SAMUELSON'
SMODELOFBUSI
NESSCYCLE
Pr
of.Samuel
son const
ruct
ed a mul
ti
pli
er-
accel
erat
ormodel
assumi
ngoneper
iodl
aganddi
ff
erentv
aluesf
ort
heMPC(
α)andt
he
accel
erat
or(
β)t
hatr
esul
tinchangesi
nthel
evelofi
ncomeper
tai
ning
t
ofi
vedi
ff
erentt
ypesoff
luct
uat
ions.
Thei
nter
act
ionoft
hemul
ti
pli
erandt
heaccel
erat
orhast
hemer
itofr
aisi
ng
nat
ionali
ncomeatamuchf
ast
err
atet
hanbyei
thert
hemul
ti
pli
erort
he
accel
erat
oral
one.I
tser
vesasausef
ult
oolnotonl
yforexpl
aini
ngbusi
ness
cy
clesbutal
soasagui
det
ost
abi
l
izat
ionpol
i
cy.Aspoi
ntedoutbyPr
of.
Kur
ihar
a,“
Iti
sinconj
unct
ionwi
tht
hemul
ti
pli
eranal
ysi
sbasedont
he
conceptofmar
ginalpr
opensi
tyt
oconsume(
bei
ngl
esst
hanone)t
hatt
he
accel
erat
ionpr
inci
pleser
vesasausef
ult
ool
ofbusi
nesscy
cleanal
ysi
sand
ahel
pfulgui
det
obusi
nesscy
clepol
i
cy.
”Themul
ti
pli
erandt
heaccel
erat
or
combi
nedt
oget
herpr
oducecy
cli
calf
luct
uat
ions.Thegr
eat
ert
hev
alueof
t
heaccel
erat
or(
β),t
hegr
eat
eri
sthechanceofanexpl
osi
vecy
cle.The
gr
eat
ert
hev
alueoft
hemul
ti
pli
er,t
hegr
eat
ert
hechanceofacy
clel
ess
pat
h.
TheSamuel
sonmodeli
s
Yt=Gt+Ct+I
t.
..
(1)
wher
eYti
snat
ionali
ncomeYatt
imetwhi
chi
sthesum of
, gov
ernmentexpendi
tur
eGt,consumpt
ionexpendi
tur
eCtandi
nduced
i
nvest
mentI
t.
Ct=αYt–1.
..
(2)
It=β(
Ct–Ct–1).
..
(3)
Subst
it
uti
ngequat
ion(
2)i
n(3)wehav
e,
It=β(
αYt
–1–αYt
–2)It=βαYt
-1–βαYt
–2.
..
(4)
Gt=1.
..
(5)
Subst
it
uti
ngequat
ions(
2),
(4)and(
5)i
n(1)wehav
e
Accor
dingt
oSamuel
son,“
Ifweknowt
henat
ionali
ncomef
ort
woper
iods,
t
henat
ional
incomef
ort
hef
oll
owi
ngper
iodcanbesi
mpl
yder
ivedbyt
aki
ng
awei
ght
edsum.Thewei
ght
sdepend,ofcour
se,upont
hev
alueschosen
f
or t
he mar
ginalpr
opensi
tyt
o consume and f
or t
he r
elat
ion (
i.
e
accel
erat
or)
”.Assumi
ngt
hev
alueoft
hemar
ginalpr
opensi
tyt
oconsume
t
obegr
eat
ert
hanzer
oandl
esst
hanone(
0<α0)
,andoft
heaccel
erat
or
gr
eat
ert
han zer
o(β > 0)
,Samuel
son expl
ains f
ivet
ypes ofcy
cli
cal
f
luct
uat
ionswhi
char
esummar
isedi
ntheTabl
e1.
SMODELOFBUSI
NESSCYCLE
Pr
of.Samuel
son const
ruct
ed a mul
ti
pli
er-
accel
erat
ormodel
assumi
ngoneper
iodl
aganddi
ff
erentv
aluesf
ort
heMPC(
α)andt
he
accel
erat
or(
β)t
hatr
esul
tinchangesi
nthel
evelofi
ncomeper
tai
ning
t
ofi
vedi
ff
erentt
ypesoff
luct
uat
ions.
Thei
nter
act
ionoft
hemul
ti
pli
erandt
heaccel
erat
orhast
hemer
itofr
aisi
ng
nat
ionali
ncomeatamuchf
ast
err
atet
hanbyei
thert
hemul
ti
pli
erort
he
accel
erat
oral
one.I
tser
vesasausef
ult
oolnotonl
yforexpl
aini
ngbusi
ness
cy
clesbutal
soasagui
det
ost
abi
l
izat
ionpol
i
cy.Aspoi
ntedoutbyPr
of.
Kur
ihar
a,“
Iti
sinconj
unct
ionwi
tht
hemul
ti
pli
eranal
ysi
sbasedont
he
conceptofmar
ginalpr
opensi
tyt
oconsume(
bei
ngl
esst
hanone)t
hatt
he
accel
erat
ionpr
inci
pleser
vesasausef
ult
ool
ofbusi
nesscy
cleanal
ysi
sand
ahel
pfulgui
det
obusi
nesscy
clepol
i
cy.
”Themul
ti
pli
erandt
heaccel
erat
or
combi
nedt
oget
herpr
oducecy
cli
calf
luct
uat
ions.Thegr
eat
ert
hev
alueof
t
heaccel
erat
or(
β),t
hegr
eat
eri
sthechanceofanexpl
osi
vecy
cle.The
gr
eat
ert
hev
alueoft
hemul
ti
pli
er,t
hegr
eat
ert
hechanceofacy
clel
ess
pat
h.
TheSamuel
sonmodeli
s
Yt=Gt+Ct+I
t.
..
(1)
wher
eYti
snat
ionali
ncomeYatt
imetwhi
chi
sthesum of
, gov
ernmentexpendi
tur
eGt,consumpt
ionexpendi
tur
eCtandi
nduced
i
nvest
mentI
t.
Ct=αYt–1.
..
(2)
It=β(
Ct–Ct–1).
..
(3)
Subst
it
uti
ngequat
ion(
2)i
n(3)wehav
e,
It=β(
αYt
–1–αYt
–2)It=βαYt
-1–βαYt
–2.
..
(4)
Gt=1.
..
(5)
Subst
it
uti
ngequat
ions(
2),
(4)and(
5)i
n(1)wehav
e
Accor
dingt
oSamuel
son,“
Ifweknowt
henat
ionali
ncomef
ort
woper
iods,
t
henat
ional
incomef
ort
hef
oll
owi
ngper
iodcanbesi
mpl
yder
ivedbyt
aki
ng
awei
ght
edsum.Thewei
ght
sdepend,ofcour
se,upont
hev
alueschosen
f
or t
he mar
ginalpr
opensi
tyt
o consume and f
or t
he r
elat
ion (
i.
e
accel
erat
or)
”.Assumi
ngt
hev
alueoft
hemar
ginalpr
opensi
tyt
oconsume
t
obegr
eat
ert
hanzer
oandl
esst
hanone(
0<α0)
,andoft
heaccel
erat
or
gr
eat
ert
han zer
o(β > 0)
,Samuel
son expl
ains f
ivet
ypes ofcy
cli
cal
f
luct
uat
ionswhi
char
esummar
isedi
ntheTabl
e1.
