
having social preferences?
The Third Fundamental Theorem of
Welfare Economics (TFTWE)
When an economy is populated by agents with
social preferences, market-perfectly
competitive or with some degree of
imperfection-outcomes are Pareto Optimal,
equitable, and Unique
Results demonstration
• First Step: We need a model of otherregarding behavior that explains altruism
– Khan (2009): Modelling Social preferences: a
generalized model of Inequity Aversion
• Extension of Khan (2009) generalized
model of inequity aversion
Endogenously generated
transfers
• Utility Function of the Rich with Social
Preferences
Vi= Vi(U1 , U2 , OSF)
Where
• Ui = Ui (X,Y)= idiosyncratic, selfish, utility of individual I
(=1,2)
• OSF = Other Social Factors
The TFTWE and Equitable
distribution
• Assume no OSF (Khan (2009) model)
Vr= Ur - β Max[Ur – er Up , 0] (β>1*)
V p= U p
Where r=rich , p=poor
er = the rich’s valuation of equitable distribution of utility (STATE
DEPENDENT, State determined by structural and psychological
parameters)
Ur – er Up = Realized utility gap (RUG)
The TFTWE and Equitable
distribution
The rich maximizes Vr s.t Mr+Mp=M
Solution:
Ur – e Up=0
For simplicity assume Ur=Mr
Up=Mp
Mr*=eM/(1+e)
Mp*=M/(1+e)
The TFTWE and Equitable
distribution
Implication:
when the initial distribution is such that
Mp<Mp*
• the rich will find it welfare improving to transfer Mp*-Mp
to the poor
• The market will work to establish Pareto optimal
allocation at the equitable distribution of resources
• IMPORTANT: gain to the poor comes at Welfare Gain to
the RICH.
Op
Y

B
E
Er
A
U pe
p’
Or
U re
X
•E= Perfect competitive eqbm w/o transfer
Er = equitable equilibrium with transfer from the rich
Interesting: Er could be outside the core Ab as well!
The TFTWE and Less than Perfect
competitive markets
• Less than perfect competitive markets with
some-degree of benevolence could replace
perfect competition if required for equitable
distribution
• Assumptions:
– Equitable distribution is affordable
– The perfect competitive outcome is the equitable
outcome
– Theoretically, the other-regarding monopolist can
sacrifice profit margin (affordable) and charge perfect
competitive price.
• Morality can replace part of the competition
– Pareto Optimality under imperfect competition!!!
OSF (Other Social Factors)
• Non-Uniqueness
• Non-convex preferences
• Market Failure
TFTWE and non-uniqueness
 when equilibrium is not unique then,
contrary to widespread interpretations of
the
Second
Welfare
Theorem,
considerable non-market intervention will
generally be needed in order to achieve
any desired Pareto optimal allocation.
 Is it the case when agents have social
preferences?
U rS
A3
A2
A4
A1
A5
p
Non-convex preferences and the
TFTWE (OSF)
Equity Efficiency Trade Off Revisited
•
Consider the usual assumptions on Production
side of the economy
–
–
•
2 Factors of production (K and L)
2 Goods: X and Y
Technology
•
•
•
•
•
•
•
CRS
the law of diminishing marginal productivity holds,
One good is labour intensive, the other capital intensive.
Fixed endowment of capital and labour in the economy.
Labour is perfectly mobile across industries in the short-run as
well as in the long-run
Capital is perfectly immobile across industries in the short run
and perfectly mobile in the long-run.
The economy is a closed one and total consumption
matches total production for each good.
Long-run PPF as envelope of
short-run PPFs.
Y
Long-run PPF
Short-run PPF
X
Y
No equity
efficiency tradeoff at this point
X
BUT…
• high wage leads to high effort due to
positive reciprocity (a cooperative
response to a generous act)
– This increases effective endowment of L
• PPF shifts out
Y
Efficiency
loss
Efficiency
gain
Efficiency
loss
X
Not Only that: We need to consider social
importance of the projects selected as well
•
•
•
•
X is an index of capital intensive projects
Y is an index of labour intensive projects
In selfish economy members projects are selected based on NPV
In an economy with individuals having social preferences
– Organize projects by NPV
– Assign weight according to social importance
• The resulted project selected might be different from the selfish
economy
• In terms of its social importance, one unit of the index in normative
economy equals more than one unit of the index in selfish
economies
• This, in effective terms, means higher PPF ( reduction in efficiency
loss zone and expansion in efficiency gain zone)
• This further discounts the equity-efficiency trade-off
– More is good if it delivers relatively more good.
SR Dynamics
• Labour is perfectly mobile
• Capital is perfectly immobile
• Both labour and capital are in fixed physical
endowment
Assumptions
• Capitalist are the rich class and the own the production
firms. Thus their income consists of rent as reward of
capital and profit as entrepreneurs.
• Labour are the poor class and their income consists of
wage income.
SR dynamics
L mobile, K immobile (SFM)
 SX   PX X  K X , LX   wLX  rK x     wLX 
FOC :
PX X L
w
1   
R  PX X
K
SR dynamics
L mobile, K immobile (SFM)
   PY Y  KY , LY   wLY  rKY     wLY 
FOC :
S
Y
L
PY Y
w
1   
R  PY Y
K
SR Dynamics: General Altruism
WX
WY
PX X L
1 
L
PY Y
1 
PX X L
PX
W0
wX 
rX 
WX
PX
wX 1
rX0
RX
PX
wX 0
W0
OX
OX
L0
LX
OY
OY
LY
L0
RX0
PX
PY
PY Y L

PY Y K KY
RX

wI 0
wY 
wI 1
rY0
rY 
RY0

PX X K K X

PY
RY
WY
PY
RY
PY
Short-run equilibrium with agents having social preferences in
one Industry, industry Y, only.
WX
WY
L
PY Y
1 
PX
PX X L
W1
W0
wX 
rX 
WX
PX
W1
W0
wX 1 wX 0 O
X
rX0 rX1
RX
PX
L1
L0
OY
OI
ON
L1
RX0
 
PY Y K KY
RX
wY 
wY 0 wY 1
rY0 rY1
rY 
L0
RX1
PX
PY
PY Y L
RY0
RY1

PX X K K X

PY
RY
WY
PY
RY
PY
Concluding Remarks
• ……