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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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7/25/2019 Christensen 71
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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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7/25/2019 Christensen 71
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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
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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.
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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.
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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
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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.
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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.
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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
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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-
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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
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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.
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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
top related