Hagen, Ku on dem
A icle
In la ion, Unemploymen and Unemploymen Bene i s
Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de
Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik
P o ided in Coope a ion wi h:
Duncke & Humblo , Be lin
Sugges ed Ci a ion: Hagen, Ku on dem (1976) : In la ion, Unemploymen and Unemploymen
Bene i s, Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de
Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik, ISSN 0342-1783,
Duncke & Humblo , Be lin, Vol. 96, Iss. 3, pp. 235-260,
h ps://doi.o g/10.3790/schm.96.3.235
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In la ion, Unemploymen and Unemploymen Bene i s
By Ku on dem Hagen*
An unemploymen compensa ion sys em is in eg a ed in o a sho - un
mac oeconomic model o p ices and employmen . The dynamic p ope ies
a e discussed and some quali ica ions a e made wi h espec o he s abilizing
e ec s o unemploymen bene i s.
I. In oduc ion
The unemploymen cum in la ion phenomenon o "s ag la ion", as
poli icians like o desc ibe i , has gained much a en ion du ing he las
decade om heo is s and p ac i ione s alike. Va ious emedies ha e
been ied wi hou signi ican success, and he gap o communica ion
and unde s anding seems o widen be weens hose who a e in cha ge o
he measu es and hose who belie e hey know wha sohuld be done.
In his pape , we shall no y o add o hese ecommenda ions, bu
a he poin ou one aspec o unemploymen which seems o ha e been
pushed aside du ing la ge pa s o he discussion: he in la iona y
e ec s o unemploymen bene i s.
Usually, he unemploymen compensa ion sys em is ega ded as some
kind o buil -in s abilize (Musg a e, 1959, pp. 505 - 6). Au ho i ies in-
s all income edis ibu ion p og ams by which, du ing pe iods o
"no mal" employmen , hose who a e employed ha e o suppo he
jobless pa o he labou o ce. I he unemploymen a io ises beyond
i s "no mal" le el, a ailable unds all sho o he amoun s needed and
go e nmen s eps in by ex ending c edi o he employmen agencies.
These loans a e o be epaid du ing he nex eco e y, when in lows
exceed disbu semen s.
I emains ques ionable, howe e , whe he we eally expe ience such
coun e cyclical swi ches om de ici spending o su plus sa ing, and
e en i his we e he case, no s aigh o wa d conclusions should be
d awn as o he s abilizing e ec s on employmen . An ex ension o
* This a icle was w i en while I was a he Uni e si y o Mannheim.
Thanks o commen s on a i s d a a e due o Ho s He be g, Hans Jü gen
Jaksch, Michael Schmid and Ann Schwa z-Mille .
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236 Ku on dem Hagen
go e nmen ans e s o households which is gea ed o a ise in he
unemploymen a io may aise e ec i e demand, bu his does no
necessa ily mean ha employmen will be aised oo. Mo eo e , he
ac ha unemployed wo ke s a e o ecei e ans e s should encou age
ade unions no o bo he oo much wi h he employmen p oblem
when ba gaining o e new wage a es. I is no su p ising ha du ing
in la iona y ecessions only employe s end o s ess he job si ua ion,
while unions concen a e on he income losses due o in la ion.
In wha ollows we shall se up a sho un mac oeconomic model o
p ices and employmen which is dynamically s able and we shall de-
sc ibe he adjus men p ocesses which may o may no be suppo ed by
employmen bene i p og ams. F om he assump ions abou he wage
de e mina ion i ollows ha , excep a he p ice o a unning in la ion,
no mone a y policy will be able o aise employmen beyond wha is
conside ed as "no mal" by he ba gaining g oups in he labou ma ke .
I also is o be shown ha , i unions dis ega d he job si ua ion du ing
ecessions (because membe s a e "insu ed" agains unemploymen ), a
s able unemploymen a io abo e he no mal le el may exis which is
accompanied by a posi i e a e o in la ion.
II. Assump ions and No a ions
The e a e h ee sec o s in he economy: i ms, p i a e households,
and a cen al bank and go e nmen sec o . Rela i e p ices o goods and
se ices p oduced by i ms emain cons an so ha o al eal ou pu
(X) can be concei ed o as one conglome a e good, which may be ei he
consumed o in es ed. To al ou pu is a unc ion o capi al (K) and
labou (N) employed, and is subjec o diminishing ma ginal e u ns.
We shall u he assume ha o he ime pe iod conside ed labou is
he only a iable ac o , i. e.
(1) X = X (N), XN >
0,
XNN < 0 .i
Fi ms a e p ice ake s in he labou ma ke , i. e. gi en he p esen
ou pu p ice (P), a which en ep eneu s expec o be able o sell hei
p oduc s, and gi en he cu en nominal wage a e (W), he demand o
labou is de e mined by he equali y o his money wage a e and he
alue o he ma ginal p oduc o labou ,
(2) W = PXN .
1 Th oughou his pape he (pa ial) de i a e o a unc ion wi h espec
o a a iable x is deno ed by x.
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In la ion, Unemploymen and Unemploymen Bene i s 237
Using w o he eal wage a e,
W
(3) w: = — ,
om (1) and (2) we ob ain a demand unc ion o labou which alls
wi h a ising eal wage,
(4) N* = N
(w),
Nw< 0 .
On he supply side o he labou ma ke i is assumed ha ade
unions ollow he concep o a " ai " eal wage a e, w*, om which
hey deduce he demanded money wage a e
(5) W = w*Pe ,
whe e Pe is he p ice le el expec ed o be alid du ing he nea u u e.
A his wage a e supply is pe ec ly elas ic, which means ha labou
demanded by i ms is always equal o labou employed
(6) Nd = N .
I , howe e , he e is a de ia ion o he amoun o labou demanded
(and employed) om some "na u al" o "no mal" le el, N, unions co -
ec hei desi ed eal wage a e acco ding o he ollowing di e en ial
equa ion:2
Dw* . N
—
N
(7) — =
X
———,
X
> 0 and cons an .
w*N
F om (5) and (7) we can de i e a co esponding adjus men equa ion
o he money wage a e,
DW
(8) —— =71
a
u ,
whe e
(9)
and
(10)
7i: =
-
DP*
p7~
u : =
N-N
N
2 D is he di e en ial ope a o d/d .
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238 Ku on dem Hagen
The unemploymen a io (10), which is based on no mal employmen
a he han on ull employmen o he whole labou o ce, is aken o
be he ele an igu e o union policy. T ade unions do no eel e-
sponsible o any kind o unemploymen ega ded as "s uc u al" o
" ic ional", bu i he a io de ined by (10) becomes posi i e, i. e. i
employmen is lowe han ega ded as no mal, hey would p e e o
gain some mo e employmen a he han o o se he expec ed a e o
in la ion comple ely. On he o he hand, i he demand o labou is
highe han N (u < 0), hey aise he money wage a e by mo e han
would be necessa y o compensa e o he expec ed eal income losses
due o ising ou pu p ices.3
Once he le el o employmen is de e mined, i ms p oduce ou pu
acco ding o p oduc ion unc ion (1) and pay ou eal income X o wage
ea ne s and sha eholde s. I o al eal sales all sho o X, unsold goods
a e s o ed. On he o he hand, i excess demand o goods and se ices
is posi i e, i ms cu down in en o ies o inished p oduc s accumula ed
in he pas .4 To keep he a gumen simple, we shall assume ha demand
is always sa is ied, i. e. any excess demand o goods and se ices will
lead o passi e disin es men o exac ly ha amoun .
The gene al idea is ha in oligopolis ic ma ke s p oduce s i s o all
y o keep p o i s in a ce ain ela ion o cos s, i. e. hey aise ou pu
p ices whene e he money wage a es ha e gone up. Unin ended in-
es men , howe e , indica es ha ma ke s ha e no been clea ed and
p ices should be checked and/o co ec ed. So any excess demand o
goods oge he wi h he co esponding change in in en o ies should
lead o a u he co ec ion o he p ices. A p ice se ing unc ion which
coin ains hese wo elemen s may be ep esen ed by he ollowing di -
e en ial equa ion
DP DW ^
(11) ——— = ———b p ,
¡x
> 0 and cons an ,5
3 The ixed no mal employmen N could also be concei ed o as a classi-
cal supply cu e o labou which is comple ely inelas ic wi h espec o he
eal wage a e. I should be men ioned, howe e , ha (7) and (8) allow o
a mo e gene al in e p e a ion, i N is no aken as a a ge igu e bu simply
indica es ha le el o employmen a which he ba gaining o ces o employ-
e s and wo ke s coun e balance each o he , hus lea ing he dis ibu ion o
eal income unchanged. See S ein (1974) o a simila e sion o his Phillips-
Lipsey ype o wage a e adjus men . In his connec ion, e e ence should
also be made h he app oach aken by Michael Mussa (1975), which was
b ough o my a en ion a e he p esen pape had been comple ed.
4 The concep o in en o ies seems a bi s ange i e e ence is made o
se ices p oduced by i ms. He e one would ha e o hink o p oduce s who
a e able o swi ch be ween " ou ine" and "p ojec " wo k, i. e. i hey ace
a posi i e excess demand o hei se ices, hey delay any ou ine wo k and
concen a e hei employees on he p ojec s o de ed.
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In la ion, Unemploymen and Unemploymen Bene i s 239
whe e is he ( ela i e) excess o planned in es men (I) and con-
sump ion (C) as explained u he below o e ou pu p oduced:
I + C-X
(12) = - .
I should be no ed ha Wal as' Law has been expelled pa ly om
he model economy. Fi s , we excluded he labou ma ke by de e -
mining ealized employmen and, consequen ly, ealized income.
Second, he goods and se ices ma ke was se led in a simila way and
we had a spillo e o he inancial ma ke s. We now assume ha he e
a e only wo inancial asse s in he economy: equi ies o owne ship o
eal capi al (K) and ia money (M). On he ma ke s o hese asse s we
shall abandon he abo e non- â onnemen p ocess and allow o any
kind o econ ac ing un il a (po olio) s ock equilib ium is eached.6
A necessa y assump ion o his ou come would be ha inancial
ma ke s a e pe ec ly o ganized and immedia ely eac o dis u bances
c ea ed by shi s in demand and/o supply. The demand o money in
eal e ms may be gi en by a con en ional liquidi y p e e ence unc ion7
(13) L = g ( , X), g < 0, gn < 0, gx > 0
whe e is he expec ed eal a e o e u n on capi al (equi ies), n
again is he expec ed a e o in la ion ( he nega i e a e o e u n on
eal balances), and X is he le el o income, which may be aken as
de e mining he ansac ions demand o money. Pe manen s ock (po -
olio) equilib ium in he money and equi ies ma ke insu es ha we
always ha e
(14)
whe e M is he amoun o ia money exis ing in he economy.
Ano he ea u e o he model is ha we shall allow he alua ion o
exis ing capi al goods (P/c) o di e in he sho un om hei ep o-
duc ion cos (P), i. e. al hough eal capi al is o be concei ed o as one
5 The adjus men coe icien j i is aken as a cons an in (11). Usually, i
should be expec ed o a y wi h he ma ke a e o in e es since passi e
in es men enla ges he need o new unds. We shall omi his aspec s o
con enience.
* In he s anda d IS-LM con ex his means ha we a e always on he LM
cu e, which is a bond (equi y) and money ma ke equilib ium cu e.
7 Weal h does no appea as an explici a iable in (13). Hence, i mus be
assumed implici ly ha along a mo ing equilib ium households would be
willing o pu all hei sa ings in o equi ies, i. e. hey a e no di e si ie s on
he ma gin al hough, acco ding o (13), hey di e si y hei a e age po olio.
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240 Ku on dem Hagen
homogeneous good (which, o con enience, may be undes uc able), he
ela i e p ice
PK
(= PK/P) may be di e en om one.8
I , o example, he demand o households o eal balances ises
ela i e o he demand o equi ies, sales on he s ock ma ke will
o ce sha e p ices down and a he same ime aise he impu ed a e
o e u n on hese sha es. Because newly c ea ed equi ies will also ha e
o be se ed a an in e es a e equal o his highe a e o e u n, in-
es men p ojec s which seemed p o i able up o his poin will ha e
o be cancelled and he le el o in es men will go down in he nex
pe iod (nex ins an ). Fo he momen , i. e. un il he slowing down o
in es men has aised he p ice o exis ing capi al goods o i s po olio
equilib ium le el, PK will s ay below one o , equi alen ly, he ma ginal
e iciency o capi al will be lowe han he ma ke a e o in e es .
The e will be an in e se ela ion be ween he ma ke alua ion, PK,
o exis ing capi al and he eal a e o e u n upon i , , i. e. i he eal
ma ginal e iciency o capi al, X/c, is expec ed o emain cons an in he
u u e, he ma ke e u n on equi ies ollows om he p esen alue
o mula
(15) = XK/pK
I should be no iced ha (15) is a de ini ion o ei he o
PK•
Once
PK
is de e mined in he ma ke , he alue o ollows and ice e sa. We
assume ha a di e ence be ween he wo a es XR and is he majo
o ce go e ning in es men decisions, i. e. aking R as an exogenous
a iable he sho un in es men unc ion is
(16) I = I ( ), I < 0 .
The demand o consump ion goods (C) is assumed o depend on cu -
en disposable income which, as long as go e nmen ac i i ies a e no
conside ed, is simply he ac o income c ea ed du ing he p oduc ion
p ocess:
(17) C = c Y, 1 > c > 0 and cons an .
Finally, expec a ions abou he a e o in la ion a e assumed o be
changed acco ding o pas expe ience:
8 By assump ion, inancial ma ke s a e clea ed a any momen in ime,
while his is no necessa ily he case in he goods ma ke s. Consequen ly,
he alua ion o capi al should only in e y special cases be he same as he
ou pu p ice. C . B aina d and Tobin (1968), Tobin (1969), and S ein (1971,
1974). F enkel and Rod iguez (1975) a i e a essen ially he same poin by
a guing in e ms o adjus men cos s. The basic e e ence o his second
app oach would be Gould (1968).
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In la ion, Unemploymen and Unemploymen Bene i s 241
(18) D n = e nj , e > 0 and cons an
The abo e o mula has wo limi ing cases o e 0 and
e
->- oo, e-
spec i ely. The i s one implies D n = 0 and is o en e e ed o as
"s a ic" expec a ions, because economic agen s do no lea n om o
eac o hei own expe ience. The second one implies "pe ec myopic
o esigh ", i. e. he obse ed a e o in la ion is expec ed o emain he
same in he nea u u e. Fo easons, which will become clea in he
nex sec ion, we shall assume ha e is ai ly small, i. e. people eac
slowly o any disc epancies be ween ealized and expec ed a es o
in la ion.
III. S abili y and Adjus men P ocesses
The model o be discussed consis s o h ee di e en ial equa ions (8),
(11) and (18), one s ock demand unc ion (13), and a ma ke clea ing
condi ion (14), which is con inuously main ained by app op ia e changes
in he ma ke a e o in e es o , equi alen ly, in he p ice o equi ies.
Assuming ha (13) can be sol ed explici ly o , we can inse (14)
and de i e he ollowing equilib ium condi ion o he money and
equi ies ma ke s
(19) = G (m, n, X) ,
1
g
whe e
(20) m : = -y- .
F om equa ions (1) - (4) and (6) i ollows ha ou pu is a unc ion o
he eal wage a e only,
(21) X = h(w), hw = XNNw<0 .
We hen may inse (16), (17) and (21) in o (12) and, subs i u ing by
equa ion (19), ew i e he ela i e excess demand o goods and se ices,
, as a unc ion o m, ny and w:
(22) = (m, n,w), m > 0, „ >0, w > 0 ,
whe e he signs o he pa ial de i a i es ollow di ec ly om he
unc ions in ol ed.
16 Zei sch i ii Wi scha s- und Sozialwissenscha en 1976/3
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242 Ku on dem Hagen
I should be emembe ed ha , since planned sa ing always equals
ealized sa ing, he e a e no in luences on om he consump ion side.
The abo e a iables wo k on only ia ealized ou pu , X, and planned
in es men , I. Planned in es men (and, consequen ly, u) sh inks when-
e e he eal a e o in e es ises, which is he case i ei he m o n (o
bo h) decline. A decline in he eal wage a e also leads o a decline in
, because ou pu , and he e o e supply, is inc eased while a he same
ime a highe demand o ansac ion balances will aise he equi ed
a e o e u n on equi ies, he eby educing planned in es men demand.
By means o (4) and (6) we can in e p e he unemploymen a io (10)
as a unc ion o he eal wage a e,
(23) u = u (w), uw > 0 .
Nex we inse (23) and (22) in o equa ions (8) and (11) and, oge he
wi h he adap i e expec a ions unc ion (18), a i e a he ollowing
di e en ial equa ions:
(24) DW/W =
7i
- Xu(w) ,
(25) DP/P = DW/W + i (m, n w) ,
(26)
D
n = s [DP/P -
n
.
A i s sigh one migh ha e he imp ession ha his sys em is
capable o p oducing a s eady s a e in la ion, whe e
DP/P = DW/W =
7i
= some posi i e cons an
a ull employmen and ze o excess demand o goods. As long as he
go e nmen emains passi e, howe e , he amoun o ia money does
no change, and a posi i e a e o in la ion will d i e eal balances
down. Lowe eal balances in u n ia he in e es a e mechanism lead
o a lowe a e o in es men which again slows down he a e o p ice
in la ion. In o he wo ds: ega dless o he o ces, which may ha e se
an in la iona y p ocess in o mo ion, i will pe e ou , i i is no ed by
an app op ia e mone a y expansion.
The o egoing a gumen becomes clea , i we eplace (24) and (25)
wi h wo di e en ial equa ions in he eal wage a e and eal balances,
espec i ely. Taking accoun o ela ionships (3) and (20) we may de i e
om (24) - (26)
(27) Dm =
—
m [n + p (m,7T,w)
—
ku (w)] .
(28) Dw =
—
w ¡i (m, n, w) ,
(29)
D
N = S [¡IV (m, TI, W)
— X
u (W)] .
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In la ion, Unemploymen and Unemploymen Bene i s 249
dogenous o ces (as, pe haps, expe ienced in he pas ), de ia ions om
N should no only be conside ed ansi o y bu also "symme ical" in
he sense ha pe iods o low employmen (N > N) will be ollowed by
pe iods o high employmen (N < N), du ing which loans a e o be
e unded.
To simpli y ma e s u he , i is assumed ha unemploymen ans-
e s a e based on po en ial a he han on pas income, i. e. e e y un-
employed wo ke is o ecei e a ce ain pe cen age a, o he wage in-
come, which he would be able o ea n. Consequen ly, o al unemploy-
men bene i s, measu ed in eal e ms, will amoun o a w (N
—
N),
whe e N s ands o ull employmen o he whole labou o ce. On he
o he hand, i insu ance p emiums a e o be ce ain ac ion, /?, o
ac ual income, eal paymen s o he insu ance agencies will be
¡3
wN
leading o a ne cash low o
(34)
¡3
w N
—
a w
(N —
N) .
Because o he abo e assump ion ha du ing "no mal" employmen
he compensa ion p og am simply consis s o a edis ibu ion o wage
income, exp ession (34) mus anish o N = N, i.e. a and ha e o be
ixed by he go e nmen in such a way as o ensu e he ollowing
balance equa ion:
(35) pwN - ocw(N -N) = 0 .
Using (35) we may subs i u e o (N) in (34) and ew i e he ne cash
low o insu ance agencies as
(36) (a + p) w
(N
- N) ,
which will be posi i e (nega i e) whene e employmen ises beyond
( alls below) i s "a e age" le el, N. By assump ion, hese ne cash in-
lows o ou lows a e pa o he go e nmen budge . Dis ega ding, as
be o e, all o he go e nmen ac i i ies, we may se (36) equal o he
change in he supply o money (in eal e ms):
DM
(37) (a + p) w (N - N) — .
Le us u he assume ha go e nmen se s N equal o N, i. e. he
insu ance p og am is based on exac ly ha le el o employmen which
indica es a s ands ill in he eal wage ba gaining p ocess.11 F om (10),
11 F om wha has been said a he beginning o his sec ion i should be
clea ha unemploymen bene i s a e no conside ed a policy ins umen . The
cen al au ho i ies jus y o ind an a e age le el o employmen such ha
hey will be able o s ay ou he insu ance business in he long un.
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250 Ku on dem Hagen
(6) and (4) we may hen subs i u e o he unemploymen a io, u (w),
and ew i e (37) as
DM
(38) -p- = B (w) ,
whe e
(39) B(w) = (a + i)Nwu(w) , Bw > 0 .
The eal low supply o money, being iden ical o a eal income ans-
e om he go e nmen o p i a e households, is an inc easing unc-
ion o he eal wage a e, and i is posi i e (nega i e) whene e u is
posi i e (nega i e).
The e a e wo channels h ough which unemploymen bene i s a ec
excess demand. They a e ep esen ed by he le and igh hand side o
(39), espec i ely. Fi s , a change in he money supply in luences he
demand o commodi ies ia he in e es a e mechanism. Second,
go e nmen ans e s a e pa o disposable income and he e o e
a ec demand ia he consump ion unc ion.
Le indica e, as be o e, he ela i e excess demand o goods and
se ices, when go e nmen emains absen . The gene al exp ession o
excess demand,
~ i + c(X + B)-X
(40) =
may hen be w i en
(41) = + c
b
,
whe e
B(w)
(42) b = and bw > 0 .
I should be unde s ood ha he ele an igu e o p ice decisions
o i ms is now gi en by ins ead o , i. e. ins ead o di e en ial
equa ion (11) we ha e
DP DW
(43) = — + [xl + cb] .
F om (43) and (38) oge he wi h (24) and (266 we may de i e he
ollowing sys em o di e en ial equa ions:
(44) Dw =
—
w
[a,
( + c b) ,
(45) D n = s [u ( + c b) -
X
u] ,
(46) Dm = B
—
m [n
— X
u + p ( + c
b)7
.
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In la ion, Unemploymen and Unemploymen Bene i s 251
The s a iona y solu ion o hese equa ions is he same as ha o
(27) - (29). F om
Dw =
0 =
D i
i ollows ha u would ha e o be ze o,
and i
u
anishes, so will bo h
B
and b, and he e o e, he di e ence
be ween sys ems (27) - (29) and (44) - (46).
As o he dynamic beha iou o he economy, we shall again dis-
ega d all bu small dis u bances and linea ize a ound he s a iona y
solu ion:
(47)
Dw
D n
Dm
- w* ¿i( w + c bw) -w*/* n
£ {M ( w + cbw) - Xuw } eii n £ * m
Bw - m* {ju ( w + cbw) - luw} - m* (1 + ¡i n) - m* ju n
w — w*
n
Til
— 771*
Since (47) and (30) a e bo h e alua ed a he same poin in he phase
space, he alues o pa ial de i a i es mus be he same. The only di -
e ence hen be ween he wo sys ems consis s o
bw
and
Bw
e ms in
he i s colums o (47). I is easily shown ha condi ions (31) and (32),
while s ill being su icien , a e no longe necessa y o s abili y, i. e.
a e in oduc ion o unemploymen bene i s weake es ic ions would
su ice.12
The unemploymen compensa ion p og am ou lined abo e hus may
be e med "s abilizing" in he gene al sense ha i enla ges he se o
pa ame e dis ibu ions, which ensu e dynamic s abili y o he sys em.
This does no necessa ily mean, howe e , ha he adjus men p ocess
will be speeded up. I Xi and (i = 1, 2, 3) a e he oo s o cha ac e -
is ic equa ions co esponding o (30) and (47), espec i ely, he ollow-
ing esul s may be ob ained:
(48)
|
X! +
x9 +
|
<
|
y, + Vq +
V3
I
and
(49) X! = yjy2y.3 ,
i. e. a leas one bu a mos wo o he e ms on he igh hand side
will be g ea e in absolu e alue han he co esponding
x%
oo s. The e-
o e, i canno be s a ed ha unemploymen bene i s always inc ease
s abili y in he sense ha a ce ain neighbou hood a ound he equilib-
ium poin will be eached in sho e ime.
12 This and he ollowing esul s a e ob ained in Appendix 2.
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252 Ku on dem Hagen
So a , we ha e desc ibed he economy by means o m, w and n. In
e ms o hese a iables, s a iona y solu ions o (27) - (29) and (44) - (46)
a e iden ical, and disequilib ium dynamics, as gi en by (30) and (47), do
no exhibi cha ac e is ic di e ences. Howe e , he e emains one im-
po an modi ica ion wi h espec o he money supply. While M was
ixed in he model o sec ion III, in he p esen amewo k i is being
changed h oughou he adjus men p ocess. As a esul , i is no pos-
sible o de e mine he inal p ice le el in he economy wi hou i s
ha ing e alua ed he change o M along he ime pa h.
A g aphic exposi ion may be gi en by means o s anda d mac o-
economic "demand" and "supply" schedules. In Figu e 3, all cu es a e
d awn unde he assump ion o ze o in la iona y expec a ions. Le A
ep esen an ini ial equilib ium iden ical o he s a ing poin o
Figu e 2, and le he au onomous shi in he demand o goods be o
he same size in bo h diag ams. We hen may iden i y wo concep ual
di e ences.
Fi s , he "demand" cu es in Figu e 3, being calcula ed om
+ cb = 0 ins ead o = 0, a e la e han he co esponding ones in
Figu e 2, while each espec i e pai has one poin in common a X = X*
(i. e. b = 0). Acco dingly, a sho un "Keynesian" solu ion unde a
ixed money supply would ep esen bo h a highe ou pu and p ice
le el han in he case o Figu e 2. (Fo compa ison, demand cu es om
Figu e 2 epea ed and appea as do ed lines in Figu e 3.)
Second, in he p esen model he pull which ca ies income away
om X* will c ea e a go e nmen su plus and hus, ia a decline in M,
shi he demand schedule downwa ds. Wi hou u he quan i a i e
speci ica ion i canno be old whe he his shi ully o pa ly com-
pensa es he upwa d mo e in he demand cu e due o ising in la ion-
a y expec a ions. As long as he ime pa h shows a cyclical pa e n,
he e will be a leas one pe iod o unemploymen accompanied by
mone a y expansion and a co esponding (pa ial) upwa d shi in he
demand cu e.
In Figu e 3, he o e all ne e ec on M is assumed o be nega i e,
i. e. he inal equilib ium poin , D, ep esen s lowe nominal money
balances han a he ou se and, consequen ly, a lowe ou pu p ice
le el.13
13 Taking in o accoun he assump ion abou s abili y and linea i y as well
as he di ec ion o he ini ial demand shi , he abo e solu ion seems mos
plausible. Howe e , a igo ous p oo has no ye been ca ied ou .
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In la ion, Unemploymen and Unemploymen Bene i s 253
P
Figu 3
V. Unemploymen plus In la ion
In his las sec ion conside he case whe e labou unions a e eluc-
an o accep any wage a es ha would lowe hei membe s' eal
income, i. e. hey es ic he wage ba gain by
(50) DW/W >
7i
.
The e may be imes du ing which unions a e nei he willing no able
o ollow he ule gi en by (50). The a e ma h o he oil c isis p o ides
a ai ly good example o hei no being ce ain as o which wage aise
hey should demand (and which migh be easible). Du ing he cou se
o a no mal ade cycle, howe e , es ic ion (50) seems qui e plausible
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254 Ku on dem Hagên
wi h espec bo h o he ade unions' a ge o de ending wha hey
ha e achie ed in he pas and he gene al asymme y o he ba gaining
p ocess.
In e ms o he wage adjus men equa ion (24) i ollows om (50)
ha
A
should become ze o whene e employmen alls below N i. e.
(51)
>
i
L>J
The model now consis s o wo dis inc pa s. Up o he ull employ-
men eal wage a e, which may be e med w°, equa ions (44) - (46) a e
s ill e ec i e while o eal wage a es highe han w° he coe icien
X
would anish:
(52) Dw =
— w ji (
+ cb) ,
(53)
D jz
= en
(u
+ cb) ,
(54) Dm = B
—
m
[JLI (
+ c
b)
+ n] .
A he ull employmen wage a e, whe e u, B and b all become ze o,
bo h sys ems o di e en ial equa ions coincide, and we shall a gue ha
w = w° as a limi ing case is con ained in ei he pa o he model.
As o equa ions (44) - (46), we know om he las sec ion ha a
s a iona y solu ion would equi e s able p ices as well as ull employ-
men , i. e. he equilib ium poin would lie on he common bo de jus
men ioned. A solu ion o (52) - (54) would equi e ze o excess demand
o goods
(55)
(m,
TT,W) + cb ( o) = 0
and
(56) B
(w)
-
m
n = 0 .
These equa ions hold no only i bo h B and n anish. I employmen
is no mal and p ices a e s able14, hey a e also compa ible wi h a whole
a ay o pai s o posi i e B and n15 o , less o mally, wi h many di e -
en combina ions o unemploymen and in la ion.
Le us inspec sys em (52) - (54) mo e closely. F om he i s wo o
hese equa ions we may de i e
(57) Dw/w =
—
D JZ / E .
14 A ze o in la ion a e would ollow om D = 0 = n.
15 Since (54) - (56) a e only alid o w > o0, ne ans e s B canno be
nega i e, and he same ollows o n in (56), since m should be posi i e o
ob ious easons.
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In la ion, Unemploymen and Unemploymen Bene i s 255
A e in eg a ing, his becomes
(58) Inw = - n/
s
+ A ,
whe e A is a cons an . In ha pa o he phase space, which is go e ned
by (52)-(54), a iables w and n ob iously ha e o s ay in a ce ain
ela ion. Mo eo e , ime does no explici ly appea in (58), so he e-
la ion mus be en i ely de e mined by he alues o w and n which
happen o be ealized when he phase pa h "c osses he bo de ", i. e.
when he unemploymen a io becomes posi i e. The eason o his is
qui e simple. F om he de ini ion o he eal wage a e i ollows ha
Dw = w [DW/W - DP/P] ,
while he adap i e expec a ions ule is
D 7i — e
[DP/P - n] .
Bo h o he b acke ed e ms abo e a e equal in absolu e alue i
DW/W =
J
,
i. e. i he change in he money wage a e is equal o in la iona y ex-
pec a ions, as assumed in (51) o employmen le els lowe han N.
As o he de e mina ion o he cons an o in eg a ion in (58), once
he alue o n is known (call i n0) a which he phase pa h goes h ough
he ull employmen coo dina e, w = w°, i ollows om (58) ha
InwO
= _ n**/e + A
and, consequen ly, o all alues o w > w°:
(59) n =
—
[In
w —
In u°7 .
Because o he nega i e slope o (59) he ini ial alue JI° is he max-
imum a e o in la ion ha may be ealized unde sys em (52) - (54). On
he o he hand, equa ion (56) equi es s a iona y alues o n o be non-
nega i e. The e o e, i happens o be nega i e, an equilib ium
solu ion o (52) - (54) does no exis wi hin he ange w° < w <C oo.
This can be demons a ed by means o Figu e 4, which is a p o-
jec ion o pa allel cu s h ough he phase space a di e en le els o m.
Equilib ium condi ion (55) is ep esen ed16 by he se o lines unning
om he w° coo dina e o he sou heas , while (56) is a bunch o ays
om a common o igin a w = w° and n = 0. No e ha he w° coo di-
na e and he abszissa i sel a e he limi ing cases o m 0 and m oo,
16 Fo con enience, bo h (55) and (56) a e linea ized.
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256 Ku on dem Hagen
espec i ely. In e sec ions o co esponding pai s o hese cu es a e
connec ed by he do ed line, which s a s om w = w° and n = 0 wi h
a posi i e slope and la e bends back owa ds he w° axis. Poin s on his
cu e a e candida es o a s a iona y equilib ium wi h bo h unemploy-
men and in la ion.
Finally, wo g aphs o equa ion (59) a e plo ed down in Figu e 4, each
s a ing a a di e en ini ial le el o n. I = n > 0, a unique equi-
lib ium is gi en by in e sec ion poin
E,
while in he second case, whe e
= n < 0, no s a iona y solu ion will exis . This las ou come (as well
as he uniqueness o he abo e equilib ium) is mainly due o he
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In la ion, Unemploymen and Unemploymen Bene i s 257
nega i e slope o (59). A p esen , howe e , we shall no discuss his
phenomenon any u he and shall con ine ou sel es o he s a emen
ha he pa i ioned sys em as gi en by (44) - (46) and (52) - (54) has a
leas one and a mos wo s a iona y solu ions, whe e he i s is always
he equilib ium de eloped in p e ious sec ions.
S abili y condi ions o he pa ial sys em (52) - (54) a e gi en in
Appendix 3. Assuming ha hey a e me we s ill canno say e y much
abou he ac ual ime pa h. I he economy s a s a a high employ-
men le el (i. e. N> N) and ollows a cyclical pa h owa ds he s a ion-
a y equilib ium, unemploymen will become posi i e a some poin in
ime and hus se beha iou al sys em (52) - (54) in o e ec . I on he
common bounda y in la iona y expec a ions a e posi i e (i. e. = 0),
he e may be a s able pa h owa ds a s a iona y solu ion cha ac e ized
by unemploymen cum in la ion, bu i his pa o he model also p o-
duces cycles, he ime pa h migh swing back o he high employmen
egion, and he abo e p ocess would s a all o e anew, wi h a di e en
alue o n0 and a di e en unemploymen equilib ium.
These ema ks may su ice o he p esen un il an analysis o join
s abili y o he wo pa ial sys ems has been ca ied h ough. Wha
seems ema kable a his poin is he endency owa ds a pa h o sel -
sus ained in la ion and unemploymen . O cou se, no go e nmen would
ole a e such a cons ella ion in he long un; new policy ools migh
be ac i a ed and, mo e impo an , he old ools would ha e o be
checked and co ec ed. In he p esen model, he p incipal sou ce o in-
la ion is he g ow h in he money supply, which could be s opped by
an app op ia e aising o unemploymen insu ance p emiums (as i was
done in Ge many a he beginning o 1976, when p emiums jumped by
i y pe cen ).
Howe e , i does no become clea om he model a which employ-
men le el au ho i ies should ix N. I he economy has eached a s able
posi ion in he unemploymen egion, a decline o N o he p e ailing
le el o employmen b ings he g ow h o money down o ze o im-
media ely, bu a bi la e he ac ha N exceeds N may c ea e new
di icul ies o i s own kind. The p oblem does no seem li le enough o
jus i y i s being neglec ed. A leas he adi ional ic ion o he s abil-
izing o ces o unemploymen bene i s should dese e a mo e c i ical
in e p e a ion.
17 Zei sch i u Wi scha s- und Sozialwissenscha en 1976/3
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258 Ku on dem Hagen
Appendix
A.l S abili y o (30)
I he cha ac e is ic equa ion o he linea ized sys em (30) is w i en as
(A.l) x3 + ax x2 +
ag
x + a3 = 0 ,
he Rou h-Hu wi z heo em s a es ha necessa y and su icien condi ions
o all oo s
Xj
(i = 1, 2,3) o ha e nega i e eal pa s a e
(A.2) <n > 0 ,
(A.3) a a2- as>0 ,
(A.4) a3 > 0 ,
whe e c^ is he nega i e o he ace o he sys em ma ix in (30), 0$ is he
sum o all second o de p incipal mino s, and is he nega i e o he
de e minan .
Inequali y (A.2) is he same as (31) in he ex and is no epea ed he e.
Expansion o he de e minan gi es us
(A.5) c g =
e
I
[a,
m*
w*
uw m > 0 ,
i. e. condi ion (A.4) will be ul illed. The sum o he second o de p incipal
mino s is
(A.6)
a-2
= ^
[m*
m
(s
+
X w*
uw)
—
s
X w*
uw j .
This exp ession is no necessa ily posi i e, bu i mus be i (A.3) holds.
Inse ing he p ope exp essions o al a.2 and a3 in (A.3) we ge
(A.7) (a! -
E)
I
m* w*
uw m >
a^ e (k
w* uw n - m* m) ,
which is he equi alen o condi ion (32).
A.2 S abili y o (47)
W i e he cha ac e is ic equa ion o (47) as
y3 + b y2 + b2y + b3 = 0
and ob ain he ollowing esul s:
b =
ju [w*
( w + c bW) - E
„
+ m* m]
(A.8) = a + /¿w* cbw> ai ,
(A.9) b2 =
02
+ Bw
w*
ii m >
02
,
(A. 10) b3 = og .
I ax and a3 a e posi i e, so will be b^ and b3.
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