Rehme, Gün he
A icle
On ' us ing' money: Sil io Gesell's Schwundgeld
econside ed. Pa I: The sho un
Re iew o Economic Analysis (REA)
P o ided in Coope a ion wi h:
In e na ional Cen e o Economic Analysis (ICEA), Wa e loo, On a io
Sugges ed Ci a ion: Rehme, Gün he (2024) : On ' us ing' money: Sil io Gesell's Schwundgeld
econside ed. Pa I: The sho un, Re iew o Economic Analysis (REA), ISSN 1973-3909,
In e na ional Cen e o Economic Analysis (ICEA), Wa e loo (On a io), Vol. 16, Iss. 2, pp. 91-131,
h ps://doi.o g/10.15353/ ea. 16i2.4942
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On 'Rus ing' Money: Sil io Gesell's Schwundgeld
Reconside ed
Pa I: The Sho Run
GÜNTHER REHME†
Technische Uni e si ä Da ms ad
Sil io Gesell hypo hesized ha money dep ecia ion is economically and socially
bene icial, an idea ha ha e o en been con ended. He e I analyze he spi i o his claims
in a Sid auski model in which households addi ionally ha e a 'lo e o weal h'mo i e. The
analysis is p esen ed in wo pa s, one ocusing on he sho and he o he one on he long
un. In he i s pa o his wo k, hese ea u es p o ide mic o- ounda ions o analyzing
Gesell's claim in he sho un. Con a y o some claims i is shown Gesell's conjec u es
may indeed be alid in a demand-de e mined, sho - un equilib ium and why money
dep ecia ion o e comes he ze o lowe bound on nominal in e es a es. These esul s a e
checked agains he ecen demone iza ion episode in India and essen ially ound o be
ue. Hence, Gesell's hypo heses can be e i ied o a plausible, sho - un en i onmen and
may be ele an o cu en economic, especially, mone a y policies.
Keywo ds: Economic Pe o mance, Dep ecia ing Money, Ze o Lowe Bound,
Demone iza ion, Lo e o Weal h
JEL Classi ica ions: E1, E5, O4
† P o esso Rehme passed away las yea . The pape is published as i was o iginally submi ed, subjec
o con e sion o he Re iew’s o ma ..
I am indeb ed o Ingo Ba ens and Thomas Fische o hei aluable help and insigh ul commen s. I
ha e also bene i ed om discussions wi h Pa an ab Basu, Ch is ian Be ke , Volke Caspa i, Ch is iane
Clemens, Alex Cukie man, Soumya Da a, Ha mu Egge , Sabine Eschenho -Kamme , Ch is ian
Gelle i, Ra ael Ge ke, Che an Gha e, Cha les Goodha , Ma cus Mille , We ne Onken, Uwe Sunde and
om eedback a U Bay eu h, LMU Munich, he 5 h In e na ional Con e ence on Sou h Asian Economic
De elopmen (SAED), Sou h Asian Uni e si y (SAU), New Delhi, India, he 5 h HenU/INFER
Wo kshop on Applied Mac oeconomics, Kai eng, Henan, China, he 50 h Anni e sa y "Money, Mac o
and Finance" (MMF) con e ence a he London School o Economics (LSE), London, Uni ed Kingdom,
he 10 h RCEA "Money-Mac o-Finance" Con e ence in Wa e loo, On a io, Canada, he 15 h Annual
Con e ence on Economic G ow h and De elopmen , New Delhi, India, in 2019, and he 65 h Münden
Talks "P oudhon, Gesell, Keynes and Nega i e In e es Ra es", Wuppe al, Ge many, in 2021. The usual
disclaime shields hem all.
© 2024 Gün he Rehme. Licensed unde he C ea i e Commons A ibu ion-Noncomme cial 4.0
Licence (h p://c ea i ecommons.o g/licenses/by-nc/4.0/). A ailable a
h p:// o ea.o g.
Re iew o Economic Analysis 16 (2024) 91-131
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1 In oduc ion
"Money is he oo ball o economic li e."
1
In his main piece o wo k "The Na u al Economic O de " Sil io Gesell, a Ge man me chan
and in ellec ual, de eloped a ious insigh ul a gumen s o imp o e he wo kings o an
economy. I was i s published in Be n in 1916 and ecei ed p aise om economis s such as
Keynes (1936) in his "Gene al Theo y o Employmen , Money and In e es ", ch. 23, and Fishe
(1932) in his "Booms and Dep essions".
In his pape , I econside his idea o Schwundgeld (demu age) and i s consequences on
economic pe o mance. I analyze whe he he spi i o his key conjec u es can be jus i ied in a
ela i ely pa simonious, mode n heo e ical amewo k. One eason is ha Gesell's claims ha e
o en been con ended by a guing ha hey canno be co obo a ed by 's a e-o - he-a ' heo y.
Al hough Gesell (1920), p. 78, acknowledges ha money is " he oo ball o economic
li e"and hus (p obably) being a key d i e o , and essen ial o , any mode n economy, he
cau ions us by a guing;"Only money ha goes ou o da e like a newspape , o s like po a oes,
us s like i on, e apo a es like e he , is capable o s anding he es as an ins umen o he
exchange o po a oes, newspape s, i on and e he . Fo such money is no p e e ed o goods
ei he by he pu chase o he selle . We hen pa wi h ou goods o money only because we
need he money as a means o exchange, no because we expec an ad an age om possession
o he money." (p. 121)
Acco ding o him placing money and commodi ies on equal 'physical' oo ing equi es ha
money dep ecia es, jus as no mal goods do due o he wea and ea in usage o s o age. In
pa icula , he a gued he ace alue o (pape ) money dep ecia es a a ce ain pe cen age o e a
pa icula pe iod. To egain he p e ious ace alue o he money (no e) used, people would
ha e o buy s amps o make up o he dep ecia ion he mone a y au ho i y would dec ee o
he money no e.
2
1
Sil io Gesell (1920) The Na u al Economic O de .
2
Conside his example o he Ame ican cu ency: "This $100 no e (bill) is shown as i will appea du ing
he week Augus 4 h-11 h, hi y-one en-cen s amps ($3.10) ha ing been a ached o i by i s a ious
holde s on he da ed spaces p o ided o he pu pose, one s amp o each week since he beginning o
he yea . In he cou se o he yea 52 en-cen s amps ($5.20) mus be a ached o he $100 no e, o in
o he wo ds i dep ecia es 5.2% annually a he expense o i s holde s." Gesell (1920), p. 121/2.
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The in oduc ion o such a mone a y a angemen would hen in luence he economy in
ways abou which he o med, among o he s, he ollowing ou hypo heses.
3
Gesell Conjec u e 1 (GC1) The in oduc ion o , and, when p esen , an inc ease in, he money
dep ecia ion a e leads o a highe eloci y o money in ci cula ion.
"E e yone, o cou se, ies o a oid he expense o s amping he no es by passing hem
on - by pu chasing some hing, by paying deb s, by engaging labou , o by deposi ing he
no es in he bank, which mus a once ind bo owe s o he money, i necessa y by
educing he a e o in e es on i s loans. In his way, he ci cula ion o money is subjec ed
o p essu e." Gesell (1920), p. 123.
Gesell Conjec u e 2 (GC2) Money dep ecia ion coupled wi h expansiona y mone a y policy
s imula es agg ega e demand and h ough ha ou pu and employmen .
"In all concei able ci cums ances, in ai wea he and oul, demand will hen exac ly
equal: - The quan i y o money ci cula ed and con olled by he S a e. Mul iplied by: The
maximum eloci y o ci cula ion possible wi h he exis ing comme cial o ganiza ion.
Wha is he e ec on economic li e? The e ec is ha we now domina e he luc ua ions
o he ma ke ; ha he Cu ency O ice, by issuing and wi hd awing money, can une
demand o he needs o he ma ke ; ha demand is no longe con olled by he holde s
o money, by he ea s o he middle classes, he gambling o specula o s o he one o
he S ock Exchange, bu ha i s amoun is de e mined absolu ely by he Cu ency O ice.
The Cu ency O ice now c ea es demand, jus as he S a e manu ac u es pos age s amps,
o as he wo ke s c ea e supply." Gesell (1920), p. 127.
Gesell Conjec u e 3 (GC3) A money dep ecia ion a e is wel a e enhancing.
"The elimina ion o in e es is he na u al esul o he na u al o de o hings when
undis u bed by a i icial in e e ence. E e y hing in he na u e o men as in he na u e o
economic li e u ges he con inual inc ease o so-called eal capi al - an inc ease which
con inues e en a e he comple e disappea ance o in e es . The sole dis u be o he
peace in his na u al o de we ha e shown o be he adi ional medium o exchange. The
unique and cha ac e is ic ad an ages o his medium o exchange pe mi he a bi a y
pos ponemen o demand, wi hou di ec loss o i s possesso ; whe eas supply, on
accoun o he physical cha ac e is ics o he wa es, punishes delay wi h losses o all
3
Mo e elabo a e jus i ica ions o Gesell's claims and ideas can be ound in he wo king pape e sion o
his pape ; see Rehme (2018), appendix F, and he quo es p esen ed a he end o his pape .
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kinds. In de ense o hei economic wel a e, bo h he indi idual and he communi y ha e
been and a e a enmi y wi h in e es , and hey would long ago ha e elimina ed in e es
i hei powe had no been ammeled by money." Gesell (1920), p. 190.
Gesell Conjec u e 4 (GC4) A money dep ecia ion a e bene i s wo ke s ela i ely mo e han
capi al owne s.
"By he laws o ee compe i ion, he manu ac u e 's p o i mus be educed o he le el
o a echnician's sala y - an unpleasan esul o many manu ac u e s whose success was
mainly due o hei comme cial abili y. Wi h ee money, c ea i e powe has become
unnecessa y in comme ce, o he di icul ies ha called o he compa a i ely a e and
he e o e ichly ewa ded comme cial alen ha e disappea ed. And someone mus
bene i om he educ ion o he manu ac u e 's p o i . Ei he goods mus become
cheape , o , o pu i he o he way abou , wages mus ise. The e is no o he possibili y."
Gesell (1920), p. 135.
As poin ed ou abo e, he p esen pape complemen s esea ch ha has used mode n economic
heo y o in es iga e whe he he Gesell hypo heses can be eplica ed in s anda d model
amewo ks. One inds ha he esul s o p e ious esea ch a e mixed.
Fo example, Rösl (2006) inds ha only he i s hypo hesis can be de i ed om Sid auski
(1967), ha is, in a money-in- he-u ili y se -up. He concludes ha Gesell neglec ed an analysis
o he long un and any possible e ec s on capi al accumula ion so he o he h ee hypo heses
u n ou o be non- alid in his model.
In u n, Menne (2011), o example, uses an elabo a e and in ol ed New Mone a is DSGE
model o ind ha "in la ion and 'Gesell axes' maximize s eady-s a e capi al s ock, ou pu ,
consump ion, in es men and wel a e a mode a e le els. In a ecession scena io, a Gesell ax
speeds up he eco e y in a simila way as a la ge iscal s imulus bu a oids 'c owding ou ' o
p i a e consump ion and in es men ." Thus, he inds suppo o he Gesell hypo heses a
mode a e le els in his business cycle model o he hi d-gene a ion mone a y sea ch models.
The p esen pape uses an al e na i e mic o- ounded and simple gene al equilib ium model
o analyze whe he he dep ecia ion o money is socially bene icial. Doing his we will abs ac
om iscal policy, as Gesell did no conside he in e ac ion o iscal and mone a y policy in
de ail.
4
4
I one likes, he esul s he e may also in e p e ed as holding ela i e o some gi en and cons an iscal
policy ope a ing in he backg ound, and Rica dian Equi alence holds. Fu he mo e, ano he wo d o
cau ion should be men ioned. I will no add ess he his o ical and he mo e ecen empi ical expe iences
ha , mos ly, local expe imen s using money dep ecia ion ha e p oduced. O cou se, he mos amous
one is he Wö gel expe imen om 1932 o 1933 which was s opped by he Aus ian Na ional Bank in
REHME Sil io Gesell's Schwundgeld Reconside ed, Pa 1
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We ollow Gesell and assume ha he e is homogeneous money ha is issued by he s a e
and by law ha money is legal ende in ansac ions.
5
Fu he mo e, his ad oca ed mone a y
sys em is one whe e ia (pape ) money is i edeemable, and, hus, di ec ly ela ed o (only
edeemable by) eal goods in he economy.
I edeemabili y implies ha you canno exchange a bankno e back in o ano he bankno e o
any colla e al ha migh back he ace o any o he ( eal) alue o he bankno e. Fo ins ance,
in he Eu o and he Fed sys em you can in p inciple edeem you bankno e, bu only o ge
ano he bankno e wi h an equally deno ed ace alue. This is no possible unde he
i edeemabili y o he bankno e and plays a ole when he e is a dep ecia ion o he ace o o he
alue o he bankno e. On he issue o i edeemabili y and ia money see, o example, Bui e
(2003).
In he pape , he basic Sid auski amewo k is changed impo an ly. Apa om he mo i e
o de i e u ili y om money i is assumed ha agen s also de i e u ili y om hei weal h.
6
People a e aken o be a ional and a e no ooled by money illusion. Thus, he agen s only
conside eal, physical capi al as weal h.
He e I ela e o his mo e gene al concep as 'lo e o weal h' in a dynamic mac oeconomic
model as in Rehme (2011). These mo i es a e impo an o de i ing nondegene a e sho - un
ela ionships be ween he nominal in e es a e and mic o- ounded consump ion (quasi-) IS and
LM cu es (in a "nominal in e es a e and consump ion" space). A simila app oach based on
he 'lo e o weal h' as a mic o- ounda ion in a dynamic model wi h a sho - un and long- un
analysis as in his pape has ecen ly been p esen ed by Michailla and Saez (2014). In his
amewo k, I analyze wo app oaches o cap u e Gesell's ideas, which a e p esen ed in wo pa s
o he analysis.
The i s app oach, he p esen Pa I, concen a es on ex book-like sho - un, demand-
de e mined equilib ia o he (quasi-, mic o- ounded) IS-LM-AS-AD a ie y, which a e based
on he mic o- ounda ions o op imal beha iou , ha is, he demand o he agen s. The link o
supply is assumed o be Keynes's "p inciple o e ec i e demand".
Sep embe 1933. The in e es ed eade will ind a ple ho a o empi ical e idence on whe he money
dep ecia ion and Gesell's ideas in gene al wo k o no in he li e a u e. He e he ocus is on heo y.
5
Thus, he assump ion implies ha we ule ou cu ency subs i u ion. Fo an analysis o dep ecia ing
money in a complemen a y cu ency sys em see, o example, Godschallk (2012).
6
This has been done, o example, by Webe (1930) and Pigou (1941) who a gue ha indi iduals de i e
u ili y om he me e possession o weal h and no simply i s expendi u e. La e Ku z (1968) p o ided
a ho ough analysis o an op imal g ow h model whe e weal h ea u es in u ili y. Fu he mo e, Zou
(1994), Bakshi and Chen (1996) and Ca oll (2000) ela e o Max Webe and a gue ha he dependence
o u ili y on weal h cap u es he "spi i o capi alism". Mo e gene ally, i cap u es 'lo e o weal h' as
a gued in Rehme (2017).
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The second one, analyzed in Pa II, complemen s he i s app oach and uses a s anda d
Ramsey-Cass-Koopmans amewo k o he long un whe e ma ke s a e as-summed o clea a
each poin in ime, and demand always equals supply.
The ollowing esul s a e hen ob ained o he i s app oach and so o Pa I o he analysis.
In a sho - un, demand-de e mined equilib ium whe e he (physical) capi al s ock, he in la ion
a e, ans e s, and money supply a e ixed, bu eal ac o p ices a e lexible, Gesell's
hypo heses GC1 - GC4 a e all alid, gi en he (demand) mic o- ounda ions o he model and
gi en ha he mic o- ounda ions ea u e di ec u ili y de i ed om money ansac ions and
'lo e o weal h', whe e only physical capi al is conside ed o be he ue sou ce o weal h.
A key assump ion o he de i a ion o his esul is ha he ma ginal p oduc i i y heo y o
dis ibu ion does no necessa ily hold in he sho un. Impo an ly, when he in la ion a e is
gi en, and he Fishe ela ionship holds, he eal in e es a e mo es in he same di ec ion as he
nominal in e es a e in any sho - un equilib ium.
7
The de ails o his a e p esen ed in he main ex . Thus, he eal in e es a e is de e mined
by o he ac o s han echnology in he sho un.
Gesell's ideas ha e been impo an in ecen discussions abou o e coming he ze o lowe
bound ha has played such an impo an ole a e he G ea Recession. One a gumen has been
o make nominal in e es a es nega i e o comba wha is called a "liquidi y ap". Fo good
su eys on his, i s ela ion o Gesell's ideas, hei ele ance o he cu en economic si ua ion
and hei his o ic p ecu so s see, o example, Da i y (1995), Ilgmann and Menne (2011) and
S ensson and Wes e ma k (2016).
In he p esen pape , i u ns ou ha many di e en combina ions o money dep ecia ion
and money supply policies can sus ain a "liquidi y ap", ha is, a si ua ion wi h a sho - un
equilib ium, ze o nominal in e es a e. These mone a y policy combina ions a e shown o ha e
non-negligible e ec s o dis ibu ion, ha is, he ewa ds o labou and capi al.
In a ious model a ian s, Bui e and Panigi zoglou (2003) and o he con ibu ions by W.
Bui e ha e shown ha money dep ecia ion may be used o make he sho - un equilib ium
in e es a e nega i e and pull an economy ou o a "liquidi y ap". In his pape , I ind he same
so complemen ing hei esul s. Bu he model s uc u e he e is qui e di e en and simple. Gi en
he p esen model's mic o- ounda ions, his esul ollows s aigh o wa dly and easily.
Ano he applica ion o he model o he sho un is he ecen episode o demone iza ion
in India whe e he 500 and 1000 upee no es (INR) we e decla ed in alid in a su p ise mo e by
7
No ice ha he "Fishe ela ionship" cap u es ha he nominal in e es a e is (app oxima ely) he sum
o he eal in e es a e and (expec ed) in la ion. This should no be equa ed wi h he "Fishe e ec "
which s a es ha he eal in e es a e is independen o he a e o in la ion. Fo his cla i ica ion see,
o example, Ahmed and Roge s (1996). Fo ex book models whe e he eal and he nominal in e es
a e mo e in he same di ec ion in he sho un, see, o example, Blancha d (2017), ch. 6 and 16.
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he Indian P ime Minis e . In India, cash is by a he mos impo an medium o economic
ansac ions. O e nigh his a ec ed 86.9 pe cen o he alue o o al cu ency in ci cula ion.
The model p edic s ha such a demone iza ion leads o lowe consump ion, agg ega e
demand, and lowe wages, bu highe eal in e es a es. Thus, he measu e does no seem o be
good o wo ke s in he sho un. These indings a e b oadly in line wi h he empi ical e idence
documen ed by he Rese e Bank o India's Mone a y Policy Depa men (MPD) (2016).
Summa izing hese indings o he sho un yields ha he p esen model amewo k is
indeed capable o e i ying Gesell's claims. In he sho - un, demand-de e mined equilib ium
all claims can be asce ained. This may p o ide a a ionale o why he enewed in e es in his
ideas plays a ole in he cu en economic policy delibe a ions.
The pape is o ganized as ollows. Sec ion 2 p esen s he model and 3 analyzes he demand-
de e mined (sho - un) equilib ium, an o e coming o he ze o lowe bound on nominal in e es
a es and, as an example, applies he model o he ecen Indian demone iza ion episode. Sec ion
4 concludes.
2 The Model
To simpli y he algeb a he model is se in con inuous ime. Fo all a iables ha a e con inuous
unc ions o ime, I use he subsc ip 𝑡 o deno e hei dependence on ime. Thus, we de ine
ℎ𝑡≡ℎ(𝑡) o some a iable ℎ depending on ime. Fu he mo e, he change o a a iable ℎ o e
ime, i.e. 𝑑ℎ𝑡
𝑑𝑡, is deno ed by ℎ˙𝑡.
By assump ion, he economy is popula ed by many, p ice- aking households. The agg ega e
esou ce cons ain o he households is gi en by
𝐶𝑡+𝐾˙𝑡+𝑀˙𝑡
𝑃𝑡+𝜎⋅𝑀𝑡
𝑃𝑡=𝑤𝑡𝑁𝑡+𝑟𝑡𝐾𝑡+𝑋𝑡 (1)
whe e 𝐶𝑡 and 𝐾𝑡 deno e agg ega e eal consump ion and he agg ega e eal capi al s ock,
espec i ely. 𝑀𝑡 ep esen s he agg ega e nominal money holdings and 𝑃𝑡 is he p ice le el. 𝑁𝑡
deno es popula ion and 𝑤𝑡 is he eal wage a e. 𝑟𝑡 deno es he eal a e o e u n on capi al, ne
o dep ecia ion o physical capi al 𝐾𝑡. The lump-sum ( eal) ans e s o he go e nmen ha a e
g an ed o he households a e deno ed by 𝑋𝑡.
Thus, he igh -hand side o he budge cons ain (1) cap u es agg ega e income, consis ing
o o al wage (𝑤𝑡𝑁𝑡) and capi al income (𝑟𝑡𝐾𝑡) as well as go e nmen ans e s (𝑋𝑡).
The le -hand side, in u n, cap u es agg ega e spending. Income is spen on consump ion
(𝐶𝑡), in es men in new capi al (𝐾˙𝑡) and acquisi ions o new, eal money holdings (𝑀˙𝑡
𝑃𝑡).
The agg ega e budge cons ain in equa ion (1) co esponds o he con en ional se -up o a
Sid auski (1967), money-in- he-u ili y- unc ion model. The no el ea u e and, o his pape ,
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he c ucial di e ence is he e m 𝜎⋅𝑀𝑡
𝑃𝑡. I cap u es he Gesell ax, ha is, he idea o " us ing
money". Tha can be in e p e ed as a dep ecia ion on he ci cula ing eal money holdings o he
households and is an amoun o a ax on hem.
Some imes i is a gued ha he Gesell ax is simply ano he o m o an in la ion a e ha
mos people also conside a ax on money holdings. Bu no ice ha he Gesell ax is di ec ly
de e mined by a poli ical en i y such as e.g. a cen al bank, and no , like he in la ion a e ( ax),
indi ec ly by he wo kings o ma ke s.
Now conside a ep esen a i e agen economy, and de ine pe capi a consump ion 𝑐𝑡, eal
money balances 𝑚𝑡, as well as he pe capi a capi al s ock 𝑘𝑡 and ans e s 𝑥𝑡 as ollows
𝑐𝑡≡𝐶𝑡
𝑁𝑡, 𝑚𝑡≡𝑀𝑡
𝑃𝑡𝑁𝑡, 𝑘𝑡≡𝐾𝑡
𝑁𝑡, and 𝑥𝑡≡𝑋𝑡
𝑁𝑡
Di iding equa ion (1) by 𝑁𝑡 and using ou de ini ions hen yields
𝑐𝑡+𝐾˙𝑡
𝑁𝑡+𝑀˙𝑡
𝑃𝑡𝑁𝑡+𝜎𝑚𝑡=𝑤𝑡+𝑟𝑡𝑘𝑡+𝑥𝑡
I is no di icul o e i y ha 𝐾˙𝑡
𝑁𝑡=𝑘˙𝑡+𝑛𝑡𝑘𝑡 and 𝑀˙𝑡
𝑃𝑡𝑁𝑡=𝑚˙𝑡+𝜋𝑡𝑚𝑡+𝑛𝑡𝑚𝑡 whe e 𝜋𝑡≡𝑃˙𝑡
𝑃𝑡
ep esen s he a e o in la ion and 𝑛𝑡=𝑁˙𝑡
𝑁𝑡 he popula ion g ow h a e. Then he budge
cons ain o he ep esen a i e household is gi en by
𝑐𝑡+𝑘˙𝑡+𝑛𝑡𝑘𝑡+𝑚˙𝑡+𝜋𝑡𝑚𝑡+𝑛𝑡𝑚𝑡+𝜎𝑚𝑡=𝑤𝑡+𝑟𝑡𝑘𝑡+𝑥𝑡.
Again, he igh -hand side co esponds o he household's income and he le -hand side
cap u es he household's expendi u e. No ice ha 𝜎𝑚𝑡 can be ega ded as an
ou lay o he household. The longe he household holds eal money balances 𝑚𝑡, he mo e is
o egone (a o m o expendi u e) in e ms o eal income. Fo a simila se -up see, o example,
Rösl (2006). I cap u es wha is called he Gesell ax.
Building on, o example, Blancha d and Fische (1989), ch. 4.5, and he Rösl se up we now
deno e eal pe capi a esou ces by 𝑎𝑡 whe e 𝑎𝑡≡𝑘𝑡+𝑚𝑡 . Thus, he household has eal
esou ces in he o m o physical capi al and eal money balances. I ollows ha 𝑎˙𝑡=𝑘˙𝑡+𝑚˙𝑡.
A e collec ing e ms and ea angemen Appendix B shows ha one hen ob ains
𝑎˙𝑡=[(𝑟𝑡−𝑛𝑡)𝑎𝑡+𝑤𝑡+𝑥𝑡]−[𝑐𝑡+(𝑟𝑡+𝜋𝑡+𝜎)𝑚𝑡] (2)
Thus, he change in eal pe capi a esou ces 𝑎˙𝑡 depends on he household's income om capi al
and eal money balances (𝑟𝑡−𝑛𝑡)𝑎𝑡 , labou income 𝑤𝑡 and ans e s 𝑥𝑡 . Consump ion hen
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Figu e 1: The LM Cu e
Resul 1 (LM Cu e): Based on he household's op imali y condi ions, equa ion (14) desc ibes
an LM cu e in (c, 𝑖 )-space o a gi en capi al s ock 𝑘, and ixed money supply 𝑚 and in la ion
a e 𝜋. I exp esses consump ion as a unc ion o he nominal in e es a e 𝑖=𝑟+𝜋, depending
on eal money balances 𝑚 and he money dep ecia ion a e 𝜎. I desc ibes equilib ium in he
money ma ke . An inc ease in he Gesell ax 𝜎 o eal money balances 𝑚 shi s he LM cu e
o he igh in a (𝑐,𝑖)-space, o a gi en nominal in e es a e
Nex , we conside equa ion (11) which, as one should ecall, is en i ely based on he demand
side o he economy, i.e. he households' op imali y condi ions. In s eady-s a e ha equa ion
educes o
(𝛿+𝛽)𝑐=(𝑟+𝜋+𝜎)𝑚−𝑟𝑎+𝜌𝑎
A e some manipula ion, using he Fishe ela ionship 𝑖=𝜋+𝑟, can be ea anged o yield;
𝐼𝑆: 𝑐=(1
𝛿+𝛽)[(𝜋+𝜎)(𝑚+𝑘)−(𝑖+𝜎)𝑘+𝜌(𝑚+𝑘)] (15)
This equa ion amoun s o a quasi-IS cu e ha has a nega i e slope wi h espec o 𝑖 in a (𝑐,𝑖)−
plane. Thus, 𝑑𝑐/𝑑𝑖∣𝐼𝑆<0 . Fu he mo e, as weal h conside a ions play a ole, i.e. 𝛽>0 , i
u ns ou ha he IS schedule also depends on eal money balances. Tha is so because h ough
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he in oduc ion o p e e ences o weal h (physical capi al) he model also implies a Pigou
e ec whe eby money posi i ely bea s on ( eal) consump ion, i.e., 𝑑𝑐/𝑑𝑚∣𝐼𝑆>0. ⬚
17
Figu e 2: The IS Cu e
The same holds o an inc ease in he in la ion a e 𝜋 , ha is, 𝑑𝑐/𝑑𝜋∣𝐼𝑆>0 . One also
e i ies ha 𝑑𝑐/𝑑𝜎∣𝐼𝑆>0. Thus, apa om an inc ease in eal money balances 𝑚, an inc ease
in he Gesell ax (an inc ease in 𝜎 ) also shi s he IS cu e o he igh o a gi en nominal
in e es a e.
Resul 2 (IS Cu e): Based on he household's op imali y condi ions, equa ion (15) desc ibes
an IS cu e in (𝑐,𝑖)-space o a gi en capi al s ock 𝑘, and ixed money supply and in la ion
a e. I exp esses consump ion as a unc ion o he nominal in e es a e 𝑖=𝑟+𝜋 and depends
on eal money balances 𝑚 and he money dep ecia ion a e 𝜎. I desc ibes equilib ium in he
goods ma ke . The IS cu e ea u es a Pigou e ec . An inc ease in eal money balances o he
in la ion a e aises consump ion and shi s he IS cu e o he igh o a gi en 𝑖. An inc ease
in he Gesell Tax shi s he IS cu e o he igh in a (𝑐,𝑖)-plane o a gi en nominal in e es
a e.
17
Pigou (1943) a gues ha ou pu and employmen can be s imula ed by inc easing consump ion due o
a ise in eal money balances. La e Pa inkin (1948) coined he e m o his e ec a e A hu Cecil
Pigou, one o he eache s o John Mayna d Keynes.
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3.1 The sho - un, demand-de e mined equilib ium
As is well known om elemen a y mac oeconomics, he in e sec ion o he LM and IS cu es
desc ibes a sho - un, demand-de e mined equilib ium. F om now on le a a iable ℎ=ℎ(𝑡) in
sho - un equilib ium be deno ed by ℎ.
Then sol ing equa ion (14) o he nominal in e es a e 𝑖 plus 𝜎, inse ing he esul in o he
𝐼𝑆 equa ion (15) and ea angemen yields he agg ega e (sho - un) demand o goods 𝑐. In
appendix D i is shown o be gi en by
𝑐=(𝜋+𝜎+𝜌)⋅𝑚
𝛿 (16)
Using equa ion (14) one e i ies ha he (sho - un) equilib ium nominal in e es a e sa is ies
𝑖=(𝜋+𝜎+𝜌)[1−(𝑚
𝑘)(𝛽
𝛿)]−𝜎 (17)
whe e he exp ession in he squa e b acke is non-nega i e by assump ion.
One can calcula e he eloci y o money as he a io o 𝑐 o eal money balances 𝑚. As bo h
quan i ies a e exp essed ela i e o he p ice le el, he eloci y o money (in e ms o
consump ion) in a sho - un equilib ium is hen gi en by
𝜈≡𝑐
𝑚=(𝜋+𝜎+𝜌)
𝛿 (18)
which is inc easing in 𝜎, and cap u es Gesell's idea ha con olling he eloci y o money has
a di ec bea ing on agg ega e ( eal) demand.
The eloci y o money is usually la ge han one which I assume o be he case.
Assump ion 2: The eloci y o money, in e ms o consump ion, is aken o be la ge han one,
ha is, 𝜈>1 and, hus, 𝛿 o be su icien ly smalle han 𝜌+𝜋+𝜎.
Thus, he a io o consump ion - o mo e con en ionally GDP - o money agg ega es like
𝑀0 (base money) o 𝑀1 is aken o be a alue o e one. As an example conside he eloci y o
𝑀1 in he U.S. be ween 1960 and oday. ⬚
18
18
Money Veloci y: Veloci y is a a io o nominal GDP o a measu e o he money supply (M1 o M2). I
can be hough o as he a e o u no e in he money supply, ha is, he numbe o imes one dolla is
used o pu chase inal goods and se ices included in GDP. Sou ce: h p://
esea ch.s louis ed.o g/ ed2/ca ego ies/32242
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Figu e 3: Veloci y o 𝑀1 in he U.S.
Sou ce: h p:// esea ch.s louis ed.o g/ ed2/ca ego ies/32242
F om he g aph, he eloci y o 𝑀1 has consis en ly been la ge han one o e he pe iod
conside ed. In his model, 𝑀 e e s o 𝑀0 (base money). I is well known ha he eloci y o
𝑀0 is usually highe han he one o 𝑀1 because 𝑀0<𝑀1 . As agg ega e consump ion
co esponds o oughly 60 pe cen o GDP in mos , especially OECD coun ies, i is sa e o say
ha empi ically he a io o 𝑀0 o agg ega e consump ion is also la ge han one. This holds no
ma e whe he we look a he s eady s a e o sho e pe iods.
Gi en he exp essions o a demand-de e mined equilib ium a ious compa a i e s a ic
in es iga ions a e hen possible. As he pape 's ocus is on Gesell's conjec u es, I concen a e
on he e ec s on he sho - un equilib ium i 𝜎 o 𝑚 is changed. Fo now, assume ha he
in la ion a e is non-nega i e, ha is, 𝜋≥0.
F om equa ions (16) and (17) agg ega e demand o goods (in sho un-equilib ium) is
inc eased and he sho - un equilib ium nominal in e es a e alls when he Gesell ax (gi en
eal money balances) o eal money balances (gi en money dep ecia ion) ise. Thus, when he
in la ion a e is non-nega i e, we ha e;
𝑑𝑐/𝑑𝜎>0, 𝑑𝑖
/𝑑𝜎<0 and 𝑑𝑐/𝑑𝑚>0, 𝑑𝑖
/𝑑𝑚<0 (19)
Tha means he (nega i e) nominal (sho - un equilib ium) in e es a e eac ion o a posi i e
change in he Gesell ax (𝜎) is la ge in absolu e alue o he LM shi han he absolu e (bu
posi i e) shi in he IS cu e. This ollows because 𝑑𝑖/𝑑𝜎∣𝐼𝑆=𝑚/𝑘 and 𝑑𝑖/𝑑𝜎∣𝐿𝑀=−1, and
by he assump ion ha 𝑚<𝑘.
Thus, i he economy's sho - un equilib ium is ini ially a poin 𝐴 , an inc ease in 𝜎 o eal
money balances will mo e he LM and he IS cu e o he igh , o end up a a poin like 𝐷 wi h
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a highe 𝑐 and a lowe nominal in e es a e 𝑖 in he new sho - un, demand-de e mined
equilib ium.
P oposi ion 1: Suppose he capi al s ock, p ices, he in la ion a e, and he ans e s a e ixed
in he sho un. Then an inc ease in he Gesell Tax 𝜎, o a gi en nominal money supply,
1. inc eases he eloci y o money 𝜈, and
2. inc eases sho - un, agg ega e consump ion 𝑐, and
3. implies a lowe sho - un nominal in e es a e 𝑖 in a (quasi-) IS-LM en i onmen in a
(𝑐,𝑖)-plane.
Figu e 4: The Sho -Run, Demand-De e mined Equilib ium
By simila a gumen s, we also ob ain ha , o a gi en 𝜎 and 𝜋≥0, an inc ease in eal money
balances, 𝑚 , inc eases sho - un, agg ega e consump ion, 𝑐 , and implies a lowe sho - un
nominal in e es a e, 𝑖.
So a we ha e igno ed ha he household's budge cons ain , ha is, equa ion (2) mus also
be sa is ied. We consequen ly need ha
𝑟⋅𝑘+𝑤+𝑥−𝑐−(𝜋+𝜎)⋅𝑚=0.
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Fo con enience deno e a iables ha a e ixed in he sho un by an uppe ba . ⬚
19
Assume ha in a demand-de e mined (sho - un) equilib ium he sum o wages and capi al
income equals ou pu , called 𝑦, which equals agg ega e supply. Then 𝑦= 𝑟⋅𝑘‾+𝑤. Gi en he
de e mina ion o consump ion by he IS-LM appa a us and in ligh o he budge cons ain
equa ion (2) we ge
𝑐+(𝜋‾+𝜎)⋅𝑚‾−𝑥‾=𝑦(𝑟,𝑤,𝑘‾)=𝑟⋅𝑘‾+𝑤 (20)
whe e he le -hand side deno es agg ega e demand (ne o ixed and gi en ans e s 𝑥‾) and he
igh -hand side is a quasi-agg ega e supply ela ionship ha depends on he ixed capi al s ock
𝑘‾, and he ac o p ices 𝑟 and 𝑤.
I he ac o p ices a e aken o a y eely and a e no ied o ma ginal p oduc i i y
emune a ion, bu some o he exogenous p ocess ha is independen o 𝑘, i is indeed possible
ha he le -hand side o he equa ion, ha is, agg ega e demand, called ad, de e mines he igh -
hand side o he equa ion.
Le ing 𝑎𝑑≡𝑐+(𝜋‾+𝜎)⋅𝑚‾−𝑥‾ deno e agg ega e demand, we ha e in a (sho - un)
demand-de e mined equilib ium ha
𝑎𝑑(𝜎;𝑚‾,𝜋‾,𝑥‾)≡𝑐+(𝜋‾+𝜎)⋅𝑚‾−𝑥‾=𝑦(𝑟,𝑤;𝑘‾)
As a consequence, we can hen de ine he ollowing:
De ini ion 1 Based on he household's op imali y condi ions in equa ions (10), (11), and (2), a
sho - un, demand-de e mined equilib ium is gi en when agg ega e demand ad (𝜎;𝑚‾,𝜋‾,𝑥‾)
equals agg ega e ou pu (supply), 𝑦(𝑟,𝑤;𝑘‾) , o a gi en capi al s ock, gi en eal money
balances and in la ion a e. Fo lexible ac o p ices 𝑟 and 𝑤, he in e sec ion o IS and LM
de e mines agg ega e demand ad (...) and wi h i ou pu 𝑦(𝑟,𝑤;𝑘‾) so ha he equilib ium is
demand-de e mined.
Wha e e he alues o he ixed a iables and he pa ame e s may be, he ac o p ices can
equilib a e sho - un demand and "supply" in such a wo ld. No ice ha we ha e no in oked
he ma ginal p oduc i i y heo y o dis ibu ion in which case he ewa ds would ul ima ely be
unc ions o 𝑘. Ins ead, he e we hink o 𝑟 and 𝑤 de e mined by (e.g. ma ke ) o ces ou side he
19
Recall ha he IS-LM appa a us holds o a simul aneous equilib ium in he goods and money ma ke .
In ha sense a gi en supply money makes i an exogenous a iable o mos o he analysis in his pa
o he pape .
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model, bu s ill assume ha hey equilib a e demand and supply in he way equi ed by he
model. I ha is he case, ad (⋅) indeed de e mines "supply" 𝑦(𝑟,𝑤;𝑘‾). ⬚
20
P oposi ion 2: Suppose he capi al s ock, ou pu p ices, he in la ion a e, he ans e s, and
he money supply a e ixed, bu eal ac o p ices a e lexible in he sho un. Then a sho -
un, demand-de e mined equilib ium, when he in la ion a e is non-nega i e, is cha ac e ized
by
ad (𝜎;𝑚‾,𝜋‾,𝑥‾)=𝑦(𝑟,𝑤;𝑘‾)
An inc ease in he Gesell Tax 𝜎 o eal money balances hen inc eases sho - un, agg ega e
demand, ad, and consequen ly sho - un ou pu and supply, 𝑦.
The p ope ies easily ollow om equa ion (20). F om he p oposi ion, we can also deduce he
ollowing. I 𝜎 ises, i ollows om P oposi ion 1 ha he (sho - un) equilib ium nominal
in e es a e 𝑖 alls. I he in la ion a e is ixed in he sho un, hen he eal in e es a e 𝑟
would ha e o all. This ollows om he Fishe ela ion 𝑖=𝑟+𝜋. I we assume ha he ac o
p ices a e ee o mo e in he sho un, hen P oposi ion 2 implies ha he wage a e 𝑤 mus
ise when 𝜎 inc eases. Thus, a highe 𝜎 implies a lowe 𝑟, o a gi en 𝜋‾, and highe 𝑎𝑑 so a
highe 𝑦 and a highe 𝑤. Hence, o a gi en capi al s ock, labou inpu and in la ion a e, he
wage ea ne s would bene i om an inc ease in he Gesell ax.
Co olla y 1: Fo ixed capi al, labou inpu and in la ion a e, he wage ea ne s may bene i
om an inc ease in he Gesell ax o eal money balances in he sho - un, demand-de e mined
equilib ium en i onmen . The capi al owne s may ea n less in such an en i onmen .
O cou se, ha begs he ques ion o he ac o p ices a e eally mo e lexible han ou pu p ices,
which de e mine he in la ion a e 𝜋. Clea ly, his dis ibu ional implica ion may no hold i he
in la ion a e is no ixed in he sho un.
Las ly, he wel a e implica ions in he sho - un, demand-de e mined en i onmen a e
conside ed. Clea ly, i he money supply and capi al s ock a e ixed in he sho un, pe iod
(sho - un) wel a e om equa ion (4) is gi en by
20
I is in e es ing o no e ha he e may be many di e en combina ions o w and ha can equilib a e
ad and y . Hence, unde he assump ions made many di e en dis ibu ional a angemen s o he
ewa ds o capi al and labou a e easible, and so he income dis ibu ion would in gene al no be
de e mina e.
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𝜑(𝑐,𝑚‾,𝑘‾)=ln 𝑐+𝛿ln 𝑚‾+ 𝛽ln 𝑘‾
Bu hen one easily e i ies ha 𝑑𝜑/𝑑𝜎=(𝑑𝑐/𝑑𝜎)/𝑐>0, because 𝑑𝑐/𝑑𝜎>0. Thus, pe iod
wel a e would ise wi h an inc ease in 𝜎.
P oposi ion 3: Suppose he capi al s ock, he in la ion a e, ans e s, and money supply a e
ixed, bu eal ac o p ices a e lexible in he sho un. Then a sho - un, demand-de e mined
equilib ium is cha ac e ized by pe iod wel a e
𝜑(𝑐,𝑚‾,𝑘‾)=ln 𝑐+ 𝛿ln 𝑚‾+ 𝛽ln 𝑘‾ wi h 𝑑𝜑
𝑑𝜎=𝑑𝑐/𝑑𝜎
𝑐 >0,𝑑𝜑
𝑑𝑚‾=𝑑𝑐/𝑑𝑚‾
𝑐 +𝛿
𝑚‾>0
ha is, pe iod wel a e is highe , when he Gesell ax o eal money balances a e highe in a
(sho - un) demand-de e mined equilib ium.
The mos in e es ing implica ion o he p oposi ions o he sho un is ha Gesell's
conjec u es a e ue in he en i onmen de eloped in his sec ion. Thus,
Theo em 1: In a sho - un, demand-de e mined equilib ium whe e he capi al s ock, he
in la ion a e, ans e s, and he money supply a e ixed, bu eal ac o p ices a e lexible and
he in la ion a e is non-nega i e, Gesell’s hypo heses GC1 – GC4 a e all gene ically alid,
gi en he (demand) mic o- ounda ions in equa ions (2), (4), (6), (7), (8), and (9), and gi en ha
he mic o- ounda ions ea u e di ec u ili y de i ed om money and “lo e o weal h” whe e
physical capi al is conside ed o be he ue sou ce o weal h.
This esul is s iking and in con as o some con ibu ions in he li e a u e. Clea ly, he heo em
is based on he non-implausible assump ions in oked he e. No ice ha he heo em is abou he
sho un. Howe e , Gesell’s ideas ha e occupied he imagina ion o esea che s and
policymake s alike in he yea s igh a e he G ea Recession. I has been and, somehow s ill,
is being el ha money dep ecia ion may be one way ou o impo an c isis p oblems, in he
sho and he longe un.
3.2 Liquidi y ap and he ze o lowe bound on nominal in e es a es
Recen ly, i has been an impo an ques ion wha mone a y policy can accomplish, i he
nominal in e es a e is a i s ze o lowe bound, ha is, i i akes on a alue close o ze o. As
men ioned abo e he e has been enewed in e es in Gesell’s ideas. To shed some led on o why
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Gesell’s ideas may be ele an in he cu en si ua ion conside money demand and sho - un
equilib ium again. ⬚
21
Money Demand Condi ions
Conside a si ua ion whe e he nominal in e es a e is a he ze o lowe bound. Le us again
concen a e on equa ion (7), which desc ibes he op imal choice (demand) o money holdings
in he p i a e sec o . Fo simplici y con inue o use 𝑚𝑡 o deno e eal money balances demanded
and supplied. Then;
𝛿
𝑧𝑡−𝛽
1−𝑧𝑡−𝜇𝑡⋅𝑎𝑡(𝑟𝑡+𝜋𝑡+𝜎)=0 (7)
So a we ha e concen a ed on an in e io solu ion implying ha he equa ion abo e is sa is ied
as an equali y. Suppose ha ha is no he case. In pa icula , suppose ha he nominal in e es
a e is a i s ze o lowe bound wi h 𝑖𝑡=𝑟𝑡+𝜋𝑡=0.
By implica ion he eal in e es a e 𝑟𝑡, he in la ion a e 𝜋𝑡 o bo h migh in p inciple be
nega i e. Bu in he sho - un equilib ium, he in la ion a e is (exogenously) gi en by
assump ion so we ake he eal in e es a e 𝑟𝑡 o adjus when 𝑖𝑡=0. Thus, he eal in e es a e
may be nega i e. The e is, o example, e idence o he U.S. ha nega i e eal in e es a es
a e a om un ealis ic as is shown e.g. by Eicheng een (2015), Figu e 1, which I ep esen he e
o con enience.
22
Now, o he ensuing analysis ecall ha 𝜇𝑡=1/𝑐𝑡 and 𝑎𝑡=𝑘𝑡+𝑚𝑡 whe e in his sec ion
now 𝑚𝑡=𝑚𝑡𝑑. We can hen in es iga e a ious cases.
Case 1: Suppose 𝑖=0,𝜎=0 and 𝛽=0. Then he le -hand side o equa ion (7) becomes 𝛿
𝑧𝑡>
0 so ha 𝑧𝑡→1 is op imal. Gi en ha 𝑚𝑡=𝑧𝑡𝑎𝑡=𝑧𝑡(𝑘𝑡+𝑚𝑡) we need ha 𝑚𝑡→∞ o
𝑚𝑡/(𝑘𝑡+𝑚𝑡)→1. Thus, people would demand an in ini e amoun o money balances and
hoa d cash.
This is he con en ional esul ollowing he Sid auski model. The common explana ion is
ha in a si ua ion whe e he oppo uni y cos o holding money is nil, people would hold all
21
The ollowing analysis is also in e es ing o ano he eason. Gesell ad oca ed a " ee money" and " ee
land" economy. Fo hose he in e es a e would e en ually ha e o abolished and any o m o c edi
would be ee o in e es acco ding o his u opia.
22
Mo e ecen e idence o a ange o coun ies can also be ound in Des oches and F ancis (20062007),
Cha B1, and Yi and Zhang (2017), Figu e 1.
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hei esou ces in he o m o eal money balances. Tha is usually associa ed wi h he no ion
o a “liquidi y ap”.
23
Figu e 5: Long-Run US In e es Ra es
Sou ce: Eicheng een (2015), p. 66, Figu e 1
Case 2: Suppose 𝑖=0,𝜎=0 and 𝛽>0 . Then equa ion (7) may yield an in e io solu ion
sa is ying 𝛿
𝑧𝑡=𝛽
1−𝑧𝑡⇔𝑚𝑡
𝑚𝑡+𝑘𝑡=𝛿
𝛽+𝛿⇔𝑘𝑡
𝑚𝑡=𝛽
𝛿
The impo an implica ion he e is ha 𝑧𝑡<1 is op imal and so he p esence o a “lo e o
weal h”-mo i e (𝛽) makes a liquidi y ap less likely. Tha should be clea om he mo i e
i sel . I people alue (physical) capi al hey will no y o ge id o all hei capi al in o de o
hoa d only cash.
23
The e m and concep o a "liquidi y ap" was well known by B i ish economis s be o e Keynes's
publica ion o he "Gene al Theo y o Employmen , Money and In e es ", who ac ually ne e used he
e m himsel . Fo de ails on ha and some cla i ica ions on misconcep ions in cu en discou se on he
phenomenon o a "liquidi y ap" see Ba ens (2011).
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Depa men (MPD) (2016) concludes ha , all in all, he nega i e e ec s we e "modes " o e
he sho pe iod om No embe 2016 o Feb ua y 2017.
Impo an ly, emone iza ion is unning in he opposi e di ec ion o demone iza ion. Thus,
we would expec he opposi e o he sho - un e ec s cap u ed by P oposi ion 7.
Finally, i ough o be ecognized ha i is s ill an un esol ed issue whe he he policy
objec i e o comba non-legal ac i i ies and ansac ions was success ully achie ed by he
Indian demone iza ion episode.
4 Conclusion
Abou one hund ed yea s ago Sil io Gesell a gued ha money should ' o ' as any o he good
does. He ad oca ed a mone a y sys em, which he called "F ee Money", whe e ia (pape )
money would be legal ende and i edeemable. He a gued ha
dep ecia ion o such money (cash) in ci cula ion would be s imula i e o economic
pe o mance and be socially bene icial.
In his pape , I ques ion he claim ha his ideas o an uncon en ional mone a y policy
canno eally be e i ied in mode n economic heo y amewo ks. To his end I ocus on ou
hypo heses Gesell made and analyze hese using s anda d con empo aneous mac oeconomic
heo y. The ollowing indings o Pa I o he analysis a e hen no ewo hy.
In a sho - un, IS-LM-AS-AD-like demand-de e mined equilib ium whe e he (physical)
capi al s ock, he in la ion a e, ans e s, and money supply a e ixed, bu eal ac o p ices a e
lexible, Gesell's hypo heses a e all alid, gi en he (demand) mic o- ounda ions o he model
which ea u e u ili y di ec ly de i ed om money and 'lo e o weal h', and physical capi al is
aken o be he ue sou ce o weal h.
This sho - un analysis also implies ha money dep ecia ion can be a policy op ion o
o e come he ze o lowe bound p oblems o nominal in e es a es. Fu he mo e, an
in e p e a ion o he economic e ec s o he ecen demone iza ion episode in India is possible
om he model.
Hence, in he p esen model amewo k, Gesell's claims can be e i ied o a sho - un
en i onmen . This may explain why he e has been enewed in e es in his way o hinking in
he p esen economic, pos -G ea -Recession si ua ion. One majo insigh o he analysis o Pa
I is, he e o e, ha in he sho - un, demand-de e mined equilib ium all o Gesell's claims can
be asce ained.
O cou se, he analysis aces se e al ca ea s. The se up o he model is simple. Al e na i e
u ili y and p oduc ion unc ions migh imply mo e complica ed equilib ia o he lack he eo .
The in oduc ion o iscal policy may make he esul s less clean. 'Lo e o weal h' was cap u ed
by a cons an . This begs he ques ion o how changes o e ime in he 'lo e o weal h' may bea
on he op imal pa hs. These and o he ex ensions o he model a e le o u he esea ch.
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Appendix
A Absolu e and ela i e weal h
Suppose he ela i e weal h o an indi idual 𝑖 is gi en by;
𝑥𝑖=𝑘𝑖
∑ 𝑘𝑗
The ela i e weal h is he (absolu e) le el o weal h 𝑘𝑖 in ela ion ( ela i e) o o al weal h
(weal h o all people). I ha indi idual's p e e ences a e 𝑢𝑖(𝑐𝑖,𝑥𝑖), hen consump ion 𝑐𝑖 and
ela i e weal h 𝑥𝑖 would ma e o pe son 𝑖 's wel a e.
I he e a e many people, 𝑗=1,…𝑁 whe e 𝑖∈[1,𝑁] wi h 𝑁 e y la ge, he e ec o
changes o 𝑘𝑖 by indi idual 𝑖 has no disce nible bea ing on o al weal h ∑𝑘𝑗 whe e he
summa ion is om 1 o 𝑁. ⬚
29
I he u ili y unc ion o indi idual 𝑖 is loga i hmic,
𝑢𝑖=ln 𝑐𝑖+𝛾ln 𝑥𝑖=ln 𝑐𝑖+𝛾ln 𝑘𝑖−𝛾ln ∑ 𝑘𝑗
hen he decisions o indi idual 𝑖 abou 𝑐𝑖 and 𝑘𝑖 would no ha e an e ec on 𝛾ln ∑𝑘𝑗 which
would be a da um o indi idual 𝑖. Tha ollows om he assump ion ha he e a e many people.
Those a gumen s jus i y wha is men ioned in he ex .
B De i a ion o equa ion (2)
The s eps leading o his equa ion a e
𝑐𝑡+(𝑘˙𝑡+𝑚˙𝑡)+(𝑛𝑡𝑘𝑘+𝑛𝑡𝑚𝑡)+𝜋𝑡𝑚𝑡+𝜎𝑚𝑡 =𝑤𝑡+𝑟𝑡𝑘𝑡+𝑥𝑡
𝑐𝑡+𝑎˙𝑡+𝑎𝑡𝑛𝑡+𝜋𝑡𝑚𝑡+𝜎𝑚𝑡 =𝑤𝑡+𝑟𝑡𝑘𝑡+𝑟𝑡𝑚𝑡−𝑟𝑡𝑚𝑡+𝑥𝑡
𝑐𝑡+𝑎˙𝑡+𝑎𝑡𝑛𝑡+𝜋𝑡𝑚𝑡+𝜎𝑚𝑡 =𝑤𝑡+𝑟𝑡𝑎𝑡−𝑟𝑡𝑚𝑡+𝑥𝑡
and so
𝑎˙𝑡=𝑤𝑡+𝑟𝑡𝑎𝑡+𝑥𝑡−𝑎𝑡𝑛𝑡−(𝑟𝑡+𝜋𝑡+𝜎)𝑚𝑡−𝑐𝑡.
Rea angemen yields equa ion (2) .
29
This is almos always assumed in his li e a u e. See, o example, Co neo and Jeanne (2001b).
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C De i a ion o equa ion (15)
F om (𝛿+𝛽)𝑐=(𝑟+𝜋+𝜎)𝑚−𝑟𝑎+𝜌𝑎 one ge s ha
(𝛿+ 𝛽)𝑐 =(𝑟− 𝑟)𝑚+ (𝜋+ 𝜎)𝑚− 𝑟𝑘+𝜌(𝑚+𝑘)
=(𝜋+ 𝜎)𝑚− 𝑟𝑘+(𝜋+𝜎)𝑘−(𝜋+𝜎)𝑘+𝜌(𝑚+𝑘)
=(𝜋+ 𝜎)(𝑚+ 𝑘)− (𝑟+ 𝜋+ 𝜎)𝑘+𝜌(𝑚+ 𝑘)
which becomes equa ion (15) by he Fishe ela ionship 𝑖=𝜋+𝑟.
D De i a ion o equa ion (16)
F om equa ion (14) we ge 𝑐[𝛿/𝑚−𝛽/𝑘]=𝑖+𝜎. Subs i u ing his in equa ion (15) implies
𝑐(𝛿+ 𝛽) =[(𝜋+ 𝜎)(𝑚+ 𝑘) −𝑐[𝛿/𝑚− 𝛽/𝑘]𝑘+ 𝜌(𝑚+𝑘)]
=(𝜌+𝜋+ 𝜎)(𝑚+ 𝑘) − 𝑐[𝛿(𝑘/𝑚) − 𝛽]
𝑐[(𝛿+ 𝛽) + 𝛿(𝑘/𝑚) −𝛽] =(𝜌+ 𝜋+ 𝜎)(𝑚+ 𝑘)
𝑐[𝛿+ 𝛿(𝑘/𝑚)] =(𝜌+ 𝜋+ 𝜎)(𝑚+ 𝑘)
𝑐𝛿[𝑚+𝑘
𝑚] =(𝜌+𝜋+ 𝜎)(𝑚+ 𝑘)
Rea angemen hen yields equa ion (16), ha is, he exp ession o 𝑐.
To ob ain he exp ession o 𝑖ˆ subs i u e he las exp ession o 𝑐𝑡 in equa ion (14) o ge ;
(𝜋+𝜎+𝜌)⋅𝑚
𝛿=(𝑖+𝜎)[𝛿
𝑚−𝛽
𝑘]−1
(𝜋+ 𝜎+ 𝜌)⋅ 𝑚
𝛿⋅[𝛿
𝑚−𝛽
𝑘]=(𝑖+𝜎)
F om his equa ion (17) and so he exp ession o 𝑖 ollows in a s aigh o wa d way.
E The ze o lowe bound on nominal in e es a es
In sho - un equilib ium he nominal in e es a e is a he ze o lowe bound, 𝑖=0, when;
(𝜋+𝜎+𝜌)((1−(𝑚
𝑘)(𝛽
𝛿))=𝜎
The o al di e en ial o equa ion (21) wi h espec o 𝜎 and 𝑚 yields
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(1−(𝑚
𝑘)(𝛽
𝛿))𝑑𝜎−(𝜋+𝜎+𝜌)(1
𝑘)(𝛽
𝛿)𝑑𝑚=𝑑𝜎
which can be simpli ied o;
−𝑑𝜎
𝜎(𝜎
𝜋+𝜌+𝜎)=𝑑𝑚
𝑚 o 𝑑𝜎
𝜎=−(𝜋+𝜌+𝜎
𝜎)𝑑𝑚
𝑚
This ela ionship upholds 𝑖ˆ=0 when one o he policy ins umen s is changed. Thus, a one-
pe cen inc ease in one ins umen equi es a co esponding pe cen age dec ease in he o he
one. Now ecall
𝑐∣𝜎=0,𝑖=0=(𝜋‾+𝜌)⋅𝑘
𝛽=(𝜋‾+𝜌)⋅𝑚0
𝛿 and 𝑐∣𝜎>0,𝑖=0=𝑚1⋅𝜎[𝛿−𝑚1
𝑘⋅𝛽]−1
whe e he indexa ion 𝑚𝑖,𝑖=0,1 exp esses he ac ha 𝑚 will be lowe when 𝜎>0, ha is,
𝑚1<𝑚0. I wan o check whe he 𝑐∣𝜎=0,𝑖=0⋛𝑐∣𝜎>0,𝑖=0. To his end le us suppose 𝑐∣𝜎=0,𝑖=0≤
𝑐∣𝜎>0,𝑖=0. Then (𝜋‾+𝜌)𝑘
𝛽≤𝑚1⋅𝜎[𝛿−𝑚1
𝑘⋅𝛽]−1,
whe e, o cou se, 𝑘=𝑘‾. Then ea angemen implies;
(𝜋‾+𝜌)𝑘
𝛽⋅[𝛿−𝑚1
𝑘⋅𝛽] ≤𝑚1⋅𝜎
(𝑘
𝑚1)(𝛿
𝛽) ≤𝜋+𝜌+𝜎
𝜋+𝜌 .
This inequali y also holds when one akes loga i hms. Thus, he claim would ha e o be ha ;
ln 𝑘− ln 𝑚1+ln (𝛿
𝛽)≤ln (𝜋+𝜌+ 𝜎) − ln (𝜋+ 𝜌)
Taking he o al di e en ial o his exp ession yields ha
−𝑑𝑚1
𝑚1≤𝑑𝜎
(𝜋+𝜌+𝜎)=𝑑𝜎
𝜎(𝜎
𝜋+𝜌+𝜎)
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would ha e o hold. Bu as can be asce ained om abo e, bo h sides o his inequali y a e equal
when 𝑖=0 is upheld. Hence, he in oduc ion o money dep ecia ion coupled wi h a lowe
money s ock when 𝑖=0 does no bea on consump ion in equilib ium when he economy's
in e es a e is a he ze o lowe bounds. This is he a gumen p esen ed in he main ex .
F Quo es
30
• "The ma e ial pa o he money has o economic li e abou he same
impo ance ha he lea he o a oo ball has o he playe s. The playe s do no
conce n hemsel es wi h he ma e ial o he ball, o wi h i s owne ship. Whe he
i is ba e ed o di y, new o old, ma e s li le; so long as i can be seen, kicked
o handled he game can p oceed. I is he same wi h money. Ou aim in li e is
an unceasing, es less s uggle o possess i , no because we need he ball i sel ,
he money-ma e ial, bu because we know ha o he s will s i e o egain
possession o i , and o do so mus make sac i ices. In oo ball, he sac i ices
a e ha d knocks, in economic li e hey a e wa es, ha is he only di e ence.
Lo e s o epig am may ind pleasu e in he ollowing: Money is he oo ball
o economic li e." (Gesell (1920), p. 78.
• "Money equi es he S a e, wi hou a S a e money is no possible; indeed he
ounda ion o he S a e may be said o da e om he in oduc ion o money.
Money is he mos na u al and he mos powe ul cemen o na ions. The Roman
Empi e was held oge he mo e by he Roman cu ency han by he Roman
legions. When he gold and sil e mines became exhaus ed, and coins could no
longe be s uck, he Roman Empi e ell asunde ." (Gesell (1920), p. 81.
• (*“Usually when a Ge man wan s any hing he also wan s he opposi e.",
Bisma ck. (Gesell (1920), p. 82.)
• "This e enue o he cu ency adminis a ion is an acciden al by-p oduc o he
e o m and is compa a i ely insigni ican . The disposal o his e enue will be
specially p o ided o by law. (*Fo o he me hods o applying he p inciple o
F ee-Money see page 245.) p.124"
• "In all concei able ci cums ances, in ai wea he and oul, demand will hen
exac ly equal: - The quan i y o money ci cula ed and con olled by he S a e.
Mul iplied by: The maximum eloci y o ci cula ion possible wi h he exis ing
comme cial o ganiza ion. Wha is he e ec on economic li e? The e ec is ha
30
These quo es may o may no be included in a published e sion.
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we now domina e he luc ua ions o he ma ke ; ha he Cu ency O ice, by
issuing and wi hd awing money, is able o une demand o he needs o he
ma ke ; ha demand is no longe con olled by he holde s o money, by he
ea s o he middle classes, he gambling o specula o s o he one o he S ock
Exchange, bu ha i s amoun is de e mined absolu ely by he Cu ency O ice.
The Cu ency O ice now c ea es demand, jus as he S a e manu ac u es
pos age s amps, o as he wo ke s c ea e supply. When p ices all, he Cu ency
O ice c ea es money and pu s i in ci cula ion. And his money is demand,
ma e ialized demand. When p ices ise he Cu ency O ice des oys money,
and wha i des oys is demand. Thus, he Cu ency O ice con ols he one o
he ma ke , and his means ha we ha e a las o e come economic c ises and
unemploymen . Wi hou ou consen , he p ice le el can nei he ise no all.
E e y mo emen up o down is a mani es a ion o he will o he Cu ency
O ice, o which i can be made esponsible. Demand as an a bi a y ac o he
holde s o money was bound o cause luc ua ions in p ices, pe iodic s agna ion,
unemploymen , and aud. F ee-Money makes he p ice le el dependen on he
will o he Cu ency O ice which uses i s powe , in acco dance wi h he
pu pose o money, o p e en luc ua ions. Con on ed wi h he new money
e e yone will be o ced o conclude ha he adi ional cus om o s o ing up
ese es o money mus be abandoned since ese e money s eadily dep ecia es.
The new money, he e o e, au oma ically dissol es all money hoa ds, hose o
he ca e ul householde , o he me chan and o he usu e in ambush o his
p ey." p. 127.
• "Unde F ee-Money, when sales slacken and p ices decline, he explana ion is
no longe gi en ha oo much wo k has been done, ha he e has been
o e p oduc ion. We now say ha he e is a sho age o money, o demand.
Whe eupon he Na ional Cu ency O ice pu s mo e money in ci cula ion: and
since money is now simply embodied demand, his o ces p ices up o hei
p ope le el. We wo k and b ing ou wa es o ma ke - ha is supply. The
Na ional Cu ency O ice hen conside s his supply and pu s a co esponding
quan i y o money on he ma ke - ha is demand. Demand and supply a e now
p oduc s o labou . The e is now no ace o a bi a y ac ion, desi es, hopes,
changing p ospec s, o specula ion, le in demand. We o de jus he amoun
o demand ha we equi e, and jus his amoun is c ea ed. Ou p oduc ion, he
supply o goods, is he o de o demand, and he Na ional Cu ency O ice
execu es he o de ." p. 134
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• "And Hea en help he con olle o he Cu ency o ice i he neglec s o do his
du y! He canno now, like he adminis a ion o he old Banks o Issue, en ench
himsel behind pla i udes abou ha ing o sa is y " he needs o comme ce". The
du ies imposed on he Na ional Cu ency O ice a e sha ply de ined and he
weapons wi h which we ha e equipped i a e powe ul. The Ge man ma k,
o me ly a ague, inde ini e hing, has now become a ixed quan i y, and o
his quan i y, he o icials o he Cu ency O ice a e held esponsible.
We a e no longe he spo o inancie s, banke s, and ad en u e s; we a e
no longe educed o wai ing in helpless esigna ion, un il, as he ph ase
used o be, " he s a e o he ma ke " has been c ea ed and imp o ed. We
now con ol demand; o money, he supply o which is in ou powe , is demand
- a ac which canno be oo o en epea ed o oo s ongly emphasized. We can
now see, g asp and measu e demand - jus as we can see, g asp and measu e
supply. Much p oduce - much money; less p oduce - less money. Tha is he
ule o he Na ional Cu ency O ice, an as onishingly simple one!" p. 134
• "Many o hose who ha e lea ned o sepa a e money om gold, who ha e
enounced he he esy o "in insic alue" and con inced hemsel es o he
impo ance o s able p ices will now be inclined o a gue as ollows: Why no
simply manu ac u e pape -money and b ing i in o ci cula ion as soon as supply
has o e aken demand o , in o he wo ds, when p ices begin o all? And
con e sely: Why no wi hd aw pape money om ci cula ion and bu n i when
demand begins o exceed supply, ha is, when p ices begin o ise? This is
me ely a ques ion o quan i y: a li hog aphic p ess and a i eplace pu i in you
powe o adap demand (money) so exac ly o supply ( he wa es) ha p ices
emain cons an ." p. 111
• "F eemoney is no edeemed by he Cu ency O ice. Money will always be
needed and used, so why should i e e be edeemed? The Cu ency O ice is,
howe e , bound o adap he issue o money o he needs o he ma ke in such
a manne ha he gene al le el o p ices emains s able. The Cu ency O ice
will he e o e issue mo e money when he p ices o goods end o all, and
wi hd aw money when p ices end o ise; o gene al p ices a e exclusi ely
de e mined by he amoun o money o e ed o he exis ing s ock o goods.
And he na u e o F ee-Money ensu es ha all he money issued by he
Cu ency O ice is immedia ely o e ed in exchange o goods." p. 123
• "The masses o pape money hoa ded by p i a e indi iduals (all p i a e o unes
would inally ha e assumed ha o m) migh any day ha e been se in mo ion
Re iew o Economic Analysis 16 (2024) 91-131
128
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by some i ial e en , and his money, being only edeemable in he ma ke in
exchange o goods, would suddenly ha e become an eno mous mass o
demand which he S a e would ha e been powe less o con ol by means o he
bonds and long- e m bills. " p. 156
• "The sale o he cu ency s amps c ea es a egula annual e enue o he
Cu ency O ice. This e enue o he cu ency adminis a ion is an acciden al
by-p oduc o he e o m and is compa a i ely insigni ican . The disposal o
his e enue will be specially p o ided o by law." p. 124
• "The money e o m dep i es he Banks o Issue o he p i ilege o issuing
bankno es. Thei place is aken by he Na ional Cu ency O ice which is
en us ed wi h he ask o sa is ying he daily demand o money.
• The Na ional Cu ency O ice does no ca y on banking business o any kind.
I does no buy o sell bills o exchange, i does no classi y business i ms as
i s , second and hi d a e.
• To pu ee money in ci cula ion all public easu ies a e ins uc ed o exchange,
when eques ed o do so, he old na ional me al money o pape money o ee
money; one dolla ( anc, o shilling) o ee money being gi en o one dolla
( anc, o shilling) o he old money.
• Anyone no consen ing o his exchange may keep his gold. No one will compel
him o exchange i ; he e will be no legal p essu e; no o ce will be employed.
The public is me ely wa ned ha a e he lapse o a ce ain e m (1,2 o 3
mon hs), he me al money will be only me al and no longe money. I by ha
ime anyone s ill possesses me al money he is ee o sell i o F ee Money o
a deale in p ecious me als, bu he mus ba gain abou he p ice. The only o m
o money ecognised by he S a e will be ee money. Gold, o he S a e, will
be a me e commodi y like wood, coppe , sil e , s aw, pape o ish oil. And
jus as oday axes canno be paid in wood, sil e o s aw, so gold will no be
a ailable o he pu pose o paying axes a e expi a ion o he e m o
exchange." p. 124.
• "Wi h Supplemen a y F ee-Money he legal dep ecia ion is compensa ed in each
ansac ion by a supplemen a y paymen by he holde o he no e, as a p esen
in many coun ies wi h he pu chase ax (sales ax). Theo e ically, he p inciple
o ee money could be applied by a con inuous egula in la ion o p ices o
5% annually, wi h, o p o ec c edi o s, a co esponding modi ica ion o long-
e m money con ac s. (Fo 18 yea s he con inuous i egula in la ion, wi hou
REHME Sil io Gesell's Schwundgeld Reconside ed, Pa 1
129
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modi ica ion o money con ac s, p ac ised by almos all coun ies, has ealised
one aim o ee money: he elimina ion o dep essions and unemploymen - bu
a he expense o c edi o s, and wi h many g a e economic dis u bances). " p.
205, he ansla o (1958). ⬚
31
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