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Multiplier theory and public goods : a macroeconomics of the mixed economies
大山, 道広(Oyama, Michihiro)
Keio Economic Society, Keio University
Keio economic studies Vol.51, (2015. ) ,p.1- 17
In this paper we reconsider and extend the economic theory of deep depression, initiated by
Keynes (1936), taking explicit account of the concept of public goods largely blurred in his
general theory and after. To contrive the model of secular stagnation where the interest rate falls
to zero and monetary policy is restricted by the zero-bound, we concentrate on "real economy"
model featuring the theory of public finance. In so doing, we synthesize the traditional theory of
public finance and the Keynesian theory of fiscal policy; and cast new light to their welfare
significance. In stead of the Samuelsonian neo-classical synthesis, we propose the neo-Keynesian
(or the mixed economy) synthesis that requires optimization of public good provision as well as
full employment of labor.
Journal Article
http://koara.lib.keio.ac.jp/xoonips/modules/xoonips/detail.php?koara_id=AA00260492-201500000001
KEIO ECONOMIC
STUDIES
51, 1-17 (2015)
h
YAM
Keio
First version
Abstract:
In
pression,
goods
initiated
stagnation
finance.
nesian
by
concentrate
In so doing,
the Samuelsonian
economy)
(1936),
we
and
account
after. To
and
economic
the traditional
theory
of the
contrive
monetary
model
policy
we
propose
optimization
of public
finance
good
of secular
is restricted
the
de-
of public
model
theory
by
the
of public
and
significance.
the neo-Keynesian
of public
of deep
concept
the
featuring
light to their welfare
synthesis,
theory
the Key-
In stead
of
(or the mixed
as well
multiplier,public goods, secular stagnation, public finance,neo-Keynesian
synthesis
as full
of labor.
Key
words:
JEL
Classification Number:
E12, E22, E24, H30, H40
1.
Since
the
explicit
and
economy"
cast new
2015
provision
employment
that requires
December
extend
taking
theory
"real
synthesize
neo-classical
synthesis
and
rate falls to zero
on
of fiscal policy;
accepted
reconsider
in his general
the interest
we
theory
we
Keynes
blurred
where
zero-bound,
received Apriion
this paper
largely
University, Tokyo, Japan
the collapse of the Bubble
ture continued
to expand
condition leaving
the government
for more
INTRODUCTION
in early 1990,
the national rate of unemployment
deficitincreased
the Japan's
government
than 20 years, but failed to improve
and consequently
accumulated
enormously.
icyHntended
toincrease the aggregate income
This experience
expendi-
the business
at high levels. In the meantime,
the balance
of the government
bond
cast doubt to the effectiveness of fiscal poland employment
multiplier theory originated in the midst of the great depression
in Japan. The Keynesian
of 1930s
has served as
Acknowledgments.
The draft of this chapter was firstpresented at the workshop presided by Ryuzo Sato
on November
29, 2014. I benefited from instructive comments
by Sato on the contributions by Richard
Musgrave regarding the concept of public goods, together with constructive discussions from other attendants
of the workshop. I am indebted to helpful comments by Masatoshi Tsumagari and an anonymous referee of
Keio Economic
Studies.
1 Fiscal policy is here defined as a macroeconomic
gregate employment
by controlling the government
policy designed to stabilizenational income
public financein the narrow sense limited to the provision of public goods.
Copyrightc2015,
by the Keio Economic
and ag-
revenue and expenditure. It should be distinguished from
Society
1
2
KEIO
the cornerstone
ECONOMIC
of the fiscal policy in the standard textbook for a long time. It empha-
sized multiplier effects of government
employment
STUDIES
symbolizing
deficit expenditure
the Keynesian
policy. The recent experience
not as large as believed in the past. Moreover,
frequent use of fiscalpolicy undermined
the government
fiscal discipline giving rise to
inefficient resource allocation in Japan as well as in many
multiplier theory typically abstracts from
goods regarding
works
the aggregate
as an important
tradable in the market.
introduced
when
considered
public
glossed over the distinction
he talked of the national product as if it were one good
(1959)
and Samuelson
their interpretation, public goods
the dictation of the government
of public and private
product. Keynes
of fiscalpolicy, but somehow
At the time of the General
by Musgrave
other countries.
the coexistence
output as a composite
element
of private and public goods
and
of the stagnation of Japan and other countries, however,
revealed that the multiplier effect was
The
on the national income
revolution in the history of macroeconomic
differ from
Theory,
(1954,
the concept of public goods
1955)
was not known
yet. In
private goods in that they are provided
while private goods
are provided
supply in the market. This distinction is not really understood
through
by
demand
and
even now, after more
than
half a century.
Another
problem
with the multiplier theory is its disregard of welfare economics.
tends to undervalue
and employment
workers
the welfare effect of public goods, while overestimating
effects arising from
for the production
surpassing its direct income
theory, however,
more
an expansion
increase in welfare
though
the accompanying
by Keynes
mines
In fact, the use of unemployed
of public goods
may
and employment
effects.In terms of the simple Keynesian
of the government
yield an increase in social welfare
deficit expenditure
brings about a far
through its multiplier effects than its direct meager
provision
himself is the employment
and digging them
public works.
It
the income
of public goods.
A well-known
of workers for burying
up again. It would
through its multiplier effect even though
effects
illustration given
old bottles in disused coal
increase the real income
of the community
there is no sense in such a project in terms of
social welfare.
One
of the most
public expenditure
national income
controversial problems
with the multiplier theory was whether
financed by the government
deficit would
the
really create much
more
than its face value. In order to finance the project, the government
must
issue the corresponding
value of bonds,
future. The
of the project to taxpayers is, therefore, equivalent, regardless
real burden
which
it has to repay later by taxation in the
of whether it is financed by deficit or by taxation. This recognition
Barro, is now
ignores
well known
the message
as the equivalence
of this theorem
theorem.2
completely.
The
due to Ricardo
simple
In fact, many
multiplier theory
public work
put into practice in Japan by deficit financing during the "lost two decades"
collapse of the bubble
number
failed to revive the slumped
of public facilitiessuch as dams
economy.
Moreover,
projects
since the
they created a
and buildings detrimental to environments
2 Ricardo's idea is recorded in his "Essays in the Funding
1979) formalized hisidea clearlyin the words of modern
System," in McCulloch
economics.
and
and
(1888). Barro (1974,
OHYAMA:
social welfare. During
debt continued
MULTIPLIER
AND
PUBLIC
the decades, the government
to increase at unprecedented
risks attributable to government
many
THEORY
3
GOODS
deficitincreased
pace.
and its resulting
In the 21st century, the sovereign
debt financing began
to threaten business prospects
of
follows, we reconsider the effects of fiscalpolicy using a simple real model
of
countries all over the world.
In what
macroeconomies.
In the absence
of the economy
may
become
of innovations
and new
frontiers,the effective demand
insufficient to ensure the full employment
interest rates decline to zero like the "liquidity trap" envisioned
In Section 2, we
consider the simple real economy
only private goods
This basic model
envisioned
are traded in the market. Money
is useful for the purpose
by Hicks
(1937)
of illuminating
as "liquidity trap" where
Hicksian liquidity trap within the framework
cause of such
edy such
a depression
are assumed
the deep depression
monetary
(1998)
of IS-LM
to introduce
equilibrium.
government
away.
economy
policy becomes
reintroduced
inef-
the concept
The
is deficiency of effective private demand.
a situation, it is necessary
the
without public goods, in which
and government
fective and fiscal policy does not exist. Krugman
even when
by Hicks (1937).3
of
fundamental
In order to rem-
fiscal policy conjugating
private and public goods.
In Section
3, we
modify
tervenes in the economy
the preceding
providing
taxation. It abides by balanced
setup and assume
public
goods
budget in the sense that its payment
and transfer is fully financed by taxation. The
by the government
democratically
amount
come
of income
expressed
taxation. One
becomes
of private goods
unit of government
by the
that the national disposable in-
constant independently
expenditure
and associated labor services meaning
of
of public goods is determined
of public goods) is determined
It will be shown
in terms of private goods
of the government
private goods
in the market.
in-
by means
for public goods
or dictatorially, while the amount
(including labor services required for production
adjustment
that the government
and transfer payment
of the level
generates one unit of
that the multiplier of government
expenditure is exactly unity.
In Section 4, we develop a two-good
are considered
model
in which
explicitly and distinctly. When
crease in the government
public as well as private goods
the economy
expenditure increases employment
good, but does not affect the national disposable income.
to be useful by a given social utility function, however,
fare. Furthermore,
if the public good
is so designed
goods, the fiscal multiplier will be strengthened.
further increase in government
public goods
This
means
If the public good is defined
it clearly increases
social wel-
to stimulate the demand
Once
an in-
full employment
for private
is realized, a
expenditure, i.e., a further increase in the provision
gives rise to "crowding
private goods.
is underemployed,
and the output of the public
out," or a corresponding
that the opportunity
of
decrease in the supply of
cost of public goods
is positive rather
than zero.
In Section 5, we explore the effects of macroeconomic
3 Ohyama
(1987, 2004, 2007) developed a version of the IS-LM
to characterize the "liquiditytrap" as its special case.
policy under full employment.
model with a microeconomic
foundation
4
KEIO
ECONOMIC
STUDIES
In this phase, an increase in public expenditure
social utilityfunction even though
it may
be desirable to decrease government
public good is illustrated by looking
the production
employment.
not be justifiedin view
expenditure.
at how
At a firstglance, this idea may
(1954).
The
optimal provision of the
The purpose
the supply of the public good
by Samuelson
of the given
the social indifference curve intersects with
frontier of public and private goods.
this phase is to optimize
introduced
may
the public good is useful on its own. In other words,
seem
of public finance in
rather than just to preserve full
to resemble
the neoclassical synthesis
But as we argue in Section 5, the government
realize full employment
and optimize
Thus it should be named
the neo-Keynesian
the supply
of the public good
(or mixed
must
at the same
time.
system) synthesis of employment
and public finance.
2.
THE
PRINCIPLE
Let us begin by considering
supposed
to be a private good
OF EFFECTIVE
a simplest model
in which
staple. A unit of rice is supposed
for h hours per day for the wage
"rice," the most popular
using a units of homogeneous
a given amount
rate wc
It is
as well as for consump-
be named
be produced
labor. The representative worker is bestowed
to work
there is only one good.
used for production, investment
tion and tradable in the market. For simplicity, it may
Japanese
DEMAND
of leisure and is supposed
determined
by labor contract on the
basis of the social convention. Figure 1 depicts the representative worker's indifference
curves between
wage
rate and leisure and the determination
vertical line showing
at a value between
the given labor hour. Contract wage
reservation wage,
which
the employers
(1981)
and Ohyama
(1987)
The total number
number
ND
the number
the above
who
of workers
how
workers,
>
or N
wc
We
requires at least and unity
1. See McDonald
in the US
then are the determinants
is denoted
N. Let us denote by Ns
or the supply of workers
When
on contract wage
stock K, which
may
contract wage
may
or Ns
of workers
of involuntary
Decades"
of social demand
=
Such
a
is insufficient
in Japan.
for national product? In the present
demand
for national product con-
/. Private consumption
consumption
C = c(wc,r,Y,K)
N.
for
as in the case of the Great
rate wc, real rate of interest r, national income
be written as an aggregate
satisfies
falls short of the
unemployment.
after the Bubble
social private demand
C and investment
the
and by
not be equilibrated to the demand
for national product at fullemployment
the government,
sists of private consumption
Solow
under unemployment.
here that the demand
and the "Lost Two
and
bargaining
by the economy.
of workers
on the
to be negotiated
is in the state of full employment,
assume
the demand
setup abstracting from
assuming
<
the supply of national product at full employment
Depression
depends
demanded
giving rise to the emergence
situation occurs when
to absorb
of wage
in the economy
the supply
ND.
supply of workers
the worker
or w_ <
are willing to be employed,
inequality, the economy
Figure 2 shows
What
for models
of workers
of workers
w_, which
can pay at most,
of contract wage
is supposed
demand
Y and capital
function
(1)
OHYAMA:
MULTIPLIER
THEORY
AND
PUBLIC
5
GOODS
w
1
w
o
Figure 1.
Standard Labor Hour
and Reservation Wage.
dc
For
simplicity,
investment
the firm's long-term
The
dc
> 0
Cyn
market
1
CV
demand
expectation
equilibrium
>
Y
goods
given
wc,
intersectionof
E
the
works
among
condition
as an adjustment
K
aggregate
determination
or Eug
supported
intervention,
and
market
by the
=
c(wc,
<0,
disposable
c*
to be given
Y,K)
the
―
oK
>0
exogenously
depending
on
+
Dd
and
income.
fails to realize
is
I
(2)
the demand
equilibrium
expenditure
and
national
45° line, while
Figure
G#.
5 shows
supply
income
Figure
the
In the absence
full employment
4 Keynes (1936), p. 25. "The point of intersection of the aggregate demand
supply function will be called the effectivedemand.
=
factors.
to equilibrate
curve
government
dc
―
or
unemployment
3 shows
demand
mechanism
Cr
other
under
factor
/. Figure
of national
0 ,
/ is supposed
Y
where
>
of private
Ye
at the
4 illustrates
equilibrium
F#
of government
in this situation.
The
function and the aggregate
6
KEIO
ECONOMIC
STUDIES
w
1
wc
w
o
YJa
N
N
Figure 2. Supply Curve of Labor.
market
gap"
equilibrium income
FG
falls short of full employment
income,
Yf, by "deflationary
in case of Figure 3, or by G a G gin case of Figure 5 implying
corresponding
unemployment.
Reverting
gap coincides with unemployment
to Figure 2, we observe
equal to segment
tical to the familiar illustration of "Keynesian
take full advantage
of the newly introduced
NeS.
the existence of
that the deflationary
Figure 3 is essentially iden-
Cross," whereas
general equilibrium
Figure
model
5 is invoked
to
covering private
and public goods.5
5
The
private goods
portion, given
becomes
convex
of public
This
the stock
used
in the production
of public
of private capital. In such
to the origin and
that the aggregate
goods
may
be subject to decreasing
a case, the production
supply
function
returns
frontier of private and public
depends
positively
to progoods
on the relative price
goods.
modification
of aggregate
supply
is not necessary,
functions.
however,
for our conclusions
but is agreeable
to the Keynesian
concepts
OHYAMA:
MULTIPLIER
THEORY
AND
PUBLIC
7
GOODS
Y
Ye
O
YE
YF
Y
Figure 3. The Principleo f EffectiveD emand.
3
GOVERNMENT
Let us now
AND
introduce
government
expenditure
endogenous
variables.
spent on government
payments
FISCAL
POLICY
government
(TWO
EQUILIBRIUM)
variables on national income
that proportion
expenditure
GENERAL
and consider the multiplier effects of changes in
and other exogenous
Suppose
GOOD
a of national tax revenue
G on public goods
and related
T is to be
and proportion (1 ― a) on transfer
R:
T = G + R
(3)
G = aT
(4)
R = (＼-a)T
(5)
Z = Y-T
+ R = Y-aT
(6)
With theintroduction of government, privateconsumption function is modified as
C = c(wc,Y
-aT,K)
(7)
Given the reservation wage wc, tax T, privateinvestment / and consumption function,
the new market equilibrium conditionis written
Y - aT
determines equilibrium income
= c(wc, Y - ccT, K) + /
Ye and disposableincome
(8)
8
KEIO
ECONOMIC
STUDIES
z
*e
Y
o
Figure 4.
The Determination of National Disposable Income.
Z(=
YE - aT).
The effectof an increase in autonomous investment on equilibrium income and dis
posable income is shown by
Marginal
propensity
to spend
smaller than 1, which
much
more
plier.The
dzE
9/
di
than 1. This conclusion is nothing
spends its tax revenue
often spend
more
to positive and
than the familiar investment
multito
than capitalistson private goods.
First suppose
that the government
This is exactly the case of Keynesian
old bottles in disused coal mines
expenditure
more
cz, is assumed
multiplier is positive and could be
wc, is not quite clear but often supposed
expenditure?
on useless goods.
an increase in government
(9)
l-cz
that the investment
about the effect of government
of burying
1
out of disposable income,
implies
effect of a rise in contract wage,
be positive as workers
How
dYE
and digging them
under balanced
parable
effect of
budget is
dYE
=
up again. The
a,
(10)
dT
To be sure, the balanced
budget
multiplier is equal to unity, or
dYE
dG
=
1
(11)
OHYAMA:
Needless
MULTIPLIER
THEORY
AND
PUBLIC
to say, the multiplier effect on the equilibrium
dZE
9
GOODS
disposable income
becomes
= 0
(12)
8G
PROPOSITION
vails
1 (balanced
under
at (I ―a)
balanced
of tax revenue,
by a but leaves
Standard
just
Here,
of tax revenue,
the standard
smaller
These
balanced
people
systems
private
to social
goods
in
financed
noted
national
and
The
to work
public
good
collaboration
like roads,
Here,
stock
(or
social
is specified
with
public
harbors,
6 Also see Musgrave
goods.
1,
per
income.
parks,
as a labor
public
is defined
service
used
investment
national
The
to poor
of the
social
most
security
are homo-
expenditure
expenditure
does
in T
brings
not
about
government
goods
on
not
affect
affect
an equal
expenditure
and
income
therefore
labor
the income
and
of the public
of employed
the increase
potential
increases
good
and
in
word
expenditure).
investment
good,
the production
forces
in addition
from
(1974)).6
of public
in public
An
employment
distinguished
of Uzawa
is investment
defense
in the government
aggregate
public
to be flow
workers
workers.
effect of government
capital in the
embankments,
(1959), pp. 13-14.
Thus,
among
workers.
capital. Public
and
for the provision
capita
among
common
rich
is one
of
as it were.
goods
good
effect
payments
that consumers
in the
used
on public
to provide
public
from
This
for public
money
sharing
sharing
net
government
but it does
and income-sharing
is supposed
payment.
aggregate
income
assume
increase
goods
taxation,
(income)
income
we
an increase
increases,
expenditure
and
government
capital
=
of or, the
transfer
of tax
government
The
Caesar's
through
2 (work
work
public
1. If a
that the
fact, however,
reform
expenditure
employment
in government
to transfer
the value
larger
is
goods.
is because
of public
in the face of constant
realizes
multiplier
The
to decrease
of public
sector.
to Caesar
amounts
tend
budget.
production
the aggregate
Proposition
increase
income
is set at 1 ― or
than
distributes
simultaneous
government
in the private
expenditure
budget
or smaller
expenditure.
In this paper
This
balanced
employment
decreases
payment
national
transfer
assumption
In
which
that a tax-financed
tax increases
is returned
the
payments
income.
under
implicit
consumption
in Japan.
transfer
in the
While
to a
obtains.
is zero.
benefits,
aggregate
employment
goods
of our
in the production
be
Ye /a
by
security
discussed
used
also
the disposable
equal
of unity
demand
regarding
therefore
It should
equilibrium
of government
becomes
the results
increasing
recently
and
pre-
transfer
unaffected.
proportion
multiplier
aggregate
problems
geneous
increase
are
on
related
thereby
controversial
unemployment
the multiplier.
payments
are often
of tax increases
income
multiplier
budget
that
of government
tells us that the balanced
that if the
tax based
conclusions
transfer
disposable
say
Suppose
the proportion
of macroeconomics
we
becomes
multiplier).
Given
a unit increase
equilibrium
textbook
unity.
budget
budget.
Here,
good
capital
in
stock
etc. that are publicly
merit wants considered there are related to flow public
10
KEIO
owned.
We
ECONOMIC
will consider the economic
capital stock in more
STUDIES
significance of public investment
For simplicity, 1 unit of public good is supposed
good.
The
workers
total number
employed
of workers
N
in the government
where
X
the mixed
economy
where
equilibrium
G
employment
Ne
through
to provide
market.
contains unemployed
The
of
the equilibrium
workers
=XE+aG
of
the public good
and
vertical axis measures
The
when
(14)
< N.
frontier between
G and X on the simpli-
that the labor coefficient a is given and fixed. The curves Ss are the
social indifference curves between
of the public goods
decreases
G and X on the assumption
given the aggregate
consumption
Su is the social indifference curve where
public goods is given
spondingly
determined
expenditure
increases
but what
that G is equal to the amount
undertakes
The curve Tt depicts a straight line production
The curve
Note
and the horizontal axis that of the private good.
NE
fying assumption
of
(13)
of the public good. Figure 5 shows
the government
expenditure
is the sum
= X + aG,
the private sector supplies private goods
the government
using a unit of private
in national production
denotes the output of the private good.
in the production
to be produced
employed
and private sectors:
N
labor employed
and public
detailin the next section.
at Ga
and the consumption
on Su.
As pointed
that the marginal
utility
of the private goods.
the government
expenditure
of the private goods
Zo
on
is corre-
out above, an increase in the government
the aggregate income
and employment
in the same
proportion,
can we say about its welfare effects? An increase in the aggregate income
employment
would
increase the expected
the probability of their employment.
of public goods
would
and
utility of the potential workers by increasing
Moreover,
the associated increase in the provision
increase the welfare (social utility)by itself. To make
clear, let us define the social utility function (the graphical representation
this point
of which
is
the social indifference curve) as
W
PROPOSITION
= u(X,G),
uG>0.
expenditure
to increase social welfare along
the expansion
to the old Keynesian
expenditure
view,
of
path EaEb-
a bond-financed
whereas
government
the future tax burden
it focuses only on the income
expenditure
a tax-financed increase in
results in an equal increase in national income.
gued, this view is untenable in that it overlooks
increase. Furthermore,
The expansion
shifts the equilibrium point under unemployment
brings about a multiplied increase in national income,
government
(15)
3 (expansion path in the presence of unemployment).
tax-financed government
According
ux>0,
As already ar-
of the expenditure
effects of the expenditure increase
neglecting its welfare effects. In light of (15), an increase in tax-financed government
expenditure
creates extra income
under unemployment.
There
are some
Itis bound
public goods
and employment
without incurring opportunity
costs
to increase social welfare.
that complement
and promote
private consumption
and
OHYAMA:
investment.
MULTIPLIER
For example,
the provision
may increase consumption
of public roads
vestments
AND
PUBLIC
11
GOODS
of care and nurse services by the government
by creating leisure time for housekeepers.
and port facilitiesmay
in general. Under
be important
these circumstances,
ten as a function of government
income
THEORY
expenditure
The maintenance
for business opportunities and in-
consumption
function may
be rewrit-
as well as on real interest rate r, national
and on capital stock:
C =c(wc,r,
Y-aT,
K,aT)
(16)
and investment function may be similarlymodified as
(17)
/ = i(r,aT,K)
where cr < 0
ir < 0.
Proposition
The balanced
expenditure
4 (government expenditure complementing
budget
multiplier of a government
privateexpenditure)
expenditure
that complements
private
has a multiplier greater than a under unemployment?
After all the prevalence
of unemployment
the result of unwillingness
shortage of public goods
stems from
deficiency of effective demand,
on the part of people to consume
in the broad
sense including
or invest. It may reflect the
those that complement
private
expenditure.
4.
In the presence
public good
FISCAL
POLICY
of unemployment,
by using labor from
and maintained,
curve Sb passing though
This means
improving
shown
however,
Eb
that the supply
no opportunity
the
full employment
is
costs. Once
frontier Tt from
of the
without reducing
down
5, indifference
left to right above
is insufficient and there are rooms
for
social welfare by increasing its supply. The socially optimal equilibrium
by E*
where
indifference
curve S* touches
from
decreased
full employment,
along Tt. Throughout
Figure
6 depicts the case where
along
of the public good
and increase
the expansion
is
how-
only if the supply
of
the process, labor
the private sector to the public sector and the equilibrium
point from
path (or adjustment
the output of the public good
optimal point F* is smaller than that of Eb.
adjustment
Tt. Under
of the public good is achievable
and the social welfare increases
EbF*.
workers
this is no longer the case. In Figure
cut production
the private good is correspondingly
to F*
EMPLOYMENT
it is possible to carry out the production
of the public good
ever, an increase in the supply
moves
FULL
the pool of unemployed
output of private goods, i.e.,incurring
achieved
UNDER
Eb
path)
at the socially
It is desirable to decrease the production
that of the private good
along
the expansion
path (or
path) EbF*.
7 Aside from the demand
increasing effectsfrom the introduction of public goods considered here, it is
also worth taking note of the supply increasing effectsfrom the public goods. In the present model, however,
the supply shocks of thiskind do not affectthe short -run adjustment process under unemployment.
We shall
explore the long-run effects of public investment (increase in the stock of public capital)later in the next
section.
12
KEIO
ECONOMIC
STUDIES
G
N/a
G*
GB
GA
O
7
Figure 5.
PROPOSITION
expenditure
5 (Expansion
Equilibrium.
Path under Full Employment).
has to be pursued
of the production
Economy
differsfrom
along
the expansion
frontier. To be more precise, ifG*
X
N
0
Path of the Mixed
that ensures the full employment
further adjustment
EbF*
An Expansion
^
Zo
*
When
the government
its socially optimal level, a
path (or adjustment
> Gb,
path)
the government
must
increase the its expenditure and the supply of public goods. In contrast, ifG*
< Gb,
government
The social
must
decrease its expenditure
and the supply
welfare increases in the process of the adjustment
5
NEO-KEYNESIAN
of public
process along
goods.
the
EbF*.
SYNTHESIS
Early in 195O's, Samuelson put forward theidea that once the government succeeds
in maintaining fullemployment, labor embodied in the employed workers will be optimally allocatedthrough market mechanism,
sis".8 If full employment
is maintained
allocation of private goods
mize
will be achieved
social welfare. Within
theorem
of welfare economics
and named it the "neo-classicalsynthe-
by the government's
the simple model
by market
devoid
optimally
to maxi-
of public goods, the fundamental
is established that general equilibrium
optimal under the condition of perfect competition
8 See Samuelson (1955), p. 212.
fiscal policy, the resource
mechanism
and in the absence
becomes
Pareto
of externalities.
OHYAMA:
MULTIPLIER
THEORY
AND
PUBLIC
13
GOODS
G
G*'
G*
o
z*
z*'
t
v
x
Figure 6. Productivity
Improvement in PrivateGood Production.
In the present model
the shortage of social public goods in the short run and social
capital stock in the long
run may
short run unemployment
and long run stagnation as mentioned
ment
depress consumption
and investment
bringing about
above. Thus
the govern-
provision of social public goods in the short run and the social capital stock in the
long run may
exert positive externalities in the sense that it promotes
tion and investment
easing short run unemployment
and 6 illustrate how
the government
ployment
equilibrium
optimal equilibrium
Proposition
the optimal
intervention
Ea
allocation of national resources
along
through
with market
private consump-
and long run stagnation. Figures 5
mechanism
full employment
may
be achieved
starting from
equilibrium
Eb
by
the unem-
culminating in the
E*.
6 (Neo-Keynesian
or mixed-economy
synthesis). Suppose
that given
14
KEIO
resource endowment,
production
ary state prevails where
ECONOMIC
STUDIES
technology
net investment
and consumers'
and saving
stabilizes at the natural level. Also suppose
ket for private goods
zero and real interest rate
that perfect competition prevails in the mar-
with no technological externalities. The government
anticipate the short-run as well as the long-run
foresight. The government
to increase employment
optimal provision
preference, static station-
become
should
is assumed
effectsof public investment
to
with perfect
then be able to use expenditure policy appropriately
in the short-run and maintain full employment
of public goods in the long-run.
and achieve
This design of economic
the
policy may
1 named ^J4-1
V
* {or
(
4-1 mixed-economy)
' J
＼synthesis.
4-1 ' y
be
the neo-Keynesian
the
So
far we
have
nology
and
public,
however,
abstracted
formation
the present
ment.
us divide
Let
latter to improve
K.
model
taking
G/.
/ is supposed
Considering
these
explicit
former
and
ci(Kg)
vestment
we
productivity
N(K,
Kg)
tion
of K,
supply
Figure
may
Kg
since
private
and
public
roads,
in future
optimal
inferior
event.
increase
the
to T't'. Given
goods,
in public
will decrease
the future
and
output
Similarly,
and
and
the
private
capital
constraint
Kg
stock
as
since
thereby
labor
government
in-
improving
labor
coefficient
a) and
units as an increasing
stock
private
frontier
labor
education
about
and
serve
as the basis
may
F*,
consumption
on
the labor
asymmetrically
the optimal
how
Tt
production
of the public
9 For simplicity, we have assumed
proposition introducing the government
good
away
as before,
a
and
of the
to T't. The
point
future
goods
frontier
effects
public
funcof labor
increase,
position
as environ-
of labor
measured
frontier expected
with
and
T't'.
future
Barring
will increase
on future
and
F*
in
such
in that
public
expand
cost of future
from
and
increase
shifts as a result
good
relative
will change
will normally
An
the present
of contact
of its expansive
coefficient
from
the
the supply
points
the production
account
on
Tt.
shift of production
curves
or the
of the present
7 depicts
investment
F*'
by
in projects
increase
a parallel upward
by
investment
is shown
productivity
the social indifference
Figure
decrease
frontier
Kg-
of private
(or lowering
in efficiency
capital
present
improving
are shown
social
Similarly,
of public
The
facilities and
units bringing
equilibria
It will
effects
frontier.
investment
harbor
of
stock
goods
to
(14')
capital
government
Gq
services
a(KG)G
function
of labor
consumption
efficiency
or
have
effects of invest-
the employment
government
of public
We
public
capital stock
a decreasing
supply
and
dynamic
tech-
private
units.
6 illustrates
in efficiency
duction
production
either
resources.
government
and
+
and
to produce
rewrite
=X
future
the national
of production
private
stock.
the
shows
in efficiency
shape
ment,
in
to be
increases
into
the quality
relationship,
is supposed
certainly
G
on production
of investment
of these
of public
N(K,KG)
where
account
is supposed
efficiency
to improve
essence
of technology
expenditure
The
the quality
effects of investment
It is the
the quality
government
investment
investment
the dynamic
that it improves
reconsider
government
from
of resources.
but the future
the pro-
public
to F*'.
As
of an
capital
good
a result,
output
of the
the externalitiesof any kind. It would be easy to extend this
tax-cum
subsidy scheme
to internalize externalities.
OHYAMA:
MULTIPLIER
THEORY
AND
PUBLIC
15
GOODS
G
N la
G*'
G*
t
o
Z*[
Figure 7.
private
good
may
growth
income
public
of resources.
educational
and
and
many
and
we
initiated
attempt
run
As
advanced
public
in the loss
10 The third arrow of "Abenomics"
both
public
economic
effects
by
countries,
and
destroy
labor
beyond
of economic
consumption
the current
however,
difficulties in
misguided
tremendous
natural
supply
and investment
private,
run.
it is vitally important
expenditure
and
as the engine
in the long
witnessed
of aggregate
CONCLUDING
(1936)
work
stock
investment
of public
to reconsider
Keynes
and
indebtedness
frontier. Therefore,
implications
by
other
untimely
of production
the welfare
run.
government
facilities resulting
In this paper
Production.
in general,
capital
positive
in the long
to serious
Useless
private
of generating
6.
pression
in Public Good
Investment
in the short
public
and
in Japan
contraction
account
run
can lead
strategy).
employment
is capable
short
finance
investment
and
and
by accumulating
in the
Productivity Improvement
7 (growth
Investment
both
X
N
decrease.
PROPOSITION
increases
Z*
public
misallocation
environment
and
in efficiency
units
to take into
full
in particular.
REMARKS
and
taking
extend
explicit
in the Japanese Economic
public investment and deregulatory measures to improve
the
economic
account
of the
theory
of deep
concept
de-
of public
policy calls for the growth strategy of useful
the opportunities of privateinvestment.
16
KEIO
ECONOMIC
STUDIES
goods largely blurred in his general theory and after. To contrive the model
stagnation where
zero-bound,
the interest rate falls to zero and monetary
we concentrate on real economy
In so doing, we
synthesize
of secular
policy is restricted by the
featuring on the theory of public finance.
the traditional theory of public finance and the Keynesian
fiscaltheory and cast new light to their welfare significance.
(1) As the basic setting, we assume
are no market-originated
fallen to zero. Using
Keynesian
a simple
involuntary
the adjustment
equilibrium
not through
of commodity
librium, it is necessary
prices. To reduce
for the government
carrying out public investment.
we
show
that
deficient Key-
is realized through
the
of interest rate nor through
or remove
to intervene
Conversely,
model
can arise there from
equilibrium
the adjustment
there
and the interest rate has
general equilibrium
This underemployment
of national income,
stationary statein which
and investment
macroscopic
unemployment
nesian effective demand.
adjustment
the Schumpeterian
private innovations
unemployment
by producing
the government
in the equi-
public goods
or
intervention in this fashion
is justified only under the present setup.
(2) In line with the Ricardo-Barro
to abide by the balanced
budget
to increase labor employment
tional disposable income
theorem,
(3) If the government
(private goods) in the government
expenditure (Propositions
expenditure
The process
services continuously. It may
librium as in EaEbE*
expenditure
(5) The
of the public good,
between
the public good
of the public good
necessary
may
whether
must
and the private good
be determined
in view
indifference curve and the production
to consume
budget (Proposition
4).
it is useful or not, incurs opportu-
and employment
Starting from
expenditure
without
is maintained,
the initial
will initiallyin-
decreasing
that of
there arises trade-off
so that a further increase in the supply
not warrant improvement
(1954) proposed
and
equi-
are useful, the national welfare
unemployment.
as full employment
tunity cost in terms of the private good.
(6) Samuelson
path of unemployment
to increase the propensity
to decrease the supply of the public good
the public good
be divided
on goods
In such a case, the multiplier of the gov-
of involuntary
of the public good
the private good, but as soon
may
increases expenditure
equilibrium, an increase in the government
crease the production
time to accomplish
to be desirable in itselfin the sense that it directly
to effective demand.
nity cost except in the presence
unemployment
1 and 2).
will be greater than 1 even under balanced
production
(income)
3).
social welfare, but it is often designed
or invest thereby adding
the na-
take some
be visualized as an expansion
is supposed
sector keeping
full employment
in Figure 5. If the public goods
(4) The public good
ernment
toward
the government
will increase along the path (Proposition
enhances
be able
is sufficiently large, it will realize full employ-
of adjustment
into discreet periods during which
is supposed
should
be called the work
theoretically in no time. In reality, however, it may
full employment.
the government
so, the government
at a constant level . This may
sharing effects of the government
ment
equivalence
discipline. Even
of national welfare. It may
on the way.
of some
become
The optimal supply of
welfare criterion and its oppor-
Figure 6 illustrates this point using the social
frontier (Proposition
5).
the so-called neo-classical synthesis to the effect that
OHYAMA:
once
full employment
the Pareto optimum
government's
optimization
THEORY
the achievement
of social welfare through
(or the mixed
foregoing
production
technology
to the "short run"
of the economy
by the advocateors
should
serve as the growth
The
of public
6).
setting where
the
and therefore the production
public as well as private, is not only conducive
growth
of the economy
through its
frontier.In fact,it extends the future production
of the accumulation
the
It extends to the
of labor is called for (Proposition
but also to the "long-run"
argued
will accomplish
above, however,
synthesis that calls for optimization
and labor resources
effects on the production
tierby means
the market
of full employment.
analysis is applicable only
to the short-run recovery
17
GOODS
appropriate provision of the public goods.
economy)
frontier are given and fixed. Investment,
dynamic
PUBLIC
is established by the government,
provision as well as for full employment
(7) The
AND
of the rest of resource allocation. As shown
role goes beyond
neo-Keynesian
good
MULTIPLIER
of public and private capital stock (Proposition
of "Abenomics",
public investment
strategy of the Japanese
economy
fron7). As
and active deregulation
stagnant over 20 years
since early 1990.
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