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KALDOR'
SMODELOFTHETRADECYCLE

Ni
chol
asKal
dorbui
l
tamodeloft
het
r
adecy
cl
ebasedont
heKey
nesi
an
t
er
mi
nol
ogyofsav
i
ngandi
nv
est
ment

...
I
nf
act
,i
ti
st
hedi
f
f
er
encebet
ween
ex
ant
esav
i
ngandi
nv
est
mentt
hatl
eadst
oacy
cl
e
...


TakeFi
gur
e(
A)and(
B)wher
eIandSar
eequal
att
heequi
l
i
br
i
um l
ev
el
ofi
ncome
Y0
...
I
nPanel(
A)oft
he
f
i
gur
ewher
eI
>St
her
ei
sanunst
abl
eequi
l
i
br
i
um posi
t
i
onbey
ondY0 because
suchasi
t
uat
i
onwi
l
ll
eadt
ol
i
mi
t
l
essexpansi
on,t
of
ul
lempl
oy
mentandhy
per
i
nf
l
at
i
on
...

Kal
dordi
scar
dsl
i
nearsav
i
ngandi
nv
est
mentf
unct
i
onsbecauset
heyf
ai
l
t
o
pr
oduceacy
cl
e
...

Anonl
i
neari
nv
est
mentf
unct
i
onIi
sshowni
nFi
gur
e
...
I
tmeanst
hat
t
her
ei
sexcesscapaci
t
yatal
owl
ev
elofi
ncomeandt
heneti
nv
est
menti
szer
o
...
I
nt
heopposi
t
ecaseofahi
ghl
ev
elofi
ncomewhent
he
economymov
esi
nt
ot
hecont
r
act
i
onphase,t
heIcur
v
ei
sagai
nf
l
atandt
henet
i
nv
est
menti
ssmal
l“
becauser
i
si
ngcost
sofconst
r
uct
i
on,i
ncr
easi
ngcost
sand
i
ncr
easi
ngdi
f
f
i
cul
t
yofbor
r
owi
ngwi
l
ldi
ssuadeent
r
epr
eneur
sf
r
om expandi
ng
st
i
l
lf
ast
er

...
I
tmeanst
hatt
he
ex
i
st
i
ngcapi
t
alst
ockandt
hecapaci
t
yar
emor
et
hant
hecur
r
entout
put

...
Thusi
ncomef
al
l
sandt
hecumul
at
i
v
e
ef
f
ecti
st
hatt
heeconomymov
esi
nt
ot
hecont
r
act
i
onphase
...
Atv
er
yl
owl
ev
el
s
ofi
ncome,sav
i
ngi
smuchr
educedandmayev
enbenegat
i
v
e
...
Atnor
mall
ev
el
sofi
ncome,sav
i
ngwi
l
l
i
ncr
easeatasmal
l
err
at
e
...
But
atv
er
yhi
ghi
ncomel
ev
el
s,sav
i
ngwi
l
lbeabsol
ut
el
yl
ar
geandpeopl
ewi
l
lsav
ea
l
ar
gepr
opor
t
i
onoft
hei
ri
ncome
...
Thef
i
gur
eshowsmul
t
i
pl
eequi
l
i
br
i
aatposi
t
i
onsA,
BandC
...

Bet
weenposi
t
i
onsCandBandbel
owposi
t
i
onA,
Ii
sgr
eat
ert
hanS
...
Bet
weenposi
t
i
onsAandCandabov
eBposi
t
i
on,
Si
s
gr
eat
ert
hanI

...


3|
M ACRO ECONOM ICS NOTES

ButAandBar
est
abl
eposi
t
i
onsonl
yi
nt
heshor
tr
un
...
Fort
hi
s,
Kal
dor
i
nt
r
oducest
hecapi
t
alst
ockasanot
herv
ar
i
abl
et
hataf
f
ect
st
her
el
at
i
onshi
p
bet
ween sav
i
ng and i
nv
est
ment

...

Ther
el
at
i
onshi
pMPI>MPSshowst
hei
nst
abi
l
i
t
yoft
heeconomywhi
chwi
l
l
mov
ei
tei
t
hert
owar
d expansi
on orcont
r
act
i
on
...
Theyar
et
hepoi
nt
satwhi
ch
4|
M ACRO ECONOM ICS NOTES

t
heeconomyal
t
er
si
t
sdi
r
ect
i
onei
t
hert
owar
dexpansi
onorcont
r
act
i
on
...
I
ti
sonl
ywhenpoi
nt
sCandBcomecl
oser
,t
he
ex
pansi
onphaseoft
hecy
cl
est
ar
t
s
...
Ont
hecont
r
ar
y
,
whenCandAcomecl
osercont
r
act
i
onst
ar
t
s
...


Expansi
onPhase
...
Butt
hi
si
st
hepoi
ntofunst
abl
eequi
l
i
br
i
um
...
Ast
he
r
at
eofi
nv
esmenti
shi
gh,t
heeconomy
’
scapi
t
alst
ocki
ncr
easesatar
api
dr
at
e
...
Thust
hesav
i
ngcur
v
e
shi
f
t
supwar
d
...
Thi
s
5|
M ACRO ECONOM ICS NOTES

pr
ocessoft
hedownwar
dshi
f
t
i
ngoft
heIcur
v
eandupwar
dshi
f
t
i
ngoft
heS
cur
v
econt
i
nuest
i
l
lt
het
wocur
v
esar
et
angent
i
alandpoi
nt
sCandBcoi
nci
de,
as
showni
nf
i
gur
est
age3
...
Sot
hi
si
san
unst
abl
e equi
l
i
br
i
um posi
t
i
on i
nt
he downwar
d di
r
ect
i
on
...


Cont
r
act
i
onPhase
...



...


I
ti
st
hepoi
ntofshor
t
r
unst
abl
eequi
l
i
br
i
um butatav
er
yl
owi
ncomel
ev
el

...
Si
mul
t
aneousl
y
,
sav
i
ngf
al
l
swhi
chshi
f
t
st
hesav
i
ngcur
v
edownwar
d
...
Thi
spr
ocesswi
l
lcont
i
nuegr
adual
l
yt
i
l
lIandScur
v
esar
c
t
angent
i
alandposi
t
i
onsAandCcoi
nci
de,asi
nst
age6f
i
gur
e
...
Thi
s
6|
M ACRO ECONOM ICS NOTES

wi
l
ll
eadt
oanexpansi
onar
ypr
ocesst
i
l
lt
heeconomyr
eachest
hehi
gherl
ev
elof
i
ncomeY2 atpoi
ntB
...
ThusKal
dor
’
s
cy
cl
i
cal
pr
ocessi
ssel
fgener
at
i
ng
...
“
Aboom l
ef
tt
oi
t
sel
f
,i
scer
t
ai
nt
ocomet
o
anend;
butt
hedepr
essi
onmi
ghtgeti
nt
oaposi
t
i
onofst
at
i
onar
i
ness,
andr
emai
n
t
her
eunt
i
l
ext
er
nal
changes(
t
hedi
scov
er
yofnewi
nv
ent
i
onsoroft
heopeni
ngup
ofnewmar
ket
s)comet
ot
her
escue
...

M Goodwi
npr
esent
ednonl
i
nearmodeloft
r
adecy
cl
esi
nanar
t
i
cl
eThe
non-Li
nearAccel
er
at
orandPer
si
st
enceofBusi
nessCy
cl
esi
n1951
...
Goodwi
npr
esent
sanonl
i
nearmodeloft
r
adecy
cl
eas
agai
nstHi
cks'
l
i
nearmodel

...

 Neti
nv
est
ment(
I
)i
sequalt
ot
her
at
eofchangei
ncapi
t
alst
ock
whi
chi
st
her
esul
tofadj
ust
mentbet
weenact
ualcapi
t
al
,K and
̅
̅
desi
r
edcapi
t
alK ,
andK =βY+αwher
eβi
st
heaccel
er
at
or

...

 Neti
nv
est
mentchangesduet
oachangei
nout
putwhi
chi
nt
ur
n,
̅
changest
hel
ev
elofdesi
r
edcapi
t
alK
...

Goodwi
nshowst
hr
eepossi
bi
l
i
t
i
esf
orneti
nv
est
ment:
̅
 When K >K,
t
her
ewi
l
lbei
ncr
easei
nt
her
at
eofneti
nv
est
mentwhi
ch
wi
l
lshi
f
tt
he economyt
of
ul
lcapaci
t
yout
putf
orcapi
t
algoods
i
ndust
r
i
es
...

e
...

̅
 WhenK>K ,
t
headj
ust
mentt
akespl
acewi
t
ht
hescr
appager
at
e,

...
Theset
aket
hesy
st
em al
onganequi
l
i
br
i
um pat
h
...
TheHi
cksi
anpat
hr
el
at
est
oast
eady
i
ncr
easei
naut
onomousi
nv
est
mentwhi
l
e`
Goodwi
n'
spat
hr
el
at
est
oar
i
sei
n
desi
r
edcapi
t
alr
esul
t
i
ngf
r
om acont
i
nuoust
echni
calchange
...

̅
TakeK >K,t
he desi
r
ed capi
t
alst
ock bei
ng mor
et
han t
he act
ualcapi
t
al
,
i
nv
est
menti
ncr
easesandt
hepr
opel
l
i
ngf
or
cesofmul
t
i
pl
i
erandaccel
er
at
orwi
l
l
8|
M ACRO ECONOM ICS NOTES

pusht
hesy
st
em i
nt
heupwar
ddi
r
ect
i
on
...
Ast
heaccel
er
at
orofGoodwi
n'
smodeli
snonl
i
near
,t
he
i
ncr
easei
nneti
nv
est
menti
snotr
el
at
edt
ot
hei
ncr
easei
nout
putbutt
ot
he
̅
di
f
f
er
encebet
weent
heact
ual
capi
t
al
st
ock(
K)andt
hedesi
r
edcapi
t
al
st
ock(K )

...
Thi
si
nv
est
ment
r
el
at
i
onshi
pbei
ngcont
i
nuous,i
nv
est
menti
si
mmedi
at
el
ypushedt
ot
heex
t
r
eme
̅
̅
posi
t
i
on
...

̅
Oncet
hedesi
r
edcapi
t
alK exceedst
heact
ualcapi
t
alst
ockK,
t
hedesi
r
ed
capi
t
al
wi
l
l
beequal
t
ot
hescr
appageorr
epl
acementr
at
eK2
...
Thust
he
̅
cont
r
act
i
onpat
hoft
hesy
st
em st
ar
t
s
...
Si
mul
t
aneousl
y
,t
he
desi
r
edcapi
t
alcont
i
nuest
or
i
sebyt
het
echnol
ogi
calgr
owt
hf
act
or

...

̅
Whent
heeconomyr
eachest
hel
owert
ur
ni
ngpoi
ntofK=K ,t
hel
ev
elof
̅
desi
r
edcapi
t
alK i
st
ober
ai
sed
...
WhenK >K,t
heexpansi
onagai
nst
ar
t
s
...
I
nf
act
,f
astt
echni
calpr
ogr
esswi
l
lexpandt
heeconomysoon
...
Rat
her
,i
tj
umpsf
r
om t
hesel
ev
el
s
...
I
ft
hegr
owt
hf
act
ordoesnotexi
sti
n
t
echnol
ogi
calchange,t
her
ewi
l
lbenoaut
onomousi
nv
est
menti
nt
hecapi
t
al
st
ock
...
Becausei
tt
akesmor
et
i
mef
orcapi
t
alt
o
depr
eci
at
et
hani
ncapi
t
alf
or
mat
i
on
...


̅
I
nt
hebegi
nni
ngoft
heexpansi
onphase,i
ncr
easest
oOAl
ev
el
K andK
̅
̅
al
sor
i
sesandequal
si
t

...
Ther
e bei
ng no
̅
t
echnol
ogi
cal
changei
nt
hegr
owt
hf
act
or
,
i
tt
akesmor
et
i
mef
orKt
oequalK
...

Whent
hedownswi
ngst
ar
t
s,t
her
ebei
ngnogr
owt
hf
act
ort
hecont
r
act
i
onphase
becomesshor
t
er

...
Thesear
eshownasupperandl
owerdot
t
ed
l
i
nesi
nt
hef
ol
l
owi
ngFi
gur
e

I
nt
hef
i
gur
eaal
i
neshowst
het
echnol
ogi
calgr
owt
hf
act
orwhi
chi
ssi
mi
l
ar
̅
̅
t
ot
heHi
cksi
anEEl
i
newher
eK=K =a
...
Pr
epr
esent
speaksandTast
r
oughswher
eK=
̅
r
act
i
onpat
hsPTbecomeshor
t
ert
hant
heexpansi
onpat
hs,
TP
...
Thecont

Cr
i
t
i
ci
sms
Thef
ol
l
owi
ngar
et
heweaknessesofGoodwi
n'
smodel

...
TheGoodwi
nmodel
i
sunr
eal
i
st
i
cont
wocount
s
...
Second,
t
hedesi
r
edst
ockofcapi
t
al
becomesconst
antatt
hepeak
 Empi
r
i
cal
l
yWr
ong
...
Thi
si
s empi
r
i
cal
l
y wr
ong because bot
hr
ecessi
on and
r
ecov
er
yar
esl
ow pr
ocesses
...


Concl
usi
on
...
Al
l
en,"
Theadv
ant
ageof
Goodwi
n'
smodeli
st
hatt
henonl
i
nearel
ementi
sbui
l
ti
n;
t
her
esul
t
i
ngosci
l
l
at
i
on
mai
nt
ai
nsi
t
sel
fwi
t
houtanydependenceonout
si
def
act
or
soronpar
t
i
cul
ari
ni
t
i
al
(
orhi
st
or
i
cal
)condi
t
i
ons
...
ButGoodwi
n'
s
model
t
r
acest
het
i
mepat
hofar
eal
i
st
i
ccy
cl
e
...
ButGoodwi
n'
smodel
i
st
hr
oughoutnonl
i
near

...
Accor
di
ng t
o Goodwi
n,gr
owt
h
depends on t
echnol
ogi
calchange whi
ch cont
i
nuousl
yi
ncr
eases t
he
pr
oduct
i
v
ecapaci
t
yoft
heeconomy

...
ButGoodwi
n'
sgr
owt
hpat
haai
sbasedont
he
̅
i
ncr
ease i
n desi
r
ed capi
t
alK whi
ch i
s t
he r
esul
t of cont
i
nuous
t
echnol
ogi
cal
changes

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