Notesale: Turn your study into money

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SAMUELSON'
SMODELOFBUSI
NESSCYCLE

Pr
of

...

Thei
nt
er
act
i
onoft
hemul
t
i
pl
i
erandt
heaccel
er
at
orhast
hemer
i
tofr
ai
si
ng
nat
i
onali
ncomeatamuchf
ast
err
at
et
hanbyei
t
hert
hemul
t
i
pl
i
erort
he
accel
er
at
oral
one
...
Aspoi
nt
edoutbyPr
of

...

”Themul
t
i
pl
i
erandt
heaccel
er
at
or
combi
nedt
oget
herpr
oducecy
cl
i
calf
l
uct
uat
i
ons
...
The
gr
eat
ert
hev
al
ueoft
hemul
t
i
pl
i
er
,t
hegr
eat
ert
hechanceofacy
cl
el
ess
pat
h
...


...

wher
eYti
snat
i
onali
ncomeYatt
i
metwhi
chi
st
hesum of

gov
er
nmentexpendi
t
ur
eGt,consumpt
i
onexpendi
t
ur
eCtandi
nduced
i
nv
est
mentI
t
...


...

(
2)
It=β(
Ct–Ct–1)
...


...


...

(
4)
Gt=1
...


...
Thewei
ght
sdepend,ofcour
se,upont
hev
al
ueschosen
f
or t
he mar
gi
nalpr
opensi
t
yt
o consume and f
or t
he r
el
at
i
on (
i

...
Assumi
ngt
hev
al
ueoft
hemar
gi
nalpr
opensi
t
yt
oconsume
t
obegr
eat
ert
hanzer
oandl
esst
hanone(
0<α0)
,andoft
heaccel
er
at
or
gr
eat
ert
han zer
o(
β > 0)
,Samuel
son expl
ai
ns f
i
v
et
y
pes ofcy
cl
i
cal
f
l
uct
uat
i
onswhi
char
esummar
i
sedi
nt
heTabl
e1
...
Thi
si
sshowni
nFi
g
...

Case2showsadampedcy
cl
i
calpat
hf
l
uct
uat
i
ngar
oundt
he
st
at
i
cmul
t
i
pl
i
erl
ev
elandgr
adual
l
ysubsi
di
ngt
ot
hatl
ev
el
,asshown
i
nFi
g
...

Case 3 depi
ct
s cy
cl
es of const
ant ampl
i
t
ude r
epeat
i
ng
t
hemsel
v
esar
oundt
hemul
t
i
pl
i
erl
ev
el

...

(
C)

...
(
D)

...
(
E)

...
Butt
hey can be r
educed t
ot
wo because case 3
per
t
ai
ni
ngt
ocy
cl
esofconst
antampl
i
t
udehasnotbeenexper
i
enced
...
Case4ofexpl
osi
v
ecy
cl
es
hasnotbeenf
oundi
nt
hepast
,
i
t
sabsencebei
ngt
her
esul
tofendogenous
economi
cf
act
or
st
hatl
i
mi
tt
heswi
ngs
...

Li
mi
t
at
i
ons
Despi
t
et
heseappar
entusesoft
hemul
t
i
pl
i
er
accel
er
at
ori
nt
er
act
i
on,t
hi
s
anal
y
si
shasi
t
sl
i
mi
t
at
i
ons:
(
1)Samuel
soni
ssi
l
entaboutt
hel
engt
hoft
heper
i
odi
nt
hedi
f
f
er
ent
cy
cl
esexpl
ai
nedbyhi
m
...

(
3)Thecy
cl
esex
pl
ai
nedi
nt
hi
smodelosci
l
l
at
eaboutast
at
i
onar
yl
ev
el
i
nat
r
endl
esseconomy

...
Thi
shasl
edHi
ckst
o
f
or
mul
at
ehi
st
heor
yoft
het
r
adecy
cl
ei
nagr
owi
ngeconomy

...

(
5)I
ti
gnor
est
heef
f
ect
sofmonet
ar
ychangesuponbusi
nesscy
cl
es
...

R
...
Tohi
m,“
t
het
heor
yoft
heaccel
er
at
i
on
and t
he t
heor
y oft
he mul
t
i
pl
i
erar
et
he t
wo si
des oft
he t
heor
y of
f
l
uct
uat
i
ons
...

I
ngr
edi
ent
soft
heTheor
y
Thei
ngr
edi
ent
sofHi
cks’
st
heor
yoft
r
adecy
cl
ear
ewar
r
ant
edr
at
eof
gr
owt
h,consumpt
i
on f
unct
i
on,aut
onomous i
nv
est
ment
,an i
nduced
i
nv
est
mentf
unct
i
on,
andmul
t
i
pl
i
er
accel
er
at
orr
el
at
i
on
...
I
ti
s
consi
st
entwi
t
hsav
i
ngi
nv
est
mentequi
l
i
br
i
um
...
Accor
di
ng t
o Hi
cks,i
ti
st
hemul
t
i
pl
i
er
accel
er
at
ori
nt
er
act
i
onwhi
chweav
est
hepat
hofeconomi
cf
l
uct
uat
i
ons
ar
oundt
hewar
r
ant
edgr
owt
hr
at
e
...
Consumpt
i
on
i
nper
i
odti
sr
egar
dedasaf
unct
i
onofi
ncome(
Y)oft
hepr
ev
i
ousper
i
od(
t
–
1)

...


Theaut
onomousi
nv
est
menti
si
ndependentofchangesi
nt
hel
ev
el
of
out
put

...

Thei
nducedi
nv
est
ment
,
ont
heot
herhand,
i
sdependentonchanges
i
nt
hel
ev
elofout
put

...

I
nt
he Hi
cksi
an t
heor
y
,t
he accel
er
at
or i
s based on i
nduced
i
nv
est
mentwhi
chal
ongwi
t
ht
hemul
t
i
pl
i
erbr
i
ngsaboutanupt
ur
n
...
Gi
v
en const
antv
al
ues oft
he mul
t
i
pl
i
erand t
he
accel
er
at
or
,i
ti
st
he'
l
ev
er
ageef
f
ect
't
hati
sr
esponsi
bl
ef
oreconomi
c
f
l
uct
uat
i
ons
...

(
2)Thesav
i
ngandi
nv
est
mentcoef
f
i
ci
ent
sar
edi
st
ur
bedov
er
t
i
mei
n
suchawayt
hatanupwar
ddi
spl
acementf
r
om equi
l
i
br
i
um pat
hl
eads
t
oal
aggedmov
ementawayf
r
om equi
l
i
br
i
um
...

(
4)Theeconomycannotexpandbey
ondt
hef
ul
lempl
oy
mentl
ev
elof
out
put

...


(
5)Thewor
ki
ngoft
heaccel
er
at
ori
nt
hedownswi
ngpr
ov
i
desani
ndi
r
ect
r
est
r
ai
ntont
hedownwar
dmov
ementoft
heeconomy

...

(
6)Ther
el
at
i
onbet
weent
hemul
t
i
pl
i
erandaccel
er
at
ori
st
r
eat
edi
na
l
agged manner
,si
nce consumpt
i
on and i
nduced i
nv
est
mentar
e
assumedt
ooper
at
ewi
t
hat
i
mel
ag
...
Thust
he
cy
cl
esar
ei
nher
ent
l
yexpl
osi
v
ebutar
econt
ai
nedbycei
l
i
ngsandf
l
oor
s
oft
heeconomy

...
bel
l
ow
...
EEi
st
heequi
l
i
br
i
um l
ev
elofout
putwhi
chdependsonAA andi
s
deducedf
r
om i
tbyt
heappl
i
cat
i
onoft
hemul
t
i
pl
i
eraccel
er
at
ori
nt
er
act
i
on
t
oi
t

...
LLi
st
he
l
ower equi
l
i
br
i
um pat
h of out
put r
epr
esent
i
ng t
he f
l
oor or '
sl
ump
equi
l
i
br
i
um l
i
ne'

...
As a r
esul
t
,t
he gr
owt
h ofout
putand i
ncome
pr
opel
l
ed byt
hecombi
ned oper
at
i
on oft
hemul
t
i
pl
i
erand accel
er
at
or
mov
est
heeconomyont
ot
heupwar
dexpansi
onpat
hf
r
om Pot
oP1
...
Butt
hi
sdoesnothappenbecauseoft
he
upperl
i
mi
torcei
l
i
ngsetbyt
hef
ul
lempl
oy
mentl
ev
elFF
...

”Thuscer
t
ai
nbot
t
l
enecksofsuppl
yemer
gewhi
chpr
ev
entout
put
f
r
om r
eachi
ngt
hepeakandi
nst
eadencount
ert
hecei
l
i
ngatP1
...
Theeconomywi
l
lmov
eal
ongt
hecei
l
i
ngf
r
om P1 t
oP2

dependi
ngupont
het
i
meper
i
odoft
hei
nv
est
mentl
ag
...

Si
ncei
ncomeatt
hi
sl
ev
eli
sdecr
easi
ngr
el
at
i
v
et
ot
hepr
ev
i
ousst
ageoft
he
cy
cl
e,
t
her
ei
sadecr
easedamountofi
nv
est
ment

...

Dur
i
ngt
hedownswi
ng,"
t
hemul
t
i
pl
i
er
accel
er
at
ormechani
sm set
si
n
r
ev
er
se,f
al
l
i
ng i
nv
est
mentr
educi
ng i
ncome,r
educed i
ncome r
educi
ng
i
nv
est
ment
, and so on, pr
ogr
essi
v
el
y

...

"Thef
al
li
nout
puti
nt
hi
scasemi
ghtbeast
eepone,
asshownby
P2P3Q
...
I
ft
hesl
umpi
ssev
er
e,
i
nducedi
nv
est
mentwi
l
l
qui
ckl
yf
al
l
t
o
zer
oandt
hev
al
ueoft
heaccel
er
at
orbecomeszer
o
...
Thust
het
ot
alamount
ofi
nv
est
menti
nt
heeconomyi
sequalt
oaut
onomousi
nv
est
mentmi
nus
t
heconst
antr
at
eofdepr
eci
at
i
on
...
AtQ2 ,t
hesl
umpr
eachest
hebot
t
om or
f
l
oorpr
ov
i
ded by t
he LL l
i
ne
...
Fi
nal
l
y
,when
al
lexcess capaci
t
yi
s exhaust
ed,aut
onomous i
nv
est
mentwi
l
lcause
i
ncomet
or
i
sewhi
chwi
l
li
nt
ur
nl
eadt
oani
ncr
easei
ni
nducedi
nv
est
ment

sot
hatt
heaccel
er
at
ori
st
r
i
gger
edof
fwhi
chal
ongwi
t
ht
hemul
t
i
pl
i
er
mov
est
heeconomyt
owar
dt
hecei
l
i
ngagai
n
...

Cr
i
t
i
ci
sms
The Hi
cksi
an t
heor
y oft
he busi
ness cy
cl
e has been sev
er
el
y
cr
i
t
i
ci
sedbyDuesenber
r
y
,
Smi
t
hi
esandot
her
sont
hef
ol
l
owi
nggr
ounds:
1
...
Hi
cks'
smodelassumest
hatt
he
v
al
ueoft
hemul
t
i
pl
i
err
emai
nsconst
antdur
i
ngt
hedi
f
f
er
entphases
of t
he t
r
ade cy
cl
e
...
Butt
hi
si
s nota r
eal
i
st
i
c assumpt
i
on,as
Fr
i
edmanhaspr
ov
edont
hebasi
sofempi
r
i
calev
i
dencet
hatt
he
mar
gi
nalpr
opensi
t
yt
oconsumedoesnotr
emai
nst
abl
ei
nr
el
at
i
ont
o
cy
cl
i
calchangesi
ni
ncome
...

2
...
Hi
ckshasal
sobeencr
i
t
i
ci
sed
f
orassumi
ngaconst
antv
al
ueoft
heaccel
er
at
ordur
i
ngt
hedi
f
f
er
ent
phasesoft
hecy
cl
e
...
These ar
e unr
eal
i
st
i
c assumpt
i
ons
becauset
hecapi
t
al
out
putr
at
i
oi
si
t
sel
fsubj
ectt
ochangeduet
o
t
echnol
ogi
calf
act
or
s,t
henat
ur
eandcomposi
t
i
onofi
nv
est
ment
,t
he
gest
at
i
onper
i
odofcapi
t
al
goods,
et
c
...

Aut
onomous I
nv
est
mentnotCont
i
nuous
...
Thi
si
sunr
eal
i
st
i
cbecausef
i
nanci
al
cr
i
si
si
n a sl
ump mayr
educe aut
onomousi
nv
est
mentbel
ow i
t
s
nor
mall
ev
el

...

4
...
Anot
herweaknessoft
heHi
cksi
anmodeli
st
hatgr
owt
h
i
smadedependentuponchangesi
naut
onomousi
nv
est
ment

...
Accor
di
ngt
oPr
of

...
I
ni
mput
i
ng gr
owt
ht
o an unexpl
ai
ned
ext
r
aneousf
act
or
,
Hi
ckshasf
ai
l
edt
opr
ov
i
deacompl
et
eexpl
anat
i
on
oft
hecy
cl
e
...

Di
st
i
nct
i
on Bet
ween Aut
onomous and I
nduced I
nv
est
mentnot

Feasi
bl
e
...
Aspoi
nt
edoutbyLundber
g,ev
er
yi
nv
est
menti
s
aut
onomousi
nt
heshor
tr
unandamaj
oramountofaut
onomous
i
nv
est
mentbecomesi
nducedi
nt
hel
ongr
un
...

6
...
Anot
herser
i
ousl
i
mi
t
at
i
on
oft
het
heor
yi
st
hati
tpr
esent
samechani
calexpl
anat
i
onoft
het
r
ade
cy
cl
e
...
Thusi
ti
samechani
calsor
tofexpl
anat
i
oni
nwhi
ch
humanj
udgement
,busi
nessexpect
at
i
onsanddeci
si
onspl
ayl
i
t
t
l
eor
nopar
t

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