Economics of Agents with Social Preferences: The Third

Fundamental Theorem of Welfare Economics!

Hayat KhanLecturer

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 self-

centered 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 other-regarding 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*)

Vp= Up

Where r=rich , p=poorer = 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.

epU

erU

Y

X rO

pO

B

Er A

p’

E

•E= Perfect competitive eqbm w/o transferEr = equitable equilibrium with transfer from the richInteresting: 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?

p

SrU

A1

A2

A3

A4

A5

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.

X

Y

Short-run PPF

Long-run PPF

Y

X

No equity efficiency trade-off at this point

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

Efficiency gain

Efficiency loss

Efficiency loss

Y

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 dynamicsL mobile, K immobile (SFM)

,SX X X X X x XP X K L wL rK wL

:

1

LX

KX

FOC

P Xw

R P X

SR dynamicsL mobile, K immobile (SFM)

,

:

1

SY Y Y Y Y Y Y

LY

KY

P Y K L wL rK wL

FOC

P Yw

R P Y

SR Dynamics: General Altruism

WX

OX OY OX OY

PX PY

PY PX

LYP Y

KX XP X K K

Y YP Y K

WY

RY RX

XX

X

Rr

P

XX

X

Ww

P

YY

Y

Rr

P

YY

Y

Ww

P

RX0 RY0

rX0

0Xw 0Iw

rY0

LXP X

YL XL

0L

0L

1

LYP Y

1

LXP X

W0 W0

1Iw 1Xw

Short-run equilibrium with agents having social preferences in

one Industry, industry Y, only.

WX

OX OY ON OI

PX PY

PY PX

LYP Y

KX XP X K

KY YP Y K

WY

RY RX

XX

X

Rr

P

XX

X

Ww

P

YY

Y

Rr

P

YY

Y

Ww

P

RX0

RY0

rX0

0Xw 0Yw

rY0

LXP X

0L

0L

1

LYP Y

W0 W0

1Yw 1Xw

rY1 rX1

W1 W1

1L

1L

RX1

RY1

Concluding Remarks

• ……