Macroeconomics with Non-Perfect Competition
Author(s): Yew-Kwang Ng
Source: The Economic Journal, Vol. 90, No. 359 (Sep., 1980), pp. 598-610
Published by: Wiley on behalf of the Royal Economic Society
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The EconomicJournal, go (SeptemberI980), 598-6I0
Printedin GreatBritain
WITH NON-PERFECT
MACROECONOMICS
COMPETITION*
The microeconomic foundation of macroeconomics has received increasing
attention by economistsin recent years. While many interestingresultshave been
obtained, basic macroeconomicmodels have retained one of its most important
traditional features, the implicit or explicit assumption of perfect competition.
Firms are taken to equate the value of the marginal product of labour to the
(money) wage-rate instead of the more general marginal revenue product. In
this paper, I incorporate the microeconomicsof non-perfectlycompetitive firms
(imperfectly competitive or monopolistic, oligopoly is ignored) into a simple
macroeconomic model. This introduces a significant complication. Instead of
price, a single variable, we now have to consider the whole demand curve (at
least over the relevant range). Perhaps this explains why people continue to use
the very restrictiveassumptionof perfect competition.
The introductionof non-perfectcompetition revealsthe importanceof business
expectation (with respect to prices).This expectation is important as it affectsthe
movement in the demand curve and hence the movement in the marginal
revenue curve. Together with the shapes (or elasticities) of the marginal cost
curve and the labour supply curve, this determines whether an increase in
(nominal) aggregate demand (through money supply in this simple model or
through other means in a more complicated model) will increase real output or
the price level. If the elasticity of the factor supply curve is equal to the negative
of the elasticity of the marginal cost curve and if firms expect no response of
prices to aggregate demand, an increase in aggregate demand increases only
real output. In most other cases, it increasesonly the price level. This contrasting
result is obtained in a model where monetary changes can only have nominal
effectsunder the assumptionof perfect competition. The breakingof the classical
dichotomy (between the real and the monetary sectors)is achieved by the introduction of non-perfect competition, not by such factors as misinformation,lags,
etc. that may break the dichotomy in the short run. Moreover, we show that our
result satisfiesrational expectation. Nevertheless,the possibilityof real expansion
hinges on rather stringent conditions. Hence, before furtherstudies, our analysis
does not adequately justify an expansionary policy even in the presence of unemployment. However, it serves to warn against contractionary policies based
purely on demand management which may just reduce real output with no
effect on the price level.
Section I outlines the simple model with perfect competition. Section II
generalises it to accommodate non-perfect competition. Mathematically unsophisticatedreadersmay find this section easier to understand after reading the
geometrical illustration in Section III. Section IV discusses and illustrates the
resultin termsof the labour market. The realisationof expectation is discussedin
* I am grateful to Lachie McGregor for stimulating discussion and to John Flemming and an
associate editor for very helpful comments.
[ 598 ]
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[SEPT.
WITH
MACROECONOMICS
I980]
NON-PERFECT
COMPETITION
599
Section V for a slightly more general model. The concluding section remarks on
the relevance and significance of our analysis.
I. THE
TRADITIONAL
MODEL-PERFECT
COMPETITION
Consider the following simple model (closed economy, no government) containing
only the essential elements for our purpose
Y= F(N),
FN=
W/P,
WIP = *(N),
PY
kM,
(I)
(2)
(3)
(4)
where Y = real output, F = production function, N = employment, W = money
wage-rate, P = price level, ?b = inverse labour supply function, k = income
velocity of circulation (assumed constant), M = (nominal) money supply, and
a subscript denotes partial differentiation.
(2) specifies the equality of the physical labour product with the real wagerate under perfect competition. This (inverse) demand-for-labour function,
together with the (inverse) labour supply function (3), determines the equilibrium level of real wage-rate W/P and employment N. Through the production
function (i), this also determines real output Y. (The capital stock is assumed
given.) Hence the real variables of the system are completely determined by
(I)-(3),
independently of (4), which implies that changes in M must lead to
proportionate changes in P in this simple model. The independence of the real
sector from the monetary sector is the so-called classical dichotomy. This
dichotomy will be maintained even if we replace the classical demand for money
function (4) by a Keynesian one and introduce the interest rate and an expenditure function. The independence of (I)-(3) is unaffected. I use (4) partly for
simplicity and partly to show that our results are not due to the liquidity
preference and income expenditure analysis.
The classical dichotomy can of course be exorcised in the short run by the
introduction of some complications such as time lags, imperfect information,
labour supply as a function of money instead of real wages (which may itself be
a result of imperfect information, see the 'new microeconomics' literature),
non-equilibrium analysis, etc. Hence, to show that our non-traditional results
stem from the introduction of non-perfect competition instead of other complications, we shall retain the simple assumptions of perfect information, no time
lags, and use only comparative static analysis. Moreover, we shall show that our
results are consistent with rational expectation.
II.
A SIMPLE
GENERAL
NON-PERFECT
MODEL-INTRODUCING
COMPETITION
Let us consider a simple model which is nevertheless general in the sense that it
accommodates both perfect and non-perfect competition. The economy is taken
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to consist of a given n identical firms. (Alternatively, we may work with a single
representativefirm. The problem of entry and exit will be consideredelsewhere.)
Each firm is taken as small in the sense that it regardsfactor prices, aggregates,
and actions of other firmsas beyond its own control. The (perceived) demand for
the product of firm i, Qi, is taken as a function of its (nominal) price Pi, the
(expected) index of prices of other firms pi, and (nominal) money supply M.
Instead of M, we could let the (nominal) aggregate demand (PY) enter the
demand function. But from (4), we may define the unit of money such that k = I,
PY = M.
(4')
Hence, the two methods are really equivalent in our simple model. While firms
would like to know the actual prices of other firms before fixing their own prices,
they cannot do so simultaneously. Thus Pi must be taken as the expected or
conjectured price index. As a condition of equilibrium, we must however have
pi = pi= P (and hence dPi= dPi for comparative analysis). But the different
rolesof Pi and Pi must be distinguished.Using pi as the scaling factor (or usingthe
output of other firms as the numeraire), we have
Qi = h(Pi/Pi, M/Pi).
(5)
We also have the production function (ignoring external economies and intermediate production)
Qi = f(Ni),
n
=
1Qi nf(Ni) F(N),
y=
where N = nNi. We thus havefNi = F,,. We also retain the (inverse) labour
supply function (3) and the classical demand-for-moneyfunction (i').
Firms maximise PiQi- WNi taking Pi, M, W as given, yielding the following
first-ordercondition,1
I +y(
where
)-
(6)
y/( ) f/(N)/FN,
aQi pi
V?
--,pi *Qi
is the elasticity of demand, and we have dropped the superscripti as it applies
to all i.
Differentiation (with respect to M) of (6) gives
yNM
where
y NM-_dN
M
IdM'N'
nM
_
VM/(I
+y)
dy M
dM
y'
(7)
(yINy_FvN),
N
N
"
?rN
NNf,
Z>f
IIV
FN'
Since y depends on the arguments of (5), we have, at equilibrium when
pi = pi = p and dPi = dPi,
1 If we rewrite (6) as P(I + i/y) Fv = W, it can immediately be seen as the equality of marginal
revenue product to the wage-rate.
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1980]
rnM = rnM/P
60I
COMPETITION
NON-PERFECT
WITH
MACROECONOMICS
(8)
( Iy_PM),
where
a'
,qMIP=-
aM/P
M/P
Y
dP M
dM P
PM
Substituting (8) into (7), we have,
A
~
NM
==
(I _ YPM)I(I
_nMIP
yNM
+yq) (yVNY_
Differentiation of (i') gives, using the differentiation of
(g)
FNN)
(i'),
PM =IyNMyYN,
(Io)
where
YN
V
-
dP-M
FN/Y
NNIy)
P
PM=dM
Differentiation of (3) yields
+y PM
VWM = .yNyNM
(II)
It may be argued that, consistent with treating Pi in (5) as expected prices, P in
(3) should also be replaced by expected prices P. This would involve replacing
yPM
in (i I) by yPM, without affecting our argument below.
Differentiation of the sum of (5), i.e. Y = nh(Pi/Pi, M/P%),at pi
VNM
= nhI2(i
PM)/
,YN
=
pi,
gives
(12)
where h2 is the partial derivative of h with respect to its second argument.
The four equations (9)-(I 2) are the comparative static conditions for equilibrium of profit maximisation at the firm level, the money market, the labour
market and the product market. For equilibrium, we must also have yPM = yPM.
00,
Consider first the traditional model of perfect competition where yyikN > on, FvN < o. This implies that yNM = O (from (9)), yPM = yPM = I (from
(i o)), and yJYM = I (from (i i )). A change in money supply does not affect reai
variables (employment N and hence outpuit Y), but changes nominal prices
(P and W) proportionately.
Now consider the case of non-perfect competition when y > - oo. It can be
seen that
yNM = O yPM = VPM = yWM = I
still satisfy
(9)-(I2).
Even with
non-perfect competition, monetary changes may still only have purely nominal
effects. But if y N - yF.N N
o, it is possible to have NM > on yPM = yPM = o, and
wm
o as y'N > o. In other words, if the elasticity of the labour supply curve
is equal to the elasticity of the marginal product curve (in particular the
condition is met if both the labour supply curve is horizontal over the relevant
range, due to say unions' insistence on a real wage-rate, and the marginal cost
curve, and hence the marginal product curve, is also horizontal), an increase/
decrease in money supply may increase/decrease employment and output while
leaving prices unchanged.
This 'anti-traditional' result, while remarkable, must not be over-emphasised
in terms of the probability of its prevailing in the real economy, at least in our
comparative static analysis. Equation (io) may be rewritten as
yNM
=
(II-PM)
/yYN.
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602
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ECONOMIC
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[SEPTEMBER
As yPM = yPM is required for equilibrium, (i o) and (I 2) imply that yNM = o
unless nh2 = i. We can in fact show (Appendix I) that nh2 = I if the expectations
of firms are correct (which must be assumed for comparative static analysis).
However, with rational expectation, it can also be shown that VflM/P = o
(Appendix I). This implies, from (9), that yN- = o unless IN - yFNN = 0.
(Further remarks on the plausibility of this condition will be offered in the
concluding section.)1
FNN = o holds, the system becomes indeterminate. It all depends
When y'Nf
on the value of yPM, the expected price change (in elasticity form). For example,
with yPM = o, we have NM = I/yYN > O from (I2). Substitute this into (io),
we have yPM = o, satisfying the requirement yPM = yPM. And yWM = y?kN/yYN
from (i i). Equation (9), being of indeterminate form, is necessarily satisfied.
On the other hand, with yPM = I, we have yNM = o from (I2), yPM = I from
(io), yWM = I from ? I i), and the indeterminate (g) is of course also satisfied. In
fact, any value of yPM will satisfy (9)-(I 2) with the resulting yPM = yPM confirming the expectation and with the corresponding (different values of)
= o, the outcome depends entirely on
yNM and yWM. Thus, with y'N _-FNN
expectation and it becomes rational to expect whatever is expected to be
expected!
-
III.
THE
GEOMETRY
OF
THE
MICROECONOMICS
The microeconomics (at the firm level) for the above result may be illustrated
in very simple terms. Fig. I presents the case of perfect competition. Unless the
MC (marginal cost) curve shifts downward (say through a reduction in real
wages), the profit-maximising level of output can only increase if the price
increases (with increases in aggregate demand). But if prices increase generally,
the wage-rate and the MC of firms will also increase. On average, AC and MC
will move up by exactly the same proportion as the increase in prices, leaving
real output unchanged.
In the case of non-perfect competition, the demand curve is downward
sloping. In fact, we have a demand hyper-surface instead of a curve as quantity
demanded is a function of the price, other prices, and aggregate demand.
Nevertheless, for two-dimensional illustration, we shall work with the demand
curve but would have to shift the curve as aggregate demand and/or the price
index changes. In Fig. 2, let DObe the initial demand curve for the product of the
firm when nominal aggregate demand PY (or money supply M) and the price
index are at their respective initial values, normalised at MO = I, PO = i. From
(A i) in Appendix I, DOis the demand curve Q = ih(P). As M increases by x %,
the demand curve will shift. But how it shifts depends also on what happens to
P. If P is expected to increase by the same proportion as M, i.e. if yPM = I
(Expectation A), the demand curve will (be perceived to) move up vertically by
the same x % to DA. This can be seen from (A i) as the quantity demanded will
# o, from (s),
But from (io),
o?
(only for
an infinitesimal change, of course). However, since #q2M/P = o follows from correct expectations
(Appendix I), it is a natural assumption for a comparative static analysis.
1 If
PM
=
yM/P
0PM
= I and qN
y-FNN
= O implies that yNM = + c0 or qPM =
riN
Thus, #q7mMIP O implies that NM
O imply oqNM
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i.
I980]
MACROECONOMICS
WITH
COMPETITION
NON-PERFECT
603
remain unchanged if P increases by the same proportion as M and P. This also
follows from the fact that quantity demanded should be homogeneous of degree
zero in all nominal values such that, as all prices and nominal money supply (or
nominal aggregate demand) increase by the same proportion, the real quantity
demanded remains unchanged. On the other hand, if P is expected to be unchanged, i.e. yPM - o (Expectation B), the demand curve will move horizontally
rightward by x %to DB. This can be seen from (A I) and follows from the homogeneity of degree one in real aggregate demand, given prices. While DA and DB
are depicted as intersecting, the range to the right of the intersection is really
irrelevant as it can be shown that the elasticity of demand is less than unity in
this range.
c
/MCI
$1~~~~~~~~~~~~~~~0
//
,AC'
,,
s_/
pl
_,-
/
AC
p0
Qo=Q'
Q
Fig.
DA
Q
Fig. 2
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[SEPTEMBER
JOURNAL
ECONOMIC
PAl
PO= PB.
(Ca)A
PO=
MR__ __
QO=
_
D~~~~~~~~~~~~~D
__
QA~
(a)
_
~
__
_
Q_
_
_
MR0
AIRB
~~~~~~~QOQ
~~~~~~~~~Q'B(b)
PI
Mc,
D'
D
MR
(C)
Fig. 3
= o. In terms of the geometry here, this means
Consider the case of yffN _FNN
that the shift (if any) of the MC curve (due to any upward sloping labour supply
curve as employment decreases) is just balanced by the downward sloping MC
curve. For simplicity, consider a special case of this when VNN = FNN= =n
i.e. a horizontal labour supply curve and a horizontal MC curve. If Expectation
A prevails, the demand curve moves up vertically by x % to DA and the MR
(marginal revenue) curve also moves up vertically by x % to MRA as illustrated
in Fig. 3 (a). Moreover, as prices are expected to go up by x % and as labour
supply is a function of real wage-rates, the MC curve also moves up by x % to
MCA to intersect MRA at the same output level. The firm thus finds it profitmaximising to hold output unchanged and increase its price by x %. On the
other hand, if Expectation B prevails, the demand curve and the MR curve both
move rightward by x % as illustrated in Fig. 3 (b). If the MC curve is horizontal
over the relevant range and does not shift as output and employment changes, it
will intersect MRB at an output level x % higher, giving the profit-maximising
price unchanged, confirming the original Expectation B. Similarly, any other
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605
I
expectation will also be realised. Fig. 3(c) illustrated the case of yPM
However, if the condition jff_N - yFNN = o does not hold, the only expectation
that will be realised is Expectation A (assuming wage-rates respond proportionately to prices). The realisation of expectation is discussed in more
detail for a more general model in Section V.
I980]
WITH
MACROECONOMICS
NON-PERFECT
COMPETITION
WI'
(Pv)
\\
E
c
DN
No
N
Fig. 4
IV.
THE
LABOUR
MARKET
A favourable condition for an expansion in real output with no increase in prices
is a low value of yAN, the elasticity of the inverse labour supply curve. This is
more likely to be so in the presence of unemployment when ,12N may be zero.
But how can unemployment co-exist with equilibrium in the labour market?
This is no place to go into a detailed discussion of this question. It is sufficient
here to note that, if labour unions attempt to maintain real wage-rate, the labour
supply curve SN may have a horizontal section as illustrated in Fig. 4. In our
simple model of a homogeneous labour force, let us abstract from the problem
of structural or frictional unemployment. Then, if the demand for labour is DN
with employment NO, we have ED amount of excess unemployment and DL
amount of voluntary unemployment.
Now consider an increase in aggregate demand. Will it increase the level of
employment? In the traditional (perfect competition) analysis, the demand for
labour is determined by W/P = FN. Since marginal physical product FN is
determined by technological (shall we add institutional and psychological?)
conditions assumed unaffected by aggregate demand, an increase in aggregate
demand can only increase the demand for labour to the extent that P is increased
and W/P reduced. The demand-for-labour function DN stays unchanged and
employment can only increase if the real wage-rate is reduced. If the unions are
successful either through wage-indexation or bargaining in maintaining the real
wage-rate, the economy is caught at the point E with excess unemployment
which cannot be reduced by stimulating demand. In contrast, in our model of
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6o6
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ECONOMIC
[SEPTEMBER
JOURNAL
non-perfectcompetition,DNis determinedby W/P = giFN/Pwherel =_aPQ/Q3Q.
While FN is technologically determined, marginal revenue at and price P are
economically determined. A change in aggregate demand may affect both ,uand
P. Moreover, these effects need not necessarily be equi-proportional and will
vary according to the pattern of expectation. To examine this, differentiate
ItFNP at given N (and hence given Q) with respect to M;
dItFNIP FN ( dg
PtdM
dM
# dP
dM'
3)
where the diffexentiation is taken at given N. In the special case of perfect
competition, ,u = P and dlt = dP. The R.H.S. of (I3) thus equals zero. With
perfect competition, an increase in money supply cannot lift the demand-forlabour function.
With non-perfect competition, it can be shown (Appendix II) that, with
Expectation A (i.e. VPM= I), the R.H.S. of (I3) equals zero; with an (realisable)
expectation, yPM < I, the R.H.S. of (I3) is positive. In this latter case, the
demand-for-labourfunction is lifted, leading to an expansion in employment at
a given real wage-rate. Geometrically, with Expectation A, both the demand
curve and MR curve move up vertically by the same proportion; hence (at
given Q)
d,u/dM _.= dP/dM
P
A
,
d
do
or__
C
dM
'
dP
P dM'
making the R.H.S. of (I3) equal zero. In contrast, if the demand curve and the
MR curve move rightward by the same proportion, the MR curve would have
moved up by proportionatelymore than the demand curve at givenQ (assuming
that the second-ordercondition for profit maximisation is satisfied), leading to
an expansion in output. But a favourable expectation is not sufficient; if the
condition yrN - yFYfN = o is not satisfied, the expectation will be frustrated,
leading to furtheradjustment.We turn now to analyse the realisationof expectation in a more general model.
V.
THE
REALISATION
OF
EXPECTATION
The realisation of expectation is important since the results need not then be
temporary.We have already brieflyremarkedon this above. Let us now examine
it more formally for a more general model in which we have, instead of (3),
W = W(P, N).
(3')
This collapses into (3) if Wp = W/P, i.e. if the wage-rate responds proportionately to the price level.
Using the same method as the derivation of (9)-(12) above, we have, while
( IO) and (i 2) remain unchanged,
1NM
V
(I+y)(I-yWP)
(I?
VPM-(I
-PM)ylM/P
V)(yWN_-yFNN)
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I980]
MACROECONOMICS
WITH
vWM =
NON-PERFECT
vWNjNM
+WP
607
COMPETITION
PM
(I I )
where vP _= WpP/W and WHN= 4vN/ IV.It may be noted that (9') and (
collapse into (g) and (I I) when yfWP = I and yWIN =-1N
For the expectation to be realised, we need
(9') into (IO), and equating yPM and
for the realisation of expectation:
yPM
=
(YWN _ IFNN)
yPM,
/[YWN
PM =
II')
Thus, substituting
gPM.
we have the following as the condition
-YFNN
(I4)
+ (I _yjWP)yjYN].
If yWP = I (i.e. the money wage-rate responds to price changes by the same
proportion; the model above), the only expectation that can be realised is
yPM = I (i.e. Expectation A of a proportionate response of prices to money
FNN = o when any expectation
will be realised. If
supply) unless yWN_:
FNN
=o
but
the
that
can be realised is
I,
only expectation
yWP
/WN
to
B
of
no
of
P
If
IPMM).
Expectation A is held,
0(i.e. Expectation
response
it can be realised if and only if yHWP= I. If Expectation B is held, it can be
= o. In general, (I 4) must be satisfied for the
realised if and only if yWN -FNN
expectation to be realised.
If we have rational expectation, it is the one that can be realised that will be
held. Thus, substituting (I4) into (I2), we have
yNM
=
(I _ 9WP) /[yWN
-FINN?+
(I -WP)y
(I5)
YN].
From this, we again have the following results: (i) yNM = 0 if yWP = I,
N
FNN = ?
o; (ii) NMyYM = I (which implies yPM = o) if yWN
FWN FN
yWP + I; (iii) the system is indeterminate if yWNy
=
and
o
gFNN
"ZP = I, and
any expectation will be realised. It may also be added that, if yWP < I, and
N,
>P
WN
NN
mayOne
may, however, argue that, while yWP may be
FN > ) NM > O. One
less than unity in the short run, it is likely to equal unity in the long run and
hence yWP = I is a more natural assumption for a comparative static analysis.
-
VI.
CONCLUDING
REMARKS
Using a simple economic model where monetary changes (or other means of
stimulating demand in a more complicated model) have only nominal effects
with perfect competition, we have shown that the introduction of non-perfect
competition reveals a possible case of purely real expansion/contraction. It is
tempting, but dangerous, to proceed to advocate expansionary policies even in
the presence of unemployment since the probability of this case being realised is
very low. If we concede that wage-rates respond proportionately to prices, the
F N = 0
possibility of real effects hinges on a knife-edge condition of yVN_
which, mathematically speaking, is of probability of measure zero. In plain
terms, the condition requires that the elasticity of the labour supply curve must
be precisely equal to that of the marginal product curve (or the negative of the
elasticity of the marginal cost curve). (This may not be regarded as impossible
by those who believe in horizontal MC and labour supply curves.) The rationale
of this condition can be seen in Fig. 3 (b). If the elasticity of the labour supply
curve is less than the negative of the elasticity of the MC curve (MC shifts upward
ECS
2I
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90
6o8
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[SEPTEMBER
by a smaller extent than it is downward sloping), profit maximisation actually
calls for a reduction in P if Expectation B is held, making the expectation 'more'
than realised. Somewhat paradoxically, the analysis above shows that, even in
this extremely favourable case, the only expectation that can be realised is
Expectation A (assuming yfP = I). The objective condition of yIf/N - yFNN < 0
seems to justify an expectation more favourable than Expectation B (i.e.
yPM < o). But if this more favourable expectation is held, prices will fall even
further (as demand becomes more elastic), still 'out-performing' the expectation.
On the other hand, if Expectation A is held, we have shown that it will be
realised irrespective of the value of yV'N -_ FNN. Nevertheless, it would take an
extremely sophisticated businessman to understand this 'paradox' and act
< o prevails
accordingly (i.e. reverting to Expectation A). Hence, if qO/N-yFNN
that we
is
likely
is
held
initially,
it
and Expectation B (or a more favourable one)
will have cumulative price reduction (or, in an inflationary context, reduction
in the rate of inflation) and real expansion until the condition no longer applies.
This, however, really goes beyond the confines of comparative statics and an
explicit dynamic analysis is called for. It suffices to note here that the condition
< o is not mathematically of probability of measure zero, though,
ipVN _qFNN
economically, we seem more likely to have yfNv -qFYV approximately equal to
zero than to have it strictly negative. (The latter is, however, not impossible in
the presence of union power and economies of scale.)
Even if yV'N -#qFNN = o holds, we need not necessarily have real expansion
(assuming yWP = i). In addition, we need an expectation more favourable than
Expectation A (i.e. yPM < i). For the expansion to be purely real, we need
Expectation B. How likely is it for a favourable expectation to prevail when it is
rational to expect whatever is expected to be expected? This seems to depend
largely on the psychology and custom of businessmen partly shaped by past
experiences. What may be of help here is the widely claimed business practice of
not adjusting prices unless justified by cost changes. If this is true, Expectation B
is more likely to occur.
For an expansion, the condition of 'N- qFNN < o is quite unlikely to hold if
the economy is not far from full employment and full capacity, or if some
important bottlenecks exist. Nevertheless, it is more likely to hold for a contraction. For example, if the labour supply curve is horizontal over the relevant
range and firms are typically situated at the point H in Fig. 5 (or if the labour
supply curve is moderately upward sloping and the MC curve is the broken one),
the condition qtN-_ qFNN = o then applies for a contraction but not for an
expansion. (The question of continuous partial derivatives is dismissed as purely
technical. Even assuming that the MC curve is smooth, what we are interested
in is more than infinitesimal changes.) An expansionary policy will then be
purely inflationary (ignoring any transitory effects). But if a contractionary
policy is used to reduce the price level (or, in a dynamic context, the rate of
inflation), the result will be a purely real contraction with no effect on prices if
Expectation B is held (or if businessmen do not adjust prices unless costs change).
This may partly explain why contractionary policies in recent years have little
effects in slowing inflation in some countries. A contractionary policy may just
-
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All use subject to JSTOR Terms and Conditions
I980]
MACROECONOMICS
WITH
NON-PERFECT
609
COMPETITION
reduce real output with no effect on prices unless simultaneous attempts have
succeeded in, say, improving the labour market and/or creating a more favourable expectation. (For a contraction, it is Expectation A that is favourable and
Expectation B unfavourable.)
$
MC
H
Q
Fig. 5
Our analysis alone is insufficient to justify an expansionary policy though it
does seem to sound a warning as to contractionary policies based purely on
demand management. For both expansion and contraction, our analysis shows
that expectation, cost and labour supply conditions are important in determining the outcome. Further studies on these factors as well as the generalisation
of our simple model are needed before more positive policy implications can be
drawn.
MonashUniversity
YEW-KWANG
NG
Date of receiptqffinaltypescript:
February1980
I
APPENDIX
Since we have n identical firms (or if we work with an average firm), the demand
function (5) in the text must be homogeneous of degree one in its second argument, given its first. We thus have, dropping superscripts,
Q
I)
ph(p,
_/ pi(P/P).
(A I)
Hence we have,
nh2= n
Since we must have P
nh
nQPM= YPIM.
P, we have, from (4'),
nh2=
I.
(A2)
21-2
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6io
THE
We also have, from (A
Q P
= h'(P/P)/h(P/P),
M/P
vnMIP -a~y
(A3)
II
APPENDIX
I),
I980]
I),
v -
From (A
[SEPTEMBER
JOURNAL
ECONOMIC
we may write the inverse demand function as
(A 4)
P kPg (QP/M),
where g is the inverse of h. And
aQ
(A5)
(
Whence, at given Q,
d-
dM
where
/1 Qzt\ dP Qa(
VP PEaQ}dM 2aQ
al
2p2
(A6)
+ Qp2Q
aQM
is the slope of the marginal revenue curve.
Substitute (A 6) into (I3) in the text, we have, at dP
where
dP,
M
dIuFN/
FN/P .dM/ =N Q(PPM-I)
(A 7)
aQ tu Q
is the elasticity of the MR curve. Thus, with Expectation A (i.e. yqPM = I), the
R.H.S. of (A 7) equals zero; an increase in M does not shift the demand-forlabour function. With yPM < I, the R.H.S. of (A 7) is positive. From the analysis
in the text, we know that yPM < I can only be realised if y1fN -qFNN = o. Thus,
even with a horizontal labour supply curve, we need a horizontal MC curve.
(With an upward sloping labour supply curve, we need a downward sloping MC
curve.) The second-order condition for profit maximisation thus requires a
downward
sloping MR curve, i.e. y/uQ < O.
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