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Economic Theory of Organisation IISource: Econometrica, Vol. 39, No. 4 (Jul., 1971), pp. 251-266Published by: The Econometric SocietyStable URL: http://www.jstor.org/stable/1912451Accessed: 01-07-2015 08:50 UTC

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2/17

86 ECONOMIC THEORY

OF ORGANISATION

II

251

goods. The consumer is able to hold his

wealth in the form of

one or more of M

assets,

of

which one is riskless. Consumer

durables are

modelled as being in part

consumption goods, and in

part assets.

The prices of goods are assumed independently and nonstationarily distrib-

uted,

so as

to allow

for

inflation. The real returns

on

the

(M

-

1) risky

assets are

assumed to be state

dependent,

and

the

consumer is

assumed

to

know

the

prob-

ability distribution

of

the states and also the

conditional distributions

of returns

given the states.

The consumer

enters a period knowing

the prices of the goods, and the

state,

and he chooses

his

consumption

of

each of the goods, and his

portfolio

decision

so

as

to

maximize his expected utility.

The problem he

faces is one of

dynamic stochastic programming. By using

particular

functional forms for

the indirect utility function it is possible to solve this

problem

by

a

recursive

procedure in order to arrive at optimal

expenditure and

investment rules for

any period

t

= 0,

. .

.,

T

After we have determined the expenditure

rule, we

convert

from the

indirect

utility function to the expenditure

function,

and differentiate

this with

respect

to

the

price

vector to arrive at the demand

equation

vector for

goods

and the services

of durables.

This has

a functional

form which

corresponds

to

the

expenditure

function.

The demand

equations for assets, and the asset component of

durables

come

directly

from

the

rule for

the

optimum portfolio

composition.

86

ECONOMIC

THEORY OF

ORGANISATION II

On

the

Motivational Stability of a Planning

Procedure for

Non-Classical Environ-

ments, Masahiko Aoki, Kyoto

University and

Harvard

University

In

recent years, various

planning procedures

have been proposed with some

desirable

performance characteristics besides their

convergence

to an optimal

resource allocation plan

[e.g.,

informational

efficiency (Arrow-Hurwicz), feasi-

bility

of a

plan constructed

in

finite

steps (Malinvaud and

Kornai) among others].

But, if we allow

for the possibility of such

non-classical

environments as increasing

returns and

externalities, it may be considered that there is a kind

of

trade-off

among

various

desirable

performance

characteristics. Especially,

informational

efficiency

as

defined by Hurwicz and

the self-interest of

individual managers will

be in

direct conflict.

In

this paper,

two kinds

of

desirable properties of

a planning procedure

from the motivational

point

of

view,

that

is,

the consistencies

of

the

operation

rules and

a

success indicator

for

managers,

will be

formulated.

If

a

planning

procedure satisfies these two

properties,

then the

procedure

will be

called

motivationally-stable.

Then

the two

procedures

that can

cope

with

increasing

returns

and

externalities

will be

proposed. They

are

both

motivationally-stable,

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3/17

252 SECOND

WORLD

CONGRESS

but informationally-less-efficient

than the

competitive procedure

as

proposed

by

Arrow and Hurwicz.

REFERENCES

[1]

AOKI,

M.: Investment

Planning Procedure for an Open

Economy with Increasing

Returns (Harvard

Economic Research Project, 1969).

[2] ARROW, K.

J.

AND

L.

HURWICZ:

Decentralization and Computation in

Resource Allocation,

in R. W. Pfouts

(ed.): Essays in Economics and Econometrics

(University

of North Carolina Press,

1960), pp. 34-104.

[3] HURWICZ,

.: Optimality and Informational Efficiency

in Resource

Allocation Processes, in

K. J. Arrow, et al. (eds.): Mathematical

Methods in the

Social Sciences, 1959 (Stanford University

Press, 1960),

pp. 27-46.

Centralization and Decentralization of Decision-Making Mechanisms: A General

Model,

Antonio Camacho,

Northwestern University

A

general

decisiort

making

model

is

presented

under which the

notions

degree

of centralization and

degree of coerciveness can

be precisely defined.

Hurwicz,

in

his 1959 pioneer paper

on this

field, Optimality

and Informational

Efficiency

in

Resource

Allocation Processes,

formalizes the notion of informa-

tion

decentralization

by imposing certain conditions

(regardingthe domain type

of

messages, etc.)

that the

response

functions

or behavior rules of the participants

in

the decision making process have to satisfy. This author followedthe same approach

in

his 1957 paper Externalities,

Optimality

and Informationally Decentralized

Resource

Allocation Mechanisms.

In the

present model,

unlike the other

two

models mentioned

above, a new

agent (the

central

agent)

is

introduced.

The

degree

of

centralization and the degree

of coerciveness are then defined by

the relation between the behavioral

rule.

of the

central agent and the behavioral

rules of the

other participants, called in

our

model the

management agents.

Several

examples

are considered

to

compare

the

performance

of centralized

and decentralized decision making processes. In particular a simple team model

with two management agents,

a central

agent,

and

a

payoff

function w

=

c

-

k1[al

-

(e1 + e2)]2 -

k2[a2-

(e1

+

e2)]2

-

k(a1

-

a2)2

is studied. If

we

accept

as a measure

of the

degree

of

externality

the

value of

(a2w)/(aalaa2)

=

2k,

it

is

shown

that

for

a

given

natural structure of information

and for

given

natural behavior rules,

the decentralized

decision

making process performs

better than the

centralized

one no

matter

how

high

the

externality

is. This

example

suggests (at

least

under the

context

of

our

model) that,

contrary

to

what has been

advocated

in

part

of the

economic

literature,

the solution to the

problem

of

externalities is not always internalizing or centralizing.

Growth,Stability,

and

Disequilibrium,

John

Ledyard, Carnegie-Mellon

University

In

this

paper,

a

disequilibrium

action, informationally

decentralized,

economic

allocation

process

is

presented

and

its

performance

in two classes of

economic



4/17

86

ECONOMIC THEORY OF

ORGANISATION

II

253

environments is

discussed. The

process allows

trading,

consumption,

and

produc-

tion

to occur

even

though

equilibrium

does

not exist, as

opposed

to the

usual

non-tatonnement

process in which

the

only

allowable

disequilibrium

action

is

trading. The process is based on the reallocation of resources towards consumers

whose

demand

prices,

marginal

utilities, are

high and

away

from those

whose

prices are

low.

Production is

price directed

as

in

the usual

competitive

market

process.

The

environments

covered are

among those

which

can be

interpreted as

optimal

control

problems, and

the process

only

requires that

each

individual

know

the

current

environmental

conditions. (E.g., no

knowledge of

future

technology

is

necessary.)

These

environments

are split

into

two classes,

pure

flow and

stock-flow

depending on

whether or not

stock

accumulation

(i.e.,

investment)

is feasible.

Since

it

is

possible for

such

a process

to

be

Pareto-satisfactory

only in

environments whose

Pareto-optimal

allocations are

steady-state solutions

and

then

only if

the initial

trading rates are

optimal, a slightly

less

restrictive

performance

criterion is

proposed.

This

requires that

the

process

closely

track the

optimal path

if it

starts

close to it. It is

shown

that,

in

pure

flow

environments,

if

the

optimal

path

is not

changing too

rapidly

then the

process

satisfies the

above criterion.

It is

also

shown

that, in

stock-flow

environments, the

process

will not

satisfy the

criterion.

In

fact,

there are a

large

number

of

processes

which

cannot track the

optimal path

in stock-flow environments. This result is based on the

lack of

Liapunov

stability

of

the

Euler-Lagrange

equations, the first

order

conditions

for

optimal

control,

and

indirectly extends

the

results of Hahn

and Kurz,

on

the instability

of com-

petitive (or

equilibrium

action) growth

paths,

to some

types of

disequilibrium

action

processes.

Planning

for

Individual

and Collective

Consumption,

E.

Malinvaud,

Institut

National de

la

Statistique

et

des Etudes

Economiques

The

theory

of

public

goods should

benefit much from

the

formal

study

of

planning

procedures since

the

problem

raised

by

collective

consumption

is

precisely to

understand how

the

provision for

this

consumption

is,

or

should

be,

decided.

Let us consider the

bipolar model

in

which the

commodities are

divided into

two

groups:

r

collective

goods

(h

=

1,

2

...

r)

that

may

be

used,

jointly

and without

any

exclusion, by

all individual

consumers

(i

=

1,

2

...

m)

simultaneously,

n

-

r

private

goods (h

=

r

+

1

...

n)

for

which use

by

one

consumer

is

exclusive

of use

by

another.

Let

the

consumptions

be

xh

and

Xih

for

commodities

in

one

and

the

other

of

these

two

groups.

Assume further

that

production

is

completely

centralized

and

that the

n-vector

y

of

quantities

available

for

consumption

is

subject

to the

constraint

f(y)

=

0.



5/17

254 SECOND WORLD CONGRESS

Looking for realistic planning procedures we

concentrate our attention

on

those

using the following

indicators

to

be sent to consumers:

-for each collective

good (h

=

1,

2. .

.

r)

the

consumption Xh,

-for each

good

that

is

individually

consumed

(h

=

r

+ 1,

...,

n) the

price

Ph,

-for each consumer

(i

=

1,

2 ...

m)

the income

Ri

to be

spent

on

private goods.

Correspondingly the proposal of consumer i

will

consist of two

parts:

-a demand

Xih

for each

private good h,

-a trade-off coefficient

7rih

=

Uih/Ufl

that the consumer considers as

applying

between

each collective

good

h and the

numeraire n.

A

consumptionprogram

will

appear

at each

stage

of the

process.

It will

be

made

of

the

Xh

indicated

by

the

board for

each collective

good

and

of

the

Xih

proposed by

each consumer

for each

private good.

But this

program will

not

necessarily be feasible. We

therefore

define also,

at each

stage

of the

process, a

consumptionplan

as

being

made of

those values

xh

and

Xih

that would be

selected

if

the

exchange

of

messages were

to end

at this stage.

The

main

point

for

a

precise

definition of the

procedure

concerns

the revision

of

indicators. We shall consider

the

following

rules:

-collective

consumption

of h is

increased

if

the sum of the

individual

trade-off coefficients exceeds

the substitution coefficient

Oh

=

f

Vf

n;

-the total

available

for individual

consumption

of h

is

increased

if its

price

exceeds

its substitution

coefficient

Oh

(for h

=

r

+

1

... n

-

1);

-the revision

of

the vector

y

is such that

it

remains

on the

production

frontier;

-the

price

of the

private good

h is increased

if

its

aggregate demand

exceeds the total

available

for

consumption;

-the

revision

of the indicator

Ri

concerning the income of

consumer i

is made of

two parts: a compensation for the simultaneous

revision of

prices

and collective

consumptions,

a

participation

to the social

surplus

that

appears

as a

result of the

exchange

of information.

The rule

for the

revision

of individual incomes

has been chosen

in

such

a

way

that all consumers

share the burden of

improving

the

feasibility

of the

'program

and that all

simultaneously

benefit from the

improvement

brought

to the

plan.

The

procedure

is therefore neutral with

respect

to

equity.

Moreover,

without

any

restrictive

assumption

on the differentiable

utility

functions

Ui,

it

may

be

shown

that,

if

the

procedure operates continuously,

it

converges locally

to an

optimum plan.



6/17

DUALITY IN

THE THEORY OF PRODUCTION 255

ConjugateDuality and the

TranscendentalLogarithmicFunction,

Laurits

R.

Christensen, University of Wisconsin;

Dale W. Jorgenson, Harvard

University;

Lawrence J. Lau, Stanford

University

This

paper

considers the transcendental

logarithmic functional

form,

which

provides a valid second order

approximation

to an arbitrary functional form.

In

particular, the

C.E.S. and the Cobb-Douglas

functions, as

well as other lesser

known varieties,

are special cases

of the Trans-Log function.

In

our

application we consider

both the trancendental

logarithmic trans-

formation function and the transcendental

logarithmic

profit function under

the

assumption

of constant returns to scale. Two

outputs, consumption and

invest-

ment,

and two

inputs, capital

and labor, are distinguished in the

empirical

analysis.

The Trans-Log transformation function is approximated by

lnF

=

xo

+

aIlnI

+

cxclnC

+

3KIlnK

+

ILlnL+?cAlnA

+ AA(l A)2 + 7''(lI)2 + 2C(l C)2

+

y(IlnIlnC

?

InlnIlnA + yCAlnClnA

+

8KK(ln

K)2

+

'ILL

(ln

L)2 +

fKL

ln K ln L +

EKA

n K ln A2 2

+

ELA

n L ln A +

bIK In

I

ln

K

+

6IL

ln

I

ln L

+

ClnKClnC

K

+

6CLlnCInL=

0.

where

I

=

quantity

of investment

C

=

quantity

of

consumption

K

=

quantity

of capital

L

=

quantity

of labor

A

=

productivity

index

which under

the

assumption

of

profit

maximization

lead to

marginal productivity

conditions

of the

type

alnF

p,I

a

ln

I

PKK

-alnF

a

n

K

ac l

y11

In

+

ycn

C+

bIK

inK

+

6ILln

L+

YIAln

A

-(K

+

bIK

nI + 6CKlnC + eKK

in

K + EKLlnL+

8KAIn

A



7/17

256

SECOND

WORLD

CONGRESS

Similarly,

the

Trans-Log

profit function is approximated by

ln(Xi

+

1)

- o0o

+

oxilnpI

+

iCclnPc

+

)BKlnPK

+

ILlnPL

+

(XAlnA

+

7AA(ln A)2

+

2(ln

P)2

+

VC

(ln

pC)2

+

yIc

ln

pIln

pC

2 2

'

2

+

VIA

In

p,

In A

+

CA

InpcInA

+

KK

(ln

PK

2

+

LL

(In

PL)2

2

2

+

8KLin

PK

ln

PL

+ ?KA

In

PK

lnA

+ rLAln

PL

ln

A

+

aIKIlnpIln PK

+

6IL

ln

pIln

PL

+

6CK

in

Pc

In

PK

+

5CL

In

Pc

In

PL

=

0

where

PI

=

price

of investment

Pc

=

price

of

consumption

PK

=

price

of

capital

PL

=

price

of labor.

By

the Shephard-Uzawa-McFadden Lemma,

the

optimal output supply

and

input

demand

functions

are

given

by equations

of

the

type

D

In

7t

(2

PI, a

In

PI

P2

__Dnp

PKK

-mInt

a

In PK

cx1

+

yII

In

PI

+

VIc

In

Pc

+

6IK

In

PK

+

6IL

In

PL

+

VIA

n

A

-

(J3K

+

6IK ln pI

+

6CKln pC

+

eKK

ln

PK

+

EKL n

PL

+ EKA n A)

Equations (1)

and

(2) form

the

basis of the

empirical

analysis.

The

data

used

are

the

aggregate

U.S. annual time

series

data

developed by Christensen and

Jorgenson.

Because

in the aggregate

the prices

and quantities

of outputs and inputs

influence

one another,

an

econometric

model is

specified so that appropriate

instrumental

variables may

be

employed

to obtain

consistent

estimates.

Various

economic

hypotheses

such as

symmetry

and

homogeneity

as

well as hypotheses

on

specific

functional

forms are formulated

and

tested.

It is found

that

while the

restrictions imposed

by economic

theory

are

true,

the

restrictions

imposed by the

specific

functional forms are

false.

This suggests

that the

Trans-Log

function

should

be employed

in the

absence

of correct

a priori

information

on the specific

functional

form.



8/17

EMPLOYMENT

AND WAGES

257

Relative Labor Employment

in Manufacturing

Industries, A. A. Cook, Jr.,

The

Rand Corporation

Over the past two decades manufacturing

output has increased

significantly

with virtually

no increase

in

the employment

of production

labor. During the

same period, the employment

of non-production

labor and capital has increased

substantially.

In

this paper

we test the hypothesis that the

increase

in

the employ-

ment of non-production

labor relative to production

labor is

due to the greater

complementarity

of

non-production

labor with capital.

The model

includes a three factor production

function: capital,

non-produc-

tion

labor,

and

production

labor.

The production function possesses non-constant elasticities of substitution.

However, the

ratio of any two

pairwise partial elasticities of substitution

is constant

and expressible wholly

in terms of the

parameters

of the production function.

Hence, estimation of

the

parameters

provides

a test for differing complementarity

between pairs

of factors.

The estimation is essentially

a two-stage process in which

the three employ-

ment

demand equations

are estimated simultaneously

and then these parameter

estimates

are

used

in

estimating the production function

and the remaining

parameters. The data consists

of quarterly time

series observations for fourteen

two digit (SIC) manufacturing industries.

The

results support the

hypothesis that

non-production labor and capital

are more

complementary than

production labor and capital.

An

Example

Comparing Bayesian Analogues

of Full and

Limited

Information

Maximum

Likelihood

Estimators,

Gordon M. Kaufman and Abba

Krieger,

Massachusetts

Institute

of

Technology

We consider the usual structural

equation system

By(i)

+

rz(i)

=

u(i),

with

{

(i)j}

a

sequence

of

mutually independent

random

variables,

identically

normal

with

mean zero and

variance matrix

E. In addition to time series data

{(y(i),z(j))}

we

have available

cross-section data

on

individual

rows of

(B F).

Given

that

the

cross-section data for

row i is

generated by

an

independent

normal

process

with

variance

proportional

to

aii,

the iith element

of

E,

we

find the exact

posterior

density

for

(Br)

unconditional

as

regards

i

when

E is

(2

x

2),

and when

the

prior

assigned

to

(B, F, i)

is

natural

conjugate,

Jeffery's-like,

or some

simple

variant.

A

functional equation (necessary

condition)

for

(B*F*)

to be

a

posterior

model

value

is

derived.

The

posterior

density

of

B

unconditional

as

regards

both

r

and

E is

also

given.

Properties

of

the

posterior

density

of

(BI')

when

the cross-section data

is

independent

of

the time-series data are outlined.

Comparisons

with

a

Bayesian analogue

of

LIMLE

are made.



9/17

258

SECOND WORLD CONGRESS

The Autonomous

Functioning of an Economic System, Janos

Kornai and Bela

Martos, HungarianAcademy

of

Sciences

Analyzing hewayaneconomicsystem afirmas well as a nationaleconomy)

works,

a

distinction

can

be madebetween ts autonomousand higher unctioning.

This

bears analogy

to

the

working

of

the

autonomousand the

higher nervous

system

n

living

organisms,

hence the

terminologyadapted.

The main

features

of

the autonomousfunctioning

of

the

economic

system

are:

1.

The

simplicity

of

the information

required

for

making

decisions. The

relativeunimportance

f

price-type

nformation.

2.

The

simplebehavioral

rules

which

rely mostly

on

habits.

This

excludes

fundamental

hanges

n

technology

as

well

as

major

nvestment

decisions,

which

arecontrolledby the highercontrolsystem.Anotherpoint of view is a problem

of restriction:

he

autonomous

unctioning

aims

only

at the survival

of

the

system,

which may

include

a

stationaryextension,

n an

essentially

unchanged

environ-

ment. Any other,

more complexgoals appear

n

the highercontrol

system.

The

autonomous

functioning

of different

ystems

seems

to be

very similar,

while he higher unctioning

s

fairlydiversified

wingto political,

social,historical

and

otherconditions.It seems

o be hard o

separate

he

effects

of the

autonomous

functioning

n

as

much as

they

are

always

mixed

up

with the effects of higher

functioning

n

any

modern

economy.

No

empirical

videnceas to the

viabilityof

apureautonomous conomycan begiven.We mustrestrict urselves o theoretical

reasoningvia simplified

ormal models.

As

a firstapproximation

f the

problem

a

simplemodel for

the Leontief-type

economy

will be demonstrated.

Simple

behavioral

rules are

applied,

where

relative

changes

n

production

and

purchasequantitiesdepend

only

on

changes

in producers'

and

consumers'

own

stocks,

sales and

consumptionquantities,

while

pricesplay

no role.

The

analysis

of the models

proves

hat such an

economy

can

survive

even

if

minor outer disturbances ccur.

The

conclusion

which

can be drawn

is

that

informationabout stocks

may

play a considerablepart in the control of any economicsystem,a much more

important

role than is

usuallyacknowledged

n

the

literature.

Solution

of Finite

Two-person

Games

with

Incomplete

Information,

W. Krelle and

J. Burgermeister,

niversity

of Bonn

The

papersuggests

a

solution

for

finite

non-cooperative wo-persongames

with

incomplete

nformation.

Either

player

belongs

to a

finitenumber

of

types

which differ

by

their

payoffs.

Each

player

knows

his

own

type

but has

only

a

subjectiveprobability

distribution

on

the

types

of his

opponent.

These

subjective

probability

distributions

re

known to both

players.

It will be

shown

n

the

paper

that

each

player

has a

uniquely

determined

optimal

counterstrategy

o each

strategy

f his

opponent.

If

there

s

to

be

an

optimalstrategy

or each

player,

hese

strategies

mustbe

optimalagainst

each

other;

that means

hey

must

be

equilibrium



10/17

OPTIMAL

ECONOMIC GROWTH

259

strategies in the sense of

Nash. It is demonstrated

by an example that there are

games without equilibrium

strategies. In this case it is suggested that each player

guesses the choice of strategy

of his opponent by forming

a subjective probability

measureon the strategies of his opponent or (alternatively) by forming conditional

subjective probabilities

on the sequences of moves of his opponent.

Un modele

de

croissance

a

deux variables de commande:

arbitrage entre loisir et

consommation, D. Lacaze

and D. Badellon, Faculte des Sciences de Paris

On aborde le

probleme

de l'arbitrage entre

loisir et consommation par

l'etude

d'un modele de croissance

global

oiu

a fonction d'utilite fair intervenir ces

deux

grandeurs.

Ce modele

comporte

un minimum

de consommation

par

tete

variable dans le temps et une demande exogene (consommation

des administrations

et investissements non productifs). Le progres technique

est

exogene.

Un

probleme

de controle

optimal

est

ainsi

defini, qui comprend

une

variable

d'etat

(le

taux de

capital)

et deux

variables de

commande

(le

taux d'activite

et

le

taux

d'epargne net).

Le

principe du maximum permet

de

decrire

avec

precision

les

trajectoires optimales

en fonction

des

conditions

initiales et finales:

capital

initial, capital final et duree

de la periode de developpement. On voit

comment les

valeurs respectives

de l'utilite marginale de la consommation, de l'utilite marginale

de

loisir et

du prix

du capital gouvernent ces evolutions. On distingue ainsi dix

regions correspondant

a difftrents comportements

economiques.

Le modele a donne

lieu

a

des applications

numeriques.

Pour cela, on a choise

comme fonction economique

une somme ponderee de logarithmes,

ce

qui

revient

a se donner l'elasticite

entre

loisir et consommation. Une

methode

originale

de

resolution s'inspirant des

resultats de la discussion mathematique a ete mise au

point.

Les

donnees numeriques

ont

ete

empruntees

aux

etudes

faites dans

le

cadre

du

Commissariat

au

Plan.

On

considere

la

famille

d'evolutions

optimales

correspondant

aux

diverses

valeurs

possibles

du

capital

final. L'une

de

ces evolutions est

reguliere

et conduit

a des

taux

d'epargne

et d'actualisation

sensiblement constants

apres

un

regime

transitoire initial: C'est

cette evolution

qui

sera retenue.

On etudie

egalement

les

variations

de

l'evolution

optimale

enfonction

de

l'importance

accordee

au loisir. Ces

resultats

conduisent

a

une valeur du

capital

final

superieure

a

celle

qui

etait retenue

jusque la,

et

'a des

valeurs satisfaisantes

des

taux

d'epargne

et d'actualisation.

On the

Theory

of Financial

Intermediation,

David H.

Pyle, University

of

California,

Berkeley

The

essential

characteristic

of a financial

intermediary

is that

it

issues claims

on

itself

and uses

the

proceeds

to

purchase

other

financial

assets.

The

principal

question

to

which

the

analysis

in

this

paper

is

addressed is: under

what

circum-



11/17

260

SECOND

WORLD

CONGRESS

stances

would a firmbe

willing

o

sell a

given

deposit

iability

and use the

proceeds

to

purchase

a

given

type

of

financialasset when

the

yields

on

both the

asset and

the

liability

are

stochastic? The

analysis

deals

with the

portfolio

problem

in

financialntermediaries hileabstractingromtheimportantproblems f liquidity

and

transactionsdemand.

In Section

II

of

thepaper,a

three-security

modelof

financial

ntermediation

is

presented. t is

shown

that a

positiverisk

premiumon

loans

and

a

negativerisk

premium n

depositsare

sufficient,

ut

not

necessary onditions or

intermediation

to take

place.

The

principal

esultsof this

section are summarizedn

terms

of

the

properties f the

joint

distribution f loan

and

deposit

yields

which

lead

to inter-

mediationwhenboth of

these

yields

are

greaterhan

the

yield

on a

riskless

ecurity.

By

using

a

mean-variance

reference

unction,

a

specific

example

of

the resultsof

SectionII is presentedn Section III.

Finally,

the

justification

or a

preference unction

approach s

discussed.

In

particular,

the role of

equilibrium

capital

asset

prices

in

the

intermediary's

portfolio

decision

is

examined.

Producing,

Storing,

Transporting,

ndUsing

Knowledge, .

Marschak,

University

of

California,Los

Angeles

Thecosts anddelaysinvolved n storingandtransporting

commodityare,

by and

large,

independent

of its

prospective

value

in

use

and of

its

production

cost.

Similarly,

he

costs and

delays

in

retaining

and

communicating

knowledge

are, by and

large,

ndependentof

both its

usefulness

o the

receiver

value of

information)

and the

cost

of

producing t

(e.g., cost of

collectingdata).

This

justifies he

attempts

o

measure

he

volume

of

information. t

would

roughly

correspond o the

physical

volume

or

weight

of

goods

in

warehouses nd

n

transit.

Essentially,

t should

measure

the number of

symbols

necessary

to

store and

transmit

a

message.

The

larger

a collectionof

symbols,

the

larger

he

equipment

or timeneededto handlethem.

However

to

return

o

our

analogy),

the

costs of

storage

and

transportation

of

commodities

is

not

completelyindependent

of

its value

in

use.

The

more

valuable

a

commodity

he

greater

will

profit

be affected

by

breakage

or

leakage,

per pound

or

gallon.

Similarly,

ome distortions

of

messages

reduce

the

benefit

more than

others.

The

code

must

be

adjusted

o a

fidelity

criterion.

Entropy

formulae

(in bits

of

information)

approximatethe

expected

number

of

necessary

ymbols,

presupposing fficient

ncodingof

events

grouped

into

long

sub-sequence

blocks ).

This

is

economically

relevant

only

if

events

follow in

quick

succession,

permittingus to

neglect

the

delays

and storage

costs

caused

by

waiting

for

the

completion

of

each

block.

The

analysis

is

carried

by

presenting

a

system(i.e.,

network or

chain)

of

processors,

beginning

with

the

processingof

events

nto

data, and

endingwith the

processingof decoded

messages

nto decisions.

Each

processor

s

characterized

by

a

transition

matrix,

a

cost

function, and a

delay function.

The

assumption



12/17

INPUT-OUTPUT

ANALYSIS

I

261

(usual

in

statistical decision theory) of costless and

instantaneous decision making

need not be made.

The user chooses the system maximizing

the expected difference

between benefit

(a function of the

sequence of events and decisions)

and total

cost-provided utility is additive in these components.

Various Turnpike Models

of the Japanese

Economy-Including an Extension of

Consumption

Turnpike Theorem,

Y.

Murakami,

K.

Tokoyama,

J.

Tsukui,

Econ-

omic Planning Agency, Japan

Following

up Tsukui's pilot

study

in

Econometrica, 1968,

we have been

trying

to develop

various

dynamic

input-output models

for an indicative planning

model of the Japanese economy; the models include technological substitution,

technological progress

and

change

in

final demand

patterns.

In

the course

of

our

developmental

efforts, we discovered

some results of theoretical

importance.

Among them,

we shall here present the following

three results,

which are all

closely related

to the so-called turnpike property

(1)

Consumption turnpike property

does

hold,

in

spite

of a

change

in

the

discount

rate associated with future consumption

in

a

target

function.

(2) Our

simulation suggests

that a

concept

of turnpike may be extended

to

models including technological

progress

which may differ from industry

to industry. Any efficientpaths starting from a given initial condition can

be

approximated

to

a certain

locus

during

most

of the

planning periods.

A

turnpike locus is generally

a curve but no longer a ray.

(3)

In

order to compute a

switching

of a

turnpike

due to a change in final

demand

patterns,

it is

necessary

to solve

a

special class of nonlinear

programming

problems.

It

can

be

shown,

however, that such

nonlinear

programming

problems can

be solved as a

particular

kind of linear

programming

or its recursion.

Computational

results are

shown to

support

each of the

above

three

properties

and related findings. As is well known, a meaning of the turnpike property in the

theory

of economic

planning

is that we can

determine an

optimal growth pattern

almost

independently

of our choice

of final

state

conditions

and/or

specification

of

target

functions.

Our results

seem to warrant that

turnpike property

holds

over a wide

range

of

multi-sectoral

growth

models

so that

computation

of a

turnpike may

be

recommended

as a reasonable approximation

to

any

efficient

growth path

in

any

national

economic

planning.

Prices,

Information

and Market

Structure,

Michael

Rothschild,

Harvard Univer-

sity

A

commonplace

of our

experience

is the

variety

and

volatility

of

prices

for

consumer

goods.

This is

in

striking

contrast

to

the

premises

and

predictions

of

economic

theory

that

in

equilibrium

markets

sustain

a

single price

for a

single good.



13/17

262 SECOND

WORLD

CONGRESS

The perversity of the real

world is attributed to markets being out of

equilibrium

and to locational monopolies and the like which make

economically different

goods out

of what

laymen regard

as

identical products. This paper

argues that

it is not necessary to resort to such explanations. Rather, variable and varying

prices

are to be

expected

in

a

world

where

consumers have limited

facilities

for

acquiring, storing

and

acting

on

information.

Furthermore,

it

is

doubtful that

the

mere

existence

of

large

numbers of

competing

sellers

will

prevent

the

exploita-

tion of limitations of

consumers'

ability

to

do

comparative shopping.

Analysis

of a model which

incorporates

these features of

consumer

behavior

reveals

that

in

such

a world

equilibrium,

in

the conventional sense of constant

prices, may not

exist

if

sellers compete

with one

another.

For,

in

this

model,

prices

must

be

equilibrium points

of a

non-cooperative game

which

may

have no

pure strategy equilibrium. When static equilibrium prices exist, this model gives

us

some reason to doubt

that

perfect competition

will

protect

the

imperfect

consumer.

In

some cases this

price

may

be

calculated

as a

function of the number

of sellers

in

the market.

Although

the

equilibrium price

falls as

the number

of

competitors increases,

it

does not

approach

the

competitive price

as the number

of

stores becomes

infinite.

This

paper

builds

on the work

of

Selten, Stigler,

and

Telser.

Procedure

to

Determine

a

Programme

in an

Economy

where

only

Collective

Goods

are

Available,

Pieter

H.

M.

Ruys,

Katholieke

Hogeschool,

Netherlands

In

an

economy

are

n

collective

(or nonexchangeable) goods

producible

in

various degrees

of

availability.

The m

individual

agents together

have

to.make

a

decision

concerning

the

(relative) availability

of the collective

goods,

which

affects an

agent

as

a

consumer

(e.g.

health

service, transportation

facilities)

and

as

a

producer (e.g.

hours

working, job appointments). Every agent

is

supposed

to

partake

of the collective

goods

vector without

being

able

to

obtain

anything

through exchange

between

individuals.

A

procedure can be

developed that

determines

a

combination

of

quantities

of

collective

goods,

such

that

any change

in

quantity causes a

disequilibrium between social benefit (a function of individual

utilities)

and social cost

(a

function of

individual

disutilities).

Given a vector

of

goods (x), every agent

determines

the direction of

the relative

changes

in

the

proposed

vector

(p)

in

which his

utility

will

be

maximized. Normal-

ized

to

an

individual

income or

influence-constraint (px

Christensen 71

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Transcript of Christensen 71