Yannacopoulos, Nicos A.
A icle
The Posi i ely Sloped IS Cu e and he Balance o
Paymen s: An Ex ension o Cebula's Model
K edi und Kapi al
P o ided in Coope a ion wi h:
Duncke & Humblo , Be lin
Sugges ed Ci a ion: Yannacopoulos, Nicos A. (1982) : The Posi i ely Sloped IS Cu e and he Balance
o Paymen s: An Ex ension o Cebula's Model, K edi und Kapi al, ISSN 0023-4591, Duncke &
Humblo , Be lin, Vol. 15, Iss. 2, pp. 275-279,
h ps://doi.o g/10.3790/ccm.15.2.275
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/292928
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The Posi i ely Sloped IS Cu e and he Balance
o Paymen s: An Ex ension o Cebula's Model
By Nicos A. Yannacopoulos, Pi aeus
I. In oduc ion
In his pape en i led "The Upwa d Sloping IS Cu e and he Con ol
o Income and he Balance o Paymen s" Ba ows (1974) in es iga ed,
among o he s, he e ec s o mone a y and iscal policy on he balance
o paymen s. He assumed ( ollowing Silbe (1971)), ha he posi i ely
sloped IS cu e is ob ained i all he p opensi ies o spend ou o income
sum o mo e han uni y. Howe e , in ano he con ibu ion, Cebula
(1976) e ained he s anda d assump ion ha he p opensi ies o spend
ou o income sum o less han uni y, bu ollowing he sugges ions by
Ya ow (1975) and Webe (1970) he assumed ha consump ion and
in es men a e inc easing unc ions o he a e o in e es . These as-
sump ions a e also consis en wi h a posi i ely sloped IS cu e. The
policy implica ions o Cebula1 s model in a closed economy ha e been
in es iga ed by Cebula himsel (Cebula 1976), and Ta las (1980). The
pu pose o his pape is o ex end he analysis, wi hin he amewo k
o Cebula's model, o include he e ec s o mone a y and iscal policy
on he balance o paymen s, unde a ixed exchange a e egime.
II. Cebula's Model and i s Ex ension
Following Ba ows (1974) we can w i e a model o an open economy,
he equilib ium condi ions o which a e:
(1) Y = C0 + C (Y, i) + I0 + I (Y, i) + B (Y) + G (commodi y ma ke )
(2) L0 + L (Y, i) = M0 + K (i) (money ma ke )
(3) F = B (Y) + K (i) (balance o paymen s)
The no a ion is s anda d:
Y = income, I = in es men , C = consump ion, i = he a e o in-
e es , L = he demand o money, Mo = he supply o money, G = go -
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276 Nicos A. Yannacopoulos
e nmen spending, B = he ne balance o ade, K = he ne capi al
in low, and F = he balance o paymen s unc ion. Co, lo, Lo a e le els
o consump ion, in es men and demand o money, espec i ely,
which do no depend on changes in income o he a e o in e es . Di -
e en ia ing equa ions (1), (2) and (3) gi e:
(4) dY = dCo + CydY + C{ di + dl0 +IydY + l{ di + BydY + dG
(5) dL0 + LydY + L{ di = dM0 + di
(6) dF = By dY + K di
whe e Cy is he ma ginal p opensi y o consume ou o income ly he
ma ginal p opensi y o in es ou o income, Q and Ii he esponse o C
and I o a change in he a e o in e es , Li he esponse in he demand
o money o a change in he a e o in e es , Ly he esponse in he
demand o money o a change in income, Ki he esponse o ne capi al
low om ab oad o a change in he a e o in e es and By he esponse
o he balance o ade o a change in income.
The ollowing es ic ions a e imposed on he sys em:
1 > Cy > 0 , 1 > Iy > 0 , Ly> 0 , L < 0 , K{ > 0 , By <0
Cebula (1976), howe e , assumes ha in e es esponsi eness o bo h
consump ion and in es men a e posi i e (i.e. Ci > 0, h > 0) and he
p opensi ies o spend ou o income sum o less han uni y (i.e.
Cy + Iy<C 1) so ha he slope o he IS cu e:
di 1
—
Cy
—
ly
—
By
(7) =
—
> 0
W dY Ci + Ii
This is consis en wi h he condi ion o s abili y in Cebula1 s model:
-U,
(8) - Cy~ ly - B?J
Ci + Ii
>
(Li
- Ki)
which says ha he sys em is s able i he slope o he LM cu e ( he
igh hand e m) is less han he slope o he IS cu e ( he le hand
e m).
The equa ions (4), (5), and (6) can be sol ed o he h ee endogeneous
a iables dY, di and dF. Ba ows (1974, p. 957) gi es he solu ion o dF
(which in e es s us he e), om which he de i es he ollowing policy
mul iplie s (Ba ows, 1974 p. 958 and p. 960):
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Posi i ely Sloped IS Cu e and he Balance o Paymen s 277
(9)
(10)
êF = - {(1 ~ Cy - ly -
By)
Kj +
By (Ci
+ Ij)}
ÏÏM0 - {(1 -Cy-Iy- By) (Li - Ki) +
('Ci
+ I{) Ly}
&F
ô
G
Ly Ki
—
By (Li Kù
- {(1 -Cy-Iy- By) (Li - Ki) + (Ci + li) Ly}
I can be easily shown ha , unde Cebula1 s assump ions and gi en he
condi ion (8), he denomina o in he mul iplie s (9) and (10) is posi i e.
Whe he he ne ou come o an inc ease in money supply (o he go -
e nmen expendi u e) on he balance o paymen s is un a ou able
/ &F / #F &F
Um^ < < 0 ) o a ou able > 0, > 0 j will de-
pend on he nume a o o he mul iplie s (9) and (10).
#
F
The condi ion o
(11)
o
(12)
#M0
<0is:
(1 -Cy-Iy- By) > By (Q +
/¿)
(j -Cy-Iy-
ci + h
By) > Bn,
K{
This means ha a de ici in he balance o paymen s a e a mone a y
expansion occu s i he slope o he IS cu e ( he le hand e m o (12))
is g ea e han he slope o he FF' cu e ( he igh hand e m o (12)),
i.e. he cu e exp essing he condi ions o equilib ium in he o eign
sec o .1
êF >0 is:
And he condi ion o ^M^
(13) (1 -Cy-Iy-
By)
K{ < By (Q + Ij)
o
(14)
ly ~ BJJ
Ci + h < Ki
Which says ha he slope o he FF' cu e is g ea e han he slope
o he IS cu e.
These condi ions a e no he same wi h hose de i ed by Ba ows
(1974) o he Silbe -Ba ows model. To be mo e p ecise he condi ion
1 The FF' cu e is he locus o pai s o i and Y which p oduce balance o
paymen s equilib ium. I s slope is ob ained by di e en ia ing equa ion (3).
FF' cu e is he same wi h Ba ow's HH cu e (Ba ows, 1974, p. 958).
19 K edi und Kapi al 2/1982
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DOI h ps://doi.o g/10.3790/ccm.15.2.275 | Gene a ed on 2023-01-16 12:47:44
278 Nicos A. Yannacopoulos
o a de ici in he balance o paymen s a e a mone a y expansion in
Cebula1s model in he same wi h he condi ion o a su plus in he
Silbe -Ba ows model; and he condi ion o a su plus in he balance
o paymen s a e a mone a y expansion in Cebula's model is he same
wi h he condi ion o a de ici in he Silbe -Ba ows model.
The condi ion o
-
êF
ê G
(15)
<0 is:
Ly Ki
<
By (Lj — K-i)
o
(16)
Li — Ki
< Bu
Ki
i.e. a de ici in he balance o paymen s occu s, ollowing an expansion
in he go e nmen expendi u e when he slope o he LM cu e is less
han he slope o he FF' cu e. And i is easily e i ied ha a su plus
in he balance o paymen s occu s when he slope o he LM cu e is
g ea e han he slope o he FF cu e. These condi ions a e he same
wi h hose de i ed by Ba ows (1974).
III. Conclusions
I u ns ou ha he di e en assump ions on which Cebula's and
Silbe 1 s models a e based a ec only he condi ions unde which an ex-
pansiona y mone a y policy a ec s he balance o paymen s. The con-
di ions o he e ec s o he iscal policy emain he same in bo h
models.
Re e ences
Paul Ba ows (1974): "The upwa d sloping IS cu e and he con ol o
income and he balance o paymen s". The Jou nal o Finance. — Richa d J.
Cebula (1976): "A b ie no e on economic policy e ec i eness" Sou he n
Economic Jou nal. —
William
L. Silbe (1971): "Mone a y policy e ec i eness:
he case o a posi i ely sloped IS cu e". The Jou nal o Finance. — Geo ge
Ta las (1980): "Economic policy e ec i eness in Hicksian analysis: an ex-
ension" K edi und Kapi al. — Wa en Webe (1970): "The e ec s o in e es
a es on agg ega e consump ion" Ame ican Economic Re iew. — Geo ge
Ya ow (1975): "G ow h maximisa ion and he i m's in es men unc ion"
Sou he n Economic Jou nal.
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Posi i ely Sloped IS Cu e and he Balance o Paymen s 279
Zusammen assung
Posi i e lau ende IS-Ku en und die Zahlungsbilanz:
eine E wei e ung des Cebulaschen Modells
Diese Bei ag be aß sich mi den bei es en Wechselku sen im Rahmen
des Cebulasehen Modells au e enden Auswi kungen de Geld- und Finanz-
poli ik au die Zahlungsbilanz und e gleich sie mi den on Ba ows e -
hal enen E gebnisse ü das Modell on Silbe -Ba ows.
Es wi d es ges ell , daß die un e schiedlichen Annahmen des Cebula sehen
und des Silbe -Ba o uschen Modells lediglich die Bedingungen beein lussen,
un e denen eine expansionis ische Geldpoli ik eine Wi kung au die Zah-
lungsbilanz ausüb . In beiden Modellen bleiben die Bedingungen ü eine
Beein lussung du ch die Finanzpoli ik gleich.
Summa y
The Posi i ely Sloped IS-Cu e and he Balance o Paymen s:
An Ex ension o Cebula's Model
This pape deals wi h he e ec s o mone a y and iscal policy on he
balance o paymen s wi hin he amewo k o Cebula's model, unde a ixed
exchange a e egime, and compa es hem wi h he esul s ob ained by
Ba ows o he Silbe -Ba ows model.
I is ound ha he di e en assump ions on which Cebula's and Silbe -
Ba ows model a e based a ec only he condi ions unde which an ex-
pansiona y mone a y policy a ec s he balance o paymen s. The condi ions
o he e ec s o he iscal policy emain he same in bo h models.
Résumé
Les cou bes posi i es In es issemen -Epa gne e la balance
des paiemen s: une ex ension du modèle de Cebula
L'a icle s'in é esse dans un égime de aux de change ixes e dans le
con ex e du modèle de Cebula aux e e s de la poli ique moné ai e e
inanciè e su la balance des paiemen s e les compa e aux ésul s ob enus
pa Ba ows su le modèle de Silbe -Ba ows.
L'au eu é abli que les di e ses hypo hèses des modèles de Cebula e de
Silbe -Ba ows n'in luen que su les condi ions dans lesquelles une poli ique
moné ai e expansionnis e exe ce une ac ion su la balance des paiemen s.
Dans les deux modèles, les condi ions d'in e en ion de la poli ique inanciè e
demeu en iden iques.
19*
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DOI h ps://doi.o g/10.3790/ccm.15.2.275 | Gene a ed on 2023-01-16 12:47:44