Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
Transcript of Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 1/12
American Economic Association
Keynes-Wicksell and Neoclassical Models of Money and GrowthAuthor(s): Stanley FischerReviewed work(s):Source: The American Economic Review, Vol. 62, No. 5 (Dec., 1972), pp. 880-890Published by: American Economic Association
Stable URL: http://www.jstor.org/stable/1815206 .
Accessed: 18/03/2013 08:00
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp
.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact [email protected].
.
American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The
American Economic Review.
http://www.jstor.org
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 2/12
Keynes-Wickselln d Neoclassical M o d e ls
o f M o n e y a n d G r o w t h
By STANLEY FISCHER*
The essential features of Keynes-Wicksell
(henceforth KW) monetary growth mod-
els, distinguishing them from neoclassical
models, are the specification of an inde-
pendent investment function and the
assumption that prices change only in
response to excess demand in the goodsmarket.! In neoclassical monetary growth
models, by contrast, there is no indepen-
dent investment function and all markets
are continuously in equilibrium.
In KW models a steady state of inflation
requires persistent excess demand in the
goods markets. This suggests that the
steady-state properties of such models are
unsatisfactory. In neoclassical models, an
instantaneous doubling of the quantity of
money, however the money is distributed,
produces an instantaneous doubling of the
price level so long as the expected growth
rate of the money supply is the same be-
fore and after the "blip" in the money
supply. This according to KW theorists
suggests that there is something amiss
in the short-run dynamics of the price level
in such models.
In this paper, the price dynamics of both
models are discussed, and a modified pricedetermination equation is incorporated
into a KW model. The standard compara-
tive dynamic exercises for monetary
growth models are undertaken in this
modified model; the modification of the
price adjustment equation ensures steady
state equilibria rather than disequilibria.
The properties of the modified KW modelare then compared with those of neoclassi-
cal models. Essentially, familiar short-run
macro-economic conclusions emerge from
consideration of short-run behavior in the
modified model and neoclassical conclu-
sions emerge from analysis of its long-run
behavior.
I. Price Dynamics
KW models use the Law of Supply and
Demand to determine the rate of inflation.2Specifically, it is assumed in KW models
that
(1) r = X(D-S), O< X < oc
where 7r s the rate of inflation, D and S are
aggregate demand for and supply of goods,
each in real terms, and Xis a constant. It is
apparent that there cannot be inflation
without excess demand if equation (1)
determines the rate of inflation, and thusa steady state with inflation requires per-
sistent excess demand. KW models can
accordingly have steady states in which
individuals are continuallv frustrated in
* Assistant professor, department of economics,
University of Chicago. I would like to thank GeorgeBorts, Rudiger Dornbusch, and Jerome Stein for theirhelpful comments on an earlier draft. Thanks for com-ments and discussion are due, too, to William Brock,Jacob Frenkel, Merton Miller, Michael Mussa, DouglasPurvis, and Richard Zecher.
1Jerome Stein-who is apparently responsible for theKW designation-has recently provided two very usefulexpositions of these models (1969, 1970). An earlierarticle of his (1966), using a KW model which is not sonamed, provides a full dynamic analysis for the typicalKW model.
2 See Kenneth Arrow. It will be assumed that the
reader is familar with both types of monetary growth
models. A two-asset (money and capital), one-sector
model is used as the paradigm of neoclassical models
(see James Tobin and Miguel Sidrauski); places where
my conclusions would differ if some other neoclassical
model were used are footnoted. My paradigmatic KW
model is contained in Stein's 1969 article.
880
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 3/12
FISCHER: MONEY AND GROWTH 881
obtaining the goods they demand, even
though their demands are based on correct
expectations and perceptions of the price
level-and they are condemned to be so
frustrated forever after. This is an un-appealing result and there are two possible
lines of attack on the problem: first, de-
mands could be expected to change in
response to such frustrations; alterna-
tively, the price determination equation
might be inadequate. I pursue the second
approach.
The question raised by (1) and similar
equations is: Whose behavior do such
equations describe? The standard Walras-
ian answer is "the auctioneer"; another
frequent answer is "somewhat less than
competitive firms."
Consider the auctioneer explanation
first. In the standard single period ex-
change model, the auctioneer calls out
prices for each good sequentially on the
basis of the mechanism:
(2) Pi,j = Pi-l,j + Xj(pi-1)
where i is the iteration number of thecurrent call, j is the number of the good, p
is the vector of prices, and xi(pi-1) is an
increasing function of excess demand for
goodj at the previously called price vector.
In intertemporal models an equilibrium
price vector is obtained by the above pro-
cess at the beginning and no further taton-
nement is required. If new information is
available in each period, as in models in-
cluding uncertainty, one supposes that
there is an "auction" each period. Thegoal of the auctioneer in each period is to
establish market-clearing prices prices at
which demands are equal to supplies.
Equation (1) is an attempt to use (2) in
a temporal context so that the i subscript
becomes a t, and to apply (2) to the aggre-
gate price level. But it ignores the motive
of the auctioneer. If the auctioneer expects
the general price level at time t to be dif-
ferent from that at t- 1, then he might use
as his rule of thumb
-e
(3) Ptj = pt-l, + xj(pi)
where fi is the general price level expected
to prevail at t, and pt-, is the general price
level at t- 1. Aggregating over goods, and
in continuous time, an analogue of (3) is:
(4) l = * + X(D-S)
where 7r is the actual rate of inflation, and
7r* is the expected rate of inflation.
The auctioneer is not present in most
markets and it is somewhat unsatisfactoryto discuss reasonable behavior for a non-
existent economic agent. Consider alterna-
tively the explanation in terms of the be-
havior of price-setting firms. As suggested
by Arrow, and developed by Robert Barro
in a recent and interesting paper, since the
existence of disequilibrium is inconsistent
with certain assumptions of the perfectly
competitive model,3 we may expect price-
setting by firms even in industries for
which the competitive model is adequate
for comparative static analysis.
Barro analyzes optimal price-setting
behavior for a monopolistic firm faced
with uncertain demand and a fixed cost of
adjusting its selling price; the optimal
policy is to adjust price only when excess
demand or supply reaches certain barriers.
He then shows that, by aggregating over
firms, the average price may be expected
to behave according to (1). Barro confineshimself to cases where the aggregate price
level is expected to remain constant. Sup-
pose now that all prices but the monopo-
list's price were expected to increase at the
rate 7r*;then costs would be expected to
rise at the rate 7r*(since the cost function
I In particular, in disequilibrium it cannot be true
that each firm can sell as much as it wants at the going
price and each consumer can purchase as much as he
wants at the going price.
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 4/12
882 THE AMERICAN ECONOMIC REVIEW
is homogeneous of degree one in prices),
and as of any given price fixed over an
interval by the monopolist, the relative
price of the monopolist's output would be
falling at the rate 7r*.Then, in adjustingprices, the monopolist could be expected
to include an adjustment for the trend in
prices over the period for which he expects
to keep his own price constant. Aggregat-
ing over firms, one would expect to reach
an equation similar to (4).
Thus, on either score, an equation such
as (4) is a more adequate representation of
price adjustment than is (1). Accordingly,
I proceed in Section II to an analysis of a
KW model incorporating equation (4).Stein (1970) has in fact suggested that an
equation like (4) might be useful in recon-
ciling KW and neoclassical models. Similar
equations may be found to describe wage
and price adjustment in the literature.4
Before presenting the modified KW
model, it is necessary to discuss the price
dynamics implicit in the usual neoclassical
model. The per capita demand for real
balances (md) is a function of the per capita
capital stock (k) and the expected rate of
inflation (r*):
(5) md = L(k, r*, Li > O,L2 < O
At any instant of time the capital stock
(we omit "per capita" where no confusion
is likely to result) and the expected rate of
inflation are given, as is the nominal money
stock and population. Then, adding to (5)the neoclassical specification that the
money market is always in equilibrium(6) M/PN m =md
is sufficient to determine the price level. In
particular, a doubling of the stock of
money will double the price level but leave
the system otherwise unaffected.5
Is there any reason to regard this instan-
taneous neutrality with suspicion? There
are circumstances under which it might be
regarded as reasonable: for instance, if it
was announced that at some point of timeevery individual's nominal money bal-
ances would be doubled, then, given some
sophistication by economic agents, it
might be realized that this action was
analogous to creation of a new unit of ac-
count and the price level might simply
double. It is, however, a basic assumption
of neoclassical models that injections of
money are not distributed on the basis of
existing holdings of money (since other-
wise the transfer payments by which the
money supply is expanded would be equiv-
alent to interest payments on money hold-
ings). Given this assumption, increases in
the nominal balances of some individuals
in the economy can be expected to produce
their effects on prices gradually, through
real balance effects, rather than instan-
taneously. Hence the KW objection to this
neutrality has force.
Using (5)and
(6),the rate of inflation in
neoclassical models is given by
1(7) w=j,-X- [L,Dk + L2Dr*]
m
where ,u is the (assumed constant) rate of
expansion of the nominal money supply, n
is the rate of population growth, and D
denotes the time derivative. In the steady
state 7rw- n; thus the rate of inflation
will be reduced below its steady-state valueby capital accumulation and raised above
its steady-state value by increases in the
expected rate of inflation. Even leaving
aside the expectational factor, D7r*, equa-
tion (7) is not analogous to (4).
4 See, for example, Edmund Phelps.I In two-sector neoclassical models (e.g., Duncan
Foley and Miguel Sidrauski) determination of the price
level requires also commodity market clearing, and the
price level cannot be said to be determined by the re-
quirement of portfolio balance. It remains true that in
such models, "jumps" in the money stock affect only the
aggregate price level.
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 5/12
FISCHER: MONEY AND GROWTH 883
11. The Modified KW Model
In outlining this KW model I shall point
to its departures from neoclassical analysis.
Both types of model have in common a
production function, stock demand func-
tions for assets, a savings function, and
an expectations function. I shall specify
forms of these functions which could be
usecl in either type of model.
The per capita output of goods is
(8) y = f(k) f' > 0, f " < 0
where, for convenience, it is assumed the
Inada conditions hold and that real bal-
ances do not enterthe
production function.It is also assumed that the labor force,
growing at the rate n, is supplied inelasti-
cally and that full employment is main-
tained.'
There are three assets: money, private
bonds, and physical capital. Stock demand
functions for real balances, real bonds (the
excess demand function, since it is assumed
there are no outside bonds), and capital are
given by (9), (10), and (11), respectively.7
The assets are assumed to be gross substi-tutes. The variable y, output, enters to
represent the transactions demand for
money. Per capita wealth, a=(k+m),
(9) md = L(y, a, f'(k) + r*, p) L1 > O,1 > L2 > O, L3 < O, L4 < 0
(10) bI = H(y, a,f'(k) + r*,p) H1 < O H, > O,H3 < O,H4 > 0
(11) kd = J(y,a,f'(k) + w*,p) Ji < O, 1 > J2 > O,J3 > O,J.j < 0
enters as the stock budget constraint.8
Bonds and capital are not perfect substi-
tutes so thatf'(k)+7r*, the expected nomi-
nal return on capital, may differ from p,
the nominal interest rate. The three de-mand functions are dependent since the
sum of the demands for assets is con-
strained by wealth at each instant.
Per capita savings is a function of dis-
posable income and wealth:
(12) s = S(ye, a), 1 > sl > (, s2 < 0
Expected disposable income, ye consists of
factor payments, f(k), plus transfer pay-
ments ym, where y is the constant and
preannounced rate of expansion of the
nominal money supply (it is assumed that
the current price level is correctly per-
ceived), minus expected capital losses on
money holdings, 7r*m.Thus
ye = f(k) + ( - 7r*)m
Saving is definitionally equal to desired
additions to asset holdings; it is the sum of
Id, h'd,and x'1which are desired additions,
per capita, to real balances, bonds andcapital, respectively. Consumption demand
and savings demand are constrained by
dlisposable income:
(13) ye = Cd + s
It is well known that the stability of
dynamic models is heavily dependent on
the expectations function. We assume
here adaptive expectations:
(14) 7r*=
f(7r-7r*),0 <
d< o
Thus far we have outlined a fairly stan-
6 For a KW model with variable employment, seeKeizo Nagatani.
I The demand functions for assets differ from thoseused in Foley and Sidrauski only in that the price ofcapital does not enter. It is assumed that productionalways takes place away from corners of the productionpossibility frontier so that the relative price of capitaland consumption goods remains fixed. I note, quoting
David Levhari and Don Patinkin, "that it would bemore consistent with general considerations of economictheorv if . . [the demands for assets] . . . were repre-sented as depending upon disposable income . .. This,however, would greatlv complicate the . .. analvsiswhich follows...." (p. 720).
8 Since there are no outside bonds in the model, the
net per capita value of bonds is zero.
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 6/12
884 THE AMERICAN ECONOMIC REVIEW
dard neoclassical model. A neoclassical
analysis would proceed as follows: assume
asset market equilibrium and use any two
of (9)-(1 1) to determine the price level and
the nominal interest rate at each instant oftime these are functions of the capital
stock and expected rate of inflation. Then
assume that consumption demand is al-
ways satisfied and obtain the rate of
capital accumulation as the residual of
output minus consumption.
The scene is then set for determining
"next instant's" short-run equilibrium; the
economy proceeds through these equi-
libria, and if it is stable, ultimately reaches
a steady state in which the capital stock
and expected rate of inflation are constant.
In fact, the model we have set up is very
similar to Levhari and Patinkin's "Money
as a Consumer Good" model.
The four KW features of the model
follow. First, there is the specification of
an investment demand function, xd. We
assume a stock adjustment demand for
investment.
(15) xd = nzk + D(kd-k), ' > O
The flow demand for capital consists of the
replacement demand, nk, plus a term
which depends on the divergence between
the actual capital stock and that de-
manded at the current levels of wealth and
current rates of return and income. The
basic justification for (15) lies in the exis-
tence of adjustment costs in changing the
capital stock: the greater the divergence
between actual and desired capital stocks,the greater the costs that can profitablv be
incurred in changing the capital stock.9
The investment demand function (15)
has the property which is the basis for
investment functions in Stein's KW mod-
els that an increase in the difference be-
tween the expected nominal return on
capital, f'(k) +7r*, and the nominal interest
rate, p, increases investment demand. 'I'hisis the "Wicksell" feature of KW models for
(16) f'(k) + * - p = f'(k) - (p -*);
the first term on the right-hand side of (16)
is the natural rate and the second is the
real rate, and differences between these
two rates affect investment demand.10
Second, there is the price adjustment
equation, in which it remains to specify
aggregate demand and supply.
(17) 7r = 7r* + X(cd + Xd -f(k))
The demand for goods consists of the de-
mands for consumption and investment;
the supply is simply full employment
output.
Third, it is specified that the bond mar-
ket be continuously in equilibrium, so that
(18) b = bd = 0
This is an assumption of conveniencerather than necessity.1"
Fourth, there is the question of the
allocation of output in periods of excess
demand or supply. Here it is assumed that
both consumption and investment plans
are partially frustrated when there is ex-
cess demand; in particular, planned invest-
ment is reduced by some positive fraction
(1 -y) of excess demand to give the actual
rate of investment.
x - (1 - y) [cd + xd f(k)j,
In general -y could be expected to be an
endogenous variable rather than a con-
I See Robert Eisner and Robert Strotz for the deriva-tion of an investment demand function such as (15);see also Marc Nerlove for critical comments on this andsubsequent developments. Note that although adjust-ment costs are invoked in explaining (15), thev are notexplicitly incorporated in the model.
10The "Keynes" part lies in the specification of an
independent investment demand function; other Kev-nesian features, such as unemployment, can be captured
in KW models with variable employment.
11 n Stein (1966), for instance, it is assumed that the
money market is in equilibrium.
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 7/12
FISCHER: MONEY AND GROWTH 885
stant; while (19) is very much a deus exmachina, theories of allocation under dis-equilibrium are not well developed andthere is no formulation which is obviously
theoretically superior at this stage. Notethat (19) is equivalent, through (17), to
(20) x = x" -( *
Before proceeding to an exposition of theshort- and long-run properties of the modi-fied model, we use the assumption that thebond market is always in equilibrium (18),to derive the implied relationship between
the nominal rate and the capital stock,real balances, and the expected rate ofinflation. Given k, m, and 7r*, here is, from(10) and (18), only one nominal interestrate which equilibrates the bond market.
Specifically
(21) p A(k, m, 7r*)
where
-1A1=- [Hif' + H2 +Hf"] < O
H1
- H,
H-
- H3A3= - > 0
H4
Ihe only ambiguity in (21) concerns theeffects of an increase in the capital stockon the nominal rate: there is, in adldition
to the substitution effect (IIff") andwealth effect (11.), an income effect, (11f');we assume that the substitution andwealth effects dominate and that the re-duced real rental on capital resulting froman increase in k leads to a decrease in thenominal rate as of any given r*. Thus, weassume that increases in the capital stockten(l to reduce the nominal rate; our earlierassumptions imply that increases in realbalances tend to reduce the nominal rate
while increases in the expected rate of
inflation tend to increase the nominal rateof interest.
III. The Short and Long Run in theModified Model
We now discuss the behavior of this KWmodel in the short and long run. Giventhe assumption that the adjustment coeffi-
cient, X, in (17) is finite, the price level is
given at any instant-that is, it is inher-ited from the past. Accordingly, m, realbalances per capita, is determined exoge-nously, for M, nominal balances, is a policyvariable. TIhe capital stock and the ex-pected rate of inflation are also inheritedfrom the past. Tlhus, at an instant of time,k, m, and r* are predetermined.
Tlhe behavioral relations of the model
determine, in the short run, the nominalrate of interest and thence, through the
goods market, the rate of inflation. Giventhe rate of inflation, and k, m, and 7r*,therate of capital accumulation is determinedfrom (19), and the rate of change of the
expected rate of inflation from (14). Thestage is then set to determine the capital
stock, real balances, and the expected rate
of inflation at the next "instant"; the econ-
omy proceeds in this way through time,
reaching a steady state if. the system is
stable. The remainder of this section con-sists of a more detailed examination of this
process.12
Given k, m, and 7r*,the predetermined
variables, the nominal interest rate is de-
termined through the requirement of bondmarket equilibrium, and is given by (21).TI at nominal rate in turn, together withthe predetermined variables, determinesthe demands for consumption and invest-
ment and the consequent rate of inflation.
12The verbal description we give of the dynamic pro-cess of this economv corresponds more closely to a dif-ference e(quationsystemn han to the differential equationsystem contained in the formal analysis; this is simp)lya matter of convenience.
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 8/12
886 THE AMERICAN ECONOMIC REVIEW
Using (17) and the flow budget constraint,
the rate of inflation is
(17') 7r= 7r*+X(xd+ (Au-7r*)m-S(ye, a))
Consider now the effects of changes in k,
m, and 7r* on the rate of inflation. The
effects of changes in k and m occur only
insofar as excess demand is affected (recall
that xd is a function of the nominal rate, so
that effects working through the bond
market must also be considered) while a
change in r*has an expectational effect on
the rate of inflation in addition to excess
demand effects. We obtain
(22) 7r= G(k, m, *, )
where
G1=XQi/ i-) -+n-sif'?S2)
G2=XQ -\dm
+ 7r*)1Sl) - S2) >O0
/ dJG3=1+--X' -m(1-sSi) > 0
GiA=Xm(l-si)>0
The derivatives of the J function are writ-
ten as total derivatives to indicate that
bond market effects are to be included.
Increases in the capital stock have an
uncertain effect on excess demand; they
reduce the stock excess demand for capi-
tal13 but may either increase or decrease
savings since the income and wealth effects
on savings work in opposite directions. If
the system is near the golden rule, then
n-sif'>O and the term (n-s1f'-s2) will
be positive. Thus the sign of G1 is am-
biguous.
Increases in real balances are inflation-
ary; they increase both consumption and
investment demand. Increases in the ex-
pected rate of inflation have a direct effect
on actual inflation throughout the expec-
tations effect-they also increase invest-ment demand but reduce consumption
demand by reducing the value of expected
transfer payments. Thus, whether the
actual rate of inflation increases by more
or less than the expected rate depends on
whether increases in the expected rate
produce an excess supply or excess demand
for goods; in other words, on whether the
reduction in consumption demand is
greater than or less than the increase in
investment demand. It later turns out that
this is an important factor in determining
the stability of the system, and it may be
seen that the smaller is 4V' the more
slowly is the capital stock adjusted the
more likely is (G3- 1) to be negative.
Finally, an increase in the rate of growth of
the money stock increases transfer pay-
ments and is inflationary.
The "short-run" position of the econ-
omy is determined by (21) and (22). Itsbehavior through time is determined by
the capital accumulation equation (20),
the rate of change of real balances equation
which can be derived by differentiating
m with respect to time, and the expecta-
tions equation (14). For convenience we
rewrite and renumber these equations
here:
(23) Dk = 44J(y, a,f'(k) + r*, A( ))-k]
- -7 [G(k,m, 7r*, ) -r
(24) Dm = - n - G(k, m,m, ,,)]m
(25) D7r* = O[G(k, m, 7r*, ) -7r*]
Consider now the steady state for this
economy. In the steady state, Dwr*= 0, and
so the actual rate of inflation is equal to the
expected rate, and, from (24), each is equal
to (,u-n). From (23), the demand for the13 This may be shown by computing the derivative
dJ/dk- 1 and using the stock budget constraint.
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 9/12
FISCHER: MONEY AND GROWTH 887
capital stock is equal to the existing capital
stock, and there is no excess demand for
capital; from the stock budget constraint
it follows that there is no excess demand
for real balances either. From (17), theexcess demand for goods is also zero and
since investment demand is satisfied, so is
consumption demand.
As in the neoclassical model, there are
no unsatisfied demands in the steady state
of the modified KW model. The ref ormula-
tion of the price adjustment equation is
thus sufficient to remove the unsatisfac-
tory feature of previously published KW
models the persistence of excess demand
in the steady state.
IV. Changes in the Stock of Money andin the Rate of Growth of Money Stock
Suppose the economy is in the steady
state and there is an increase in the money
stock, but no change in the rate of growth
of the money supply. T hen since , is the
only exogenous variable in the system in
the long run, it is apparent that if the sys-
tem is stable, it will return to the samesteady state. However, this economy, un-
like our earlier neoclassical system, will be
forced out of equilibrium by the increase
in the money stock, and will take time to
return to its steady state. T he steady-state
neutrality is of course neoclassical but
the dynamics is not.
Consider now the impact effects of an
increase in the money stock. The nominal
interest rate is reduced, and the rate of
inflation is increased because excess de-mand is increased. The increase in the rate
of inflation increases the expected rate of
inflation and begins to reduce real bal-
ances. The effects of the increase in the
money stock on capital accumulation are
ambiguous: the demand for both invest-
ment goods and consumption goods is
increased, and investment is more likely
to increase the relatively greater are real
balance effects on investment demand and
the more fully are investment plans, rather
than consumption plans, realized. This
short-run story is very Keynesian insofar
as the effects of the change in the money
stock manifest themselves in the bondmarket and result in an increase in invest-
ment demand through the lowering of the
nominal rate. If we had been dealing with
a model with unemployed resources, the
story would have been even more Key-
nesian for the increase in both consump-
tion and investment demand could have
called forth more output, rather than
resulting in inflation.
The path followed by the economy
thereafter depends on its stability prop-
erties, which are analyzed in the Appendix.
It is shown in the Appendix that if the
steady state is near the golden rule capital
stock, then a necessary condition for sta-
bility is that increases in the expected rate
of inflation reduce excess demand this,
as discussed above, is helped by the slow
adjustment of investment demand to
changes in the desired capital stock, and
damaged by a great sensitivityof the de-
mand for capital to the expected rate of
inflation. It is also shown that slow adjust-
ment of expectations as in the neoclassi-
cal model and rapid adjustment of prices
to eliminate excess demands are conducive
to stability. However, the conditions for
the rapid adjustment of expectations a
large 0 to produce instability are less
stringent than they are in neoclassical
models.
Finally, we consider the comparativesteady-state properties of the modified KW
model. An increase in the growth rate of
the nominal money supply ultimately in-
creases the expected rate of inflation by the
same amount as the increase in the mone-
tary growth rate. T he higher expected rate
of inflation increases the demand for capi-
tal and reduces the demand for real bal-
ances; one of the factors determining the
new stea(ly state is thus the asset demand
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 10/12
888 THE AMERICAN ECONOMIC REVIEW
functions and the fact that there will be noexcess demands in the long run; the otherfactor determining the new steady state is
savings behavior. Working with our full
system of differential equations, we obtain
dk* Om'VX dJ(26) - = - *- - (n(1-S1) -S2)
d,u Z3 dr*
and
dm* fmc'X dJ(27) -- = __ * (n-Slf'-S2)
d,u Z3 dr*
where Z3 is the determinant of the matrixin the Appendix which has to be negative
for stability. This negativity is assured if
(n-slf'-s2) > 0
Thus we can say that if the system is ina stable steady state, increases in the rateof growth of money unambiguously in-increase the equilibrium capital intensity;and if that steady state is near the goldenrule capital stock, increases in the rate ofgrowth of money reduce equilibrium real
balances. In any event, if increases in the
capital stock reduce savings, so s1f'-s2<0, then increases in ,u increase k* andreduce m*.
These results are familiar and early
comparative steady state neoclassical
propositions. We obtain them, of course,because this KW system has the same
steady-state properties as our neoclassicalmodel of Section JI, which was set up to be
very similar to earlier neoclassical mone-
tary growth models."4 Although we chose
to represent our steady state by using(23)-(25) we could equally well have been
neoclassical and described the steady statein terms of asset market equilibrium andthe requirement that savings be just suf-ficient to maintain real per capita assetsconstant.
It is, incidentally, interesting to use (20)
to examine the impact effect on invest-
ment of an increase in the growth rate
of the money supply. The demand for
investment goods Xd is unaffected by in-creases in . Thus the impact effect of a
change in depends only on its effect on
the rate of inflation. The rate of inflation
increases with ,, so that the actual rate
of investment falls when , is increased.
The increase in , increases consumption
demand but not investment demand and
so some investment is displaced. Thus,
initially the capital stock falls when the
rate of growth of money is increased,
though ultimately the capital stock in-
creases. This is similar to the behavior of
the capital stock following an increase in
, in Sidrauski.
V. Conclusions
The purpose of this paper has been to
modify a KW model in a way which re-
moves the feature of steady-state excess
demand in such models and to compare the
resulting model with a neoclassical model
based on the same demand functions for
assets and savings. The paper has made it
clear that the element producing the un-
satisfactory features of KW models is the
price adjustment equation, and argu-
ments have been presented for using an
alternative adjustment equation in which
prices may change because they are ex-
pected to change, as well as because there
is excess demand. The potential of KWmodels for a useful theory of short-run
dynamics, emphasized by others, has been
demonstrated in the context of the modi-
fied model. It has also been shown that
there is no inherent reason for the long-
run properties of KW and neoclassical
models to differ, so long as the KW in-
vestment demand function is consistent
with the neoclassical stock demand func-
tion for capital.
14 In particular, our use of output rather than dispos-ab)le income in the asset demand functions, and theomission of imputed interest on real balances enable usto avoid several pitfalls.
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 11/12
FISCHER: MONEY AND GROWTH 889
-/dJ \ 1-z y dJ 1-y dJ 1-y
(Al)~~b
i)-
l-G1
K1'd
---
G24td*--
(31
-Gim - G2m - G3m
gcG13G2 O(G3 1) _
APPENDIX
Stability Conditions
The matrix involved in determining thelocal stability of the system (23)-(25) is
shown in (Al) above.Let Z1 be the trace of Z, Z2 the sum of its
second-order principal minors, and Z3 its
determinant. Necessary and sufficient condi-
tions for local stability are
z1 < 0
(A2) Z3 < 0
Z1Z2 - Z3 < 0
A necessary condition implied by (A2) is that
Z2 be positive.Now,
(A3) Z, = -Om(G3-1) Gs[ --1)
1-- -yG < 0
From the derivatives given in (22), we know
that G2 is positive; it follows that the productof
(G3 - 1) and
[ (dJ 1 -y 1
must be positive. These are, respectively, the
terms a(Dr*)/a7r* and &(Dk)1ak. Consider
first &(Dk)/ k which is
a(Dk) /dJA4) - = yq/ - - 19k \dk
- (1 - Y)(n - Slf - 2)
The first term in parentheses is negative by
virtue of the gross substitute assumption,
and if (n-s1lf-s2)>0, the whole expression
will be negative. Now, at low levels of the
capital stock, f' is very large and the above
expression may be negative unless y is close
to unity; for higher levels of the capital
stock, and certainly when it is near the
golden rule, we are assured that 3(Dk) 8k is
negative. We shall assume that the steady
state about which we are examining thedynamics is such that nt-s1f'- s2>O and
hence &(Dk)ak< O.
Given this, it is necessary that (G3-1) be
negative, or that the direct effects of an in-
crease in the expected rate of inflation in the
goods market be negative-this requires that
the adjustment coefficient in the investment
equation, V', be sufficiently small and/or
that dJ/d7r* be small.
Second
dJ(A5) Z3= -flC/m G1-
_dm
/dJ \-G2 - -1 < O
dk /
dJ--AX4'm _- (n-sif'-s2)
_dm
-(- -1) (n( 1- SI) -S2)]
Given the assumption n-s1f'- s2>0, this isnegative.
The value of Z2 iS
/dJ\Z29=mt3G2+I3KP' (G3-1) (k -1
(A6)
-Gi- -->O
The sign of the bracketed term is ambiguous:
after substitution the term becomes
This content downloaded on Mon, 18 Mar 2013 08:01:00 AMAll use subject to JSTOR Terms and Conditions
7/27/2019 Fischer - Keynes Wicksell and Neoclassical Models of Money and Growth
http://slidepdf.com/reader/full/fischer-keynes-wicksell-and-neoclassical-models-of-money-and-growth 12/12