DBJ Discussion Paper Series, No.0906

A Pure Theory of Aggregate Price Determination

Masayuki Otaki(Institute of Social Science, University of Tokyo)

June

2010

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings,
conclusions or recommendations expressed in these papers are those of the authors and do
not reflect the views of the Institute.

A Pure Theory of Aggregate Price Determination†

Masayuki Otaki

Institute of Social Science, University of Tokyo

7-3-1 Hongo Bukyo-ku, Tokyo 113-0033, Japan.
E-mail: ohtaki@iss.u-tokyo.ac.jp
Phone: +81-3-5841-4952†

Fax: +81-3-5841-4905

The author thanks Hirofumi Uzawa for his profound and fundamental lessons about“The General Theory of Employment, Interest and Money.” He is also very grateful to
Masaharu Hanazaki for his constructive discussions.

Abstract
This article considers aggregate price determination related to the neutralityof money. When the true cost of living can be deﬁned as the function ofprices in the overlapping generations (OLG) model, the marginal cost of aﬁrm solely depends on the current and future prices. Further, the sequenceof equilibrium price becomes independent of the quantity of money. Hence,money becomes non-neutral. However, when people hold the extraneous belief that prices proportionately increase with money, the belief also becomes
self-fulﬁlling so far as the increment of money and the true cost of living are
low enough to guarantee full employment.

Key Words:

Marginal cost, True cost of living, Neutrality ofmoney, Credibility of money, Rational extraneous belief

JEL Classiﬁcation: E24, E31, E40

11Introduction

As Keynes [5] points out, there appears to be a serious crack between
macroeconomics and microeconomics on the mechanism of price determination.1 In microeconomics, prices are governed by marginal costs. However, macroeconomics emphasizes the role of money in the process of aggregate price determination. How are these theses related to each other? The
present paper explores this problem.
Such a crack is deeply connected to the neutrality of money. Otaki[9], [10] has already shown that the equilibrium sequence of the aggregate
price can be independent of the quantity of money, using the standard deterministic two-period overlapping generations (OLG) model of production
economy. On the other hand, Lucas [7] proves that the quantity theory ofmoney strictly holds in certainty.2
These seemingly contradictory results suggest the following theoretical
hypothesis: The assumption that prices are determined by marginal costsmeans that the equilibrium production and employment level is an interior
solution. That is, the economy is located at imperfect employment.
The interior solution emerges from to the lack of purchasing power ofmoney. By some plausible assumption, the true cost of living becomes the1

In Keynes’ words, “For it is far from being consistent with the general tenor of theclassical theory, which has taught us to believe that prices are governed by marginal
prime cost in terms of money and that money-wages largely govern marginal prime cost.
Thus if money-wages change, one would have expected the classical school to argue thatprices would change in almost the same proportion, leaving the real wage and the level of
unemployment practically the same as before, any small gain or loss to labour being at
the expense of proﬁt of other elements of marginal cost which have been left unaltered.
They seem, however, to have been diverted from this line of thought, partly by the settled
conviction that labour is in a position to determine its own real wage and partly, perhaps,
by preoccupation with the idea that the prices depend on the quantity of money.”2
Although Lucas [7] uses a dynamic stochastic general equilibrium model, uncertainty
is not essential for proving the neutrality of money [Theorem 2]. In addition, whether ﬁrms
are price makers or takers is also irrelevant to the theory extended in the article. As Otaki[9] and [10] show, the concept of monopolistic competition plays a crucial role in proving
the welfare-improving eﬀect of the expansionary monetary policy and the existence of
involuntary unemployment in a frictionless economy.

2

function of the current and future prices independent of quantities. Hence,
the nominal reservation wage also depends on the same factors. Thus, whenthe equilibrium current price is equal to the marginal cost, the equilibrium
price sequence becomes independent of the quantity of money. If the quantity of money is suﬃciently relatively small to the equilibrium price level
determined beforehand, some individuals are unemployed, and the interior
equilibrium emerges without any price stickiness. In other words, money is
non-neutral unless some additional conditions are satisﬁed.3
The boundary solution, namely, the quantity theory of money, can beattained by the following two conditions. First, people hold the extraneous
belief that the price level proportionately varies with the quantity of money.4
Second, the increased rate of money, that is, the inﬂation rate, is suﬃciently
modest to reduce the true cost of living, and every individual wishes towork.5
Under these conditions, for an arbitrarily given money supply, the current price level ﬂexibly adjusts the purchasing power of money to attainthe full-employment equilibrium. Thus, one-to-one correspondence emerges
between the current price level and the quantity of money. Namely, thequantity theory of money holds and money becomes neutral under the two
assumptions above.
Consequently, money is intrinsically non-neutral and aﬀects the employment and output level without any price friction as Keynes [5] tacitly considers.6 The quantity theory of money is upheld by the extraneous belief
3

Most new Keynesian economists believe that a price-stickiness assumption is unavoid-

able for obtaining the non-neutrality of money. For example, see Calvo [2] and Mankiw
and Reis [8]. Galı́ [4] provides a summary of the new Keynesian economics from thisperspective.
4
Lucas [7] speciﬁes the equilibrium price function as p = mϕ(z) to support the quantity theory of money under perfect information. This assumption corresponds to theextraneous belief in this article.
5
The method of injection of money also leads to a diﬀerent consequence. We shalldiscuss this problem in Section 4.
6
According to Keynes [5], “The division of economics between the theory of value anddistribution on the one hand and theory of money on the other hand is, I think, a false
division. The right dichotomy is, I suggest, between the theory of the individual industry

3

that money is only a measure of value and possesses no substantial value.
The contents of the paper are follows. Section 2 exhibits the basic modeland indicates the non-neutrality of money under perfect competition. Section 3 provides a suﬃcient condition for supporting the quantity theory ofmoney. It also discusses the diﬀerence in the Keynesian and monetarist
views on money. Section 4 explains how the methods of injecting moneyaﬀect the conclusion. Section 5 provides concluding remarks.

2

The basic model

2.1

Optimization problems of economic agents

2.1.1

Individuals

We consider a standard two-period OLG model with money and one perishable good under certainty. Individuals are born with continuum density
between [0, 1] in each period, and live for two periods: the youth and the oldage. They can supply unit labor at their discretion when they are young.
The disutility is denoted as α. The lifetime utility function of each individual
U is
U (c1t , c2t+1 , δt ) ≡ u(c1t , c2t+1 ) − δt · α,(1)where c1t and c2t+1 are the current and future consumption of generation t
respectively. δt is a deﬁnition function that takes the value of unity when
the individual works and zero when he/she does not work.
u( · ) is the well behaved homothetic function that represents the lifetime utility derived from consumption.7 Although the separability between
the consumption stream and leisure seems restrictive, the assumption canbe justiﬁed by Diewert’s discussion as follows [W.E. Diewert “Cost of living indexes and exact index numbers” Discussion Paper 09-06, Departmentof Economics, University of British Columbia, August 6, 2009]: “Althoughor ﬁrm and of the rewards and the distribution between diﬀerent uses of a given quantityof resources on the one hand, and the theory of output and employment as a whole on theother hand.”7
Shephard [11] proves that iﬀ the utility function is homothetic, the true unit cost ofliving becomes the function of prices independent of the consumption quantity.

4

this (homothetic) assumption is generally not justiﬁed when we consider the
consumer’s overall cost of living index, it can be justiﬁed in the context of asubaggregate if we assume that the consumer has a separable subaggregator
function, f (q), which is linearly homogenous. In this case, q is no longer
interpreted as the entire consumption vector, but refers only to a subaggregate such as “food” or “clothing” or some more narrowly deﬁned aggregate.”
From the economic perspective, Diewert suggests that aggregation shouldbe performed among similar goods. In this sense, in (1) we assume that
consumption and leisure have quite diﬀerent properties as compared to thecurrent and future consumption.
The budget constraint that each individual faces is
pt c1t + Mt ≤ δt Wt ,pt+1 c2t+1 ≤ Mt ,(2)

where pt is the price of the good; Wt is the nominal wage; and Mt is thenominal money demand of generation t to prepare for future consumption.
The proﬁts of the ﬁrm can also become the income. However, we assume
that all the markets (goods, money, and labor) are in perfect competition.
Hence, we can neglect the proﬁts as a source of income.
An individual maximizes (1) on (c1t , c2t+1 , Mt , δt ) subject to (2). Since
U is homothetic, the true cost of living function Ψ exists such thatΨ(pt , pt+1 , u) = f (u)ψ(pt , pt+1 ),(3)

where ψ( · ) is a linear homogenous function. It also increases with pt andpt+1 . We can calculate the nominal reservation wage WtR by using the true
cost of living function (3) as
WtR = f (α)ψ(pt , pt+1 ).

(4)

In addition, the aggregate current consumption function of the young generation, Ct , becomes
C = c(

pt+1)[wt lt ],
pt

wt ≡

Wt
,
pt

(5)

where lt is the employment level that is located within the interval (0, 1).

5

2.1.2

Firms

Next, we proceed to the optimization problem of a representative ﬁrm. The
only production factor is labor. For simplicity, the representative ﬁrm faces
the constant return production function:yts = lt ,(6)

where yts denotes the output level. Since the ﬁrm acts as a price taker,
the proﬁts become zero in the equilibrium. Hence, using (4), we obtain thefollowing important diﬀerence equation. Namely,p∗t = WtR⇒p∗t = f (α)ψ(p∗t , p∗t+1 )⇔1 = f (α)ψ(1,

p∗t+1
).
p∗t

(7)

Thus, we obtain
Lemma 1 If equilibrium employment is located within (0, 1), that is, theequilibrium price is determined by the marginal cost, the equilibrium pricesequence, {p∗t+j }+∞j=0 , is determined independently of the sequence of thequantity of money {Mt+j }+∞j=0 . Furthermore, the equilibrium inﬂation rate,∗
pt+j+1
ρK ≡ ∗, is constant over time.
pt+j
2.1.3

The government

Finally, we must specify the money-supply rule. New money is injected
through the government expenditure Gt .8 Thereafter, money is supplied to
Mt+j ∞
Mt
keep the real cash balance {}j=1 equal to the initial level m ≡
.
pt+j
pt
Therefore, using Lemma 1, the real government expenditure gt+j is expressedbygt+j ≡

2.2

Mt − Mt−1


,


Gt+j
pt
=
1

pt+j

 (1 − K )m,ρ

if j = 0,
if j ≥ 1.

(8)

Market equilibrium

There are three kinds of markets in the model: goods market, labor market,
and money market. Following Walras’ Law, we conﬁne our attention to8

For simplicity, all goods that the government purchases are assumed to be wasted.

6the former two markets. When the labor market is in interior equilibrium,
0 < lt < 1, the equilibrium nominal wage is equal to the nominal reservation
wage WtR .
The aggregate demand for the good ytd is deﬁned byytd ≡ Ct + gt +

Mt−1
.
Pt

(9)

Substituting (5), (6), (8), and the zero-proﬁt condition of the ﬁrm into (9),and using Lemma 1, we obtainytd = c(ρK )yts + m.
Since y ∗ = y d = y s , the equilibrium condition of the goods market isy ∗ = c(ρK )y ∗ + m.

(10)

Consequently, we obtain
Theorem 1 If m is suﬃciently small, there is an interior equilibrium inthe sense that some individuals are unemployed and
0 < y∗ < 1holds.
Proof.

Since u( · ) is homothetic, 0 < c(ρK ) < 1 holds. By Lemma 1, thechange of nominal money supply M does not aﬀect the price of the good p.
Hence, we can choose a suﬃciently small m such that Eq.(10) has a solution
within (0, 1).
Figure 1 illustrates Theorem 1. When the prices are determined by themarginal cost, the Hicks-Samuelson 45◦ line analysis is justiﬁed under perfectcompetition and rational expectations without any price stickiness. If the
expansionary monetary-ﬁscal policy is implemented, AD line shifts upward,
and the employment and output increase. Thus, money is non-neutral. The
1
ﬁscal multiplier is, as shown by elementary macroeconomics.9
1 − c(ρK )9

Kiyotaki and Wright [6] provide an alternative and persuasive theory of money. They

criticize OLG model method because it cannot endure the “rate of return dominance.”
Nevertheless, the search model is not necessarily suitable for analyzing the neutrality ofmoney because it lacks the path through which money is injected into the economy.

7

We must note that the induced eﬀective demand theory, which is summarized by Eq.(10), corresponds to the long-run stationary equilibrium without
any price friction. It implies that the friction or stickiness concerning prices
is not a necessary condition for the non-neutrality of money, as most new
Keynesian economists implicitly consider. Furthermore, the property of thebasic model clearly diﬀers from the new Keynesian economics, as in money
is non-neutral even in the long run and that the theory extended in Keynes[5] can be interpreted as the economics of the stationary state.

3

On the quantity theory of money

The previous section proves that money is intrinsically non-neutral, and an
expansionary ﬁscal-monetary policy stimulates the employment and output.
This section deals with a suﬃcient condition for sustaining the quantity
theory of money in the basic model.

3.1

Two diﬀerent beliefs on the value of money

The basic model supports the Keynesian view that imperfect unemployment
equilibrium emerges from the lack of eﬀective demand without any friction
on prices. Eq.(7) plays a crucial role in this assertion. This equation implies
that individuals believe that money has an intrinsic value in that young individuals are ready to accept all forms of additional money at the prevailing
price of the good. Here, we deﬁne the credibility of money as
Deﬁnition 1 We say that money is credible when newly issued money canbe exchanged for a unit of the good at the prevailing price.
Even if money is credible, the value of money is determined by its own future(rational) expectation. Eq.(7) also implies that if individuals expect money
to become more valuable in the future, it is soon transmitted to its current
value appreciation (deﬂation) and vice-versa. Such fragility of the base of
the credibility of money is rooted in the fact that money does not provide anyutility by itself. These properties of money resemble those of the ﬁat money
we actually use. To sum up, when prices are determined by marginal costs,
8

the value of money is determined not by its quantity but by its credibility.
This is considered to be the Keynesian view on money.
In other words, the fact that the price of the good is insensitive or sticky
to a monetary shock does not indicate the signiﬁcant existence of menu cost
but the high credibility of money.
On the other hand, monetarist regards money only as a measure of value;
hence, individuals believe that the increase in the quantity of money brings
about a proportional price increase, and has no eﬀect on the employment
and output level under rational expectations.10
In comparison to the Keynesian view, which considers that people believe in the intrinsic value of money, monetarist entirely lacks the view ofcredibility of money. Friedman and Schwartz [3] consider that money canbe circulated solely on the basis of the “conﬁdence of others will.”
Although the two concepts, the credibility of money and the conﬁdenceof others will, appear to resemble each other, the situation where the ‘conﬁdence of others will’ becomes indispensable to sustain the monetary economy, by itself, reveals that the credibility of money is entirely lost and thatthe role of money has become quite restrictive. This is because estimating
the will of numerous and anonymous others is far more diﬃcult than assuming each individual simply believes in the intrinsic value of money. Furthermore, even if the conﬁdence exists, there is another problem. Namely,
how much money do young individuals require in exchange for a unit ofgoods when the credibility collapses? Thus, once the credibility of money islost, money ceases to have absolute substance and is reduced to the relative
measure of value. It is plausible for each individual to expect prices are
determined by the quantity of money in such cases.
Such a phenomenon occurs in the following two polar cases. In theﬁrst case, the economy is located at the full-employment equilibrium. In
this case, any additional money does not produce any output. Accordingly,
prices proportionately increase with money. Keynes [5] calls such an inﬂation
10

According to Friedman and Schwartz [3], “Money is a veil. The ‘real’ forces are thecapacities of the people, their industry and ingenuity, the resources they command, theirmode of economic and political organization, and the like.”9

as true inﬂation.
The second is the polar case of hyperinﬂation in which money utterly
loses credibility and is used only as a measure of value.
Note that the seminal empirical work of Cagan [1] concerning the quantity theory of money conﬁnes the data to the period of hyperinﬂation in six
European countries immediately after World War I and II.11 According to
Cagan [1],“Even a substantial fall in real income, which generally has notoccurred in hyperinﬂations, would be small compared with the typical risein prices. Relations between monetary factors can be studied, therefore, inwhat almost amounts to isolation from the real sector of the economy.”
However, there are two persuasive reasons that the credibility of money ishighly damaged soon after the World Wars. First, the potential production
capacity of the economy was at its lowest. In addition, governments wereforced to monetize huge amounts of debt issued for military expenditure.
Such aspects of hyperinﬂation are similar to those of true inﬂation.
The second reason, which is more important than the ﬁrst, concerns the
incentive of labor supply. When individuals hold the extraneous belief thatprices increase in proportion to the quantity of money, the rate of increaseof nominal money supply is equal to the equilibrium inﬂation rate. Oncethe inﬂation rate is higher than some threshold,12 the equilibrium nominal
reservation wages begin to exceed the price of the current good because thetrue cost of living index ψ becomes extremely high owing to the accelerationof inﬂation. Consequently, individuals begin to lose their incentive to work.
The credibility of money is entirely lost in this polar case. Contrary to
Cagan [1], hyperinﬂation can be regarded as the pathology of the monetary
economy.
On the basis of the above discussion, in the next subsection, we shallshow how the basic model is transformed into a model that justiﬁes thequantity theory of money.

11
12

Greece is an exception. The data used for Greece belong to the World War II period.
The critical value of the inﬂation rate is ρK deﬁned by Eq.(7). We shall comprehen-sively discuss this problem in the next subsection.

10

3.2

Rational extraneous belief and the monetary policy

To transform the basic model into the monetarist model, we need to assume
the following.
Assumption 1 Every individual believes that money is not credible andholds an extraneous belief that the price of a good is proportional to thequantity of money. That is, each individual considers that the equilibrium
price function takes the following form:
pt+j = κ−1 Mt+j ,

∀ j.

(11)

Under Assumption 1, we can prove the following theorem:
Theorem 2 There is a rational extraneous belief equilibrium under full emMt+j+1
that satisfy
ployment. That is, there exist pf ∗ , κf ∗ , and µf ∗ ≡Mt+j
Eq.(11) and y ∗ = 1 for an arbitrarily given Mt .
Proof.

To attain the full employment equilibrium, the price of the goodmust exceed the equilibrium reservation wage. From Eq.(7), the equilibrium
price pft ∗ should satisfy
pft ∗ > WtR⇒∗)
pft ∗ > f (α)ψ(pft ∗ , pft+1⇔

1 > f (α)ψ(1,

∗
pft+1

pft ∗

). (12)Since each individual agrees with Eq.(11), substituting it into (12), we obtain
1 > f (α)ψ(1, µf ∗ ).

(13)

Because ψ is a continuous and increasing function on µ, taking Eq.(7) into
consideration, µf ∗ must satisfy
ρK > µf ∗ .

(14)

By the continuity of ψ, it is certain that there exists µf ∗ that satisﬁes (14).
Condition (14) assures full employment. Next, we determine (pf ∗ , κf ∗ )in order to be consistent with Eq.(11) and note that y ∗ = 1. Then, using
Eqs.(10) and (11), we obtain
1 = c(µf ∗ ) + κf ∗⇒11

κf ∗ = 1 − c(µf ∗ ).

(15)

By Eqs.(11) and (15), we ﬁnally determine the equilibrium price function as
Mt+jpft ∗ = f ∗ .
(16)κThis equation completes the proof.
Next, we shall deal with the case of hyperinﬂation. To avoid the unboundedness of the current equilibrium price, we make the following assumption:
Assumption 2 There are some individuals whose disutility of labor is zero.
Their Lebesgue measure is ϵ, 0 < ϵ ≪ 1.13
Under this assumption, we obtain the following theorem concerning hyperinﬂation.
Theorem 3 There is a rational extraneous belief equilibrium where the employment and output level is at its lowest ϵ. That is, there exist ph∗ , κh∗ ,and µh∗ that satisfy Eq.(11) andy ∗ = l∗ = ϵ.

(17)Furthermore, the equilibrium inﬂation rate ρh∗ is the highest in comparison
with the economies described by Theorems 1 and 2.
Proof.

From Eq.(7), the following inequality is the necessary and suﬃcientcondition that the employment and output level at its lowest ϵ:
pt+1
R
ph∗
⇔ 1 < f (α)ψ(1,) = f (α)ψ(1, µh∗ ) ⇔ ρK < ρh∗ . (18)t < Wtpt
By the continuity of ψ, there exists µh∗ that satisﬁes (18).
Next, we prove the existence of κh∗ . Using Eq.(10),ϵ = c(µh∗ )ϵ + κh∗ ⇒ κh∗ = (1 − c(µh∗ ))ϵ.
Finally, by Eq.(11), we obtain the equilibrium price function as
Mt+j
ph∗
.
t+j =
κh∗
By Eqs.(14) and (18), the equilibrium inﬂation rate is shown asρf ∗ < ρK < ρh∗ .

(19)

(20)

This completes the proof.
13

Note that this additional assumption does not aﬀect the validity of Theorems 1 and

2.

12

4

On the injection methods of money

In the previous section, we assume that money is supplied through the government expenditure and is equally distributed to each individual. However,it diﬀers from the rule in Lucas [7]. Lucas [7] assumes that new money is injected into the economy as interest on the existing money. In this section, we
consider how such a diﬀerence in money supply rule aﬀects the conclusions
in Theorems 1, 2, and 3.
Let us denote the gross rate of interest of money during period t as xt .
Hence, the money supply rule obeys
Mt+1 = xt+1 Mt .

(21)

In addition, we assume that Assumption 2 holds, and all individuals expect
the equilibrium price as in Eq.(11).
Then, the budget constraint of each employed individual becomes
pt c1t + Mt ≤ Wt , pt+1 c2t ≤ xt+1 Mt ⇒ c1t +pt+1
c2t ≤ wt .
pt xt+1(22)

Since from Eq.(11),pt = κ−1 Mt , pt+1 = κ−1 xt+1 Mt .

(23)

Substituting (23) into (22), we obtain
c1t + c2t ≤ wt = yt .

(24)Thus, the value of x is irrelevant to an individual’s consumption-leisuredecision. It implies that money is neutral to any equilibrium employment
and output level, [ϵ, 1]. Consequently, we obtain
Theorem 4 When every individual holds the extraneous belief of Eq.(11),and money supply obeys rule (21), money is neutral to any equilibrium employment and output level y ∗ , 0 < y ∗ ≤ 1, in the sense that x and M do notaﬀect y ∗ and κ∗ .
Proof.

First, we show that the equilibrium output level y ∗ is independentof M and x. Since the eﬀective inﬂation rate is unity in this case, by Eq.(7),13y ∗ is classiﬁed into the following three cases:

y∗ =











ϵ,

if 1 > ρK ,y∗,if 1 = ρK ,1,

if 1 < ρK .

(25)

y ∗ = y ∗ in Eq.(25) is used as the following sense. Namely, when 1 = ρ∗ ,the utility derived from consumption is equal to the disutility of labor forthe majority, 1 − ϵ, and they are indiﬀerent whether work or not. Thus,
the equilibrium output level becomes indeterminate within (ϵ, 1). It implies
that when individuals decide to work, the equilibrium output increases along
their intention. Thus we can ascertain that y ∗ is independent of M and x.
Finally, we show that κ∗ possesses the same properties as y ∗ . Eq.(24) canbe reinterpreted as the goods market equilibrium condition. Let us denotethe optimal consumption decision as (c∗1 , c∗2 ). Furthermore, note that thesevalues are independent of equilibrium prices (p∗1 , p∗2 ) because the equilibrium
output y ∗ is determined by Eq.(25). Then, by Eqs.(11) and (24),c∗1 (y ∗ ) + c∗2 (y ∗ ) = y ∗ ⇒M= c∗2 (y ∗ ) ⇒ κ∗ = c∗2 (y ∗ ).
p∗

(26)

This completes the proof.
A monetarist may ﬁnd Theorem 4 to be very eﬀective at the ﬁrst glance.
It implies that the quantity theory of money is upheld even in the normal
economy at least mathematically. Nevertheless, we must note that some
unusual phenomenon shall be observed in this economy. That is, even if
the economy possesses idling resources, and the marginal cost is constant,
additional money only raises the price level. In other words, the credibilityof money is entirely lost in the economy.
Eq.(11) in Assumption 1 and Eq.(21) are crucial factors. The newly
issued money subject to Eq.(21) refers to a kind of denomination -the changeof the unit of money- and hence, it is possible for individuals to lose thecredibility of money. As a result, individuals hold an extraneous belief thatprices increase proportionately with the quantity of money. Such a methodof injecting money, that is, continuous denomination, which reduces moneyfrom the absolute substance to the relative measure of value, is scarcely
14

adopted in fact. Therefore, the relevance of Theorem 4 is much lower thanthat of Theorem 1.

5Concluding remarks

We have analyzed the mechanism of aggregate price determination, whichclosely relates to the problem of the neutrality of money. The results obtained are as follows.
First, when the economy stays within imperfect employment equilibrium,
the price of the good is determined by its marginal cost, independent of
the quantity of money. It conversely implies that imperfect employment
equilibrium emerges from the lack of eﬀective demand (or money).
The stickiness of the aggregate price, which the new Keynesian economists
emphasize, may not indicate the substantial cost of changing the price, but
the high credibility of money. We have succeeded in proving the aggregate
price stability by introducing the concept of credibility of money by usinga model in which prices can change ﬂexibly in accordance with exogenous
shocks.
Second, we have also succeeded in transforming the basic Keynesianmodel into a monetarist model in which the quantity theory of money isupheld and money is insigniﬁcant.
The transformation requires two additional conditions to the basic model.
One is the extraneous belief on the equilibrium aggregate price level. Namely,
all individuals believe that the aggregate price level changes proportionately
with the quantity of money. The other is the qualiﬁcation on the rate ofincrease of money supply.
Under such an extraneous belief, the inﬂation rate becomes equal to therate of increase of money supply. Accordingly, if the rate of increase ofmoney supply is suﬃciently low, nominal reservation wages will be lower
than the current price of the good. Hence, full-employment equilibrium isattained. Since newly issued money cannot bear any output, the extraneous
belief becomes self-fulﬁlling. Keynes [5] calls this case true inﬂation.
The other polar case is hyperinﬂation. When the rate of increase of15

money supply (the inﬂation rate) is high enough, nominal reservation wages
exceed the current price of the good. In such a case, massive unemployment
emerges and the production level falls to its lowest. Thus, the quantity
theory of money holds.
To sum up, the quantity theory of money is valid in the two polar cases
where money loses its intrinsic value and only operates as a relative measureof value. Although the money supply rule that new money is added asinterest on the outstanding money strengthens the monetarist’s proposition,such a rule is rarely adopted in reality.

16

References[1] P. Cagan, The monetary dynamics of hyperinﬂation, in: M.Friedman(ed.), Studies in the Quantity Theory of Money, University of Chicago
Press, Chicago, 1956, pp.25-117.
[2] G. Calvo, Staggered prices in a utility maximizing framework,
J.Monet.Econ. 12 (1983), 383-398.
[3] M. Friedman, A.J.Schwartz, A Monetary History of the United States
1867-1960, Princeton University Press, Princeton, 1963.
[4] J. Galı́, Monetary Policy, Inﬂation, and the Business Cycle: An Introduction to the New Keynesian Framework, Princeton University Press,
Princeton, NJ, 2008.
[5] J.M. Keynes, The General Theory of Employment, Interest and Money,
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[6] N. Kiyotaki, R. Wright, A contribution to the pure theory of money,
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Jr.,

Expectations and the neutrality of money,

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[8] N.G. Mankiw and R. Reis, Sticky information vs. sticky prices: A proposal to replace the new Keynesian Phillips curve, Quart.J.Econ. 100(2002), 529-539.
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[10] M. Otaki, A welfare economics foundation for the full-employment policy, Econ.Letters (2009), 1-3.
[11] R.W. Shephard, Cost and Production Functions (2nd edition),
Springer-Verlag, Berlin, 1981.

17

Figure 1
ydADy d = c(ρ∗ )y s + m

y∗

m

45◦
ys
0

18