Content uploaded by Andrés Álvarez
Author content
All content in this area was uploaded by Andrés Álvarez on Apr 18, 2016
Content may be subject to copyright.
Smoking or trading ?
On cigarette money in post WW2 Germany
Vincent Bignon∗
Preliminary version
University of Paris 10 at Nanterre, FORUM,
Bât. K, 200, avenue de la République;
F-92001 Nanterre cedex
e-mail : vbignon@u-paris10.fr
February, 2004
Abstract
Just after world war II, the German money at that time - the
Reichsmark - was refused in about 50% of the transactions of consumer
goods and had been replaced by barter or commodity moneys such as
cigarette. Surprisingly, this episode which is often mentioned (e.g.
Friedman 1951, Klein, 1976) has never been studied extensively. Using
german and US historical records, this paper built 1/ the history of
this cigarette money episode and 2/ a model explaining the use of this
commodity money. As we indicate, the appropriate framework to deal
with is the money search approach. Our model indicates that the use
of cigarette as money depends 1/ on the relative utility of smoking
relative to the consumption of other goods and 2/ on the importance
of the consuymption demand for this good.
Keywords : commodity money, search, Germany
JEL ClassiÞcation : D83, E40, N14
∗This paper was mostly written during my visiting stay at the University of Pennsyl-
vania. I acknowledged this University for the invitation and the emulating environment
it had provided to me and the Ecole Polytechnique which funded part of my visiting po-
sition at Penn. To wrote this paper, I have beneÞted from useful discussions and remarks
of Andres Alvarez, Regis Breton, Ken Burdett, Jean Cartelier, Xavier Cuadras Morato,
Pierre-Cyrille Hautcoeur, Jean-Paul Pollin, François Velde and Randy Wright. This paper
also beneÞted from helpfull comments made by participants of the 18th Congress of the
European Economic Association (Stokholm, august 2003), of the 4th workshop "Money
and Market" held in September 2003 at the University of Paris 10 - Nanterre and of the
52th congress of the Association Française de Sciences Economiques (Paris, September
2003). I thank them and stay, as usual, responsible of all remaining errors.
1
1 Introduction
The use of cigarette as money in Germany after world war II is one of the
most striking examples in economic history of a pure commodity money1.
Yet, despite its attracting intellectual power, little work has been done to
establish and explain the basic history of this episode, mentioned2,e.g.,.
by Friedman (1951) and Klein (1976). The silence of historical studies is
more surprising because the episode was not anecdotal: cigarette was used
by the whole German population during 3 years, from 1945 to 1948. A
better explanation of our silence lies in the lack of a suitable theoretical
framework to deal with this kind of event. The increasing research on the
microfoundations of money gives us such a framework. This paper presents
new historical facts on the use of cigarette as money and proposes a model
that can account for its use by the German population. More precisely,
we propose the Þrst description of the way exchanges were carried on in
post WW II Germany (very disorganized). This allows us to use the search
theoretic framework to analyze this historical episode. Then, we construct a
search model that can explain the differences in the means of payment used
by people, including the cigarette money.
From May, 1945 to the 20th of June, 1948 — when the Deutsche Mark was
introduced — Germany experienced a monetary crisis and became a barter
economy. Black market exchanges grew quickly to amount to 50% of all
exchanges of consumer goods (Menderhauser, 1949). The Reichsmark had
ceased to circulate as money in most illegal exchanges and had been replaced
by goods. All goods, in that economy, had been used as means of payments.
However, just a few of them — including cigarettes, chocolate and alcohol
— had became commodity moneys. Their main characteristics, compared
to other goods, was that everyone used it, at least partly, as money. The
probability of selling other goods to one agent taken at random was lower.
Some of these goods were partial intermediary of exchanges (non-consumer
of it have an interest to accept them in order to resell it to one consumer)
and the rest of the goods were only a mean of payment of direct barter trade.
This allow us to separate the set of goods used as means of payment into
three subsets. The Þrst one is commodity moneys (e.g. cigarette, chocolate,
alcohol), the second is partial intermediary of exchange (e.g. tires, butter,
1The other example of cigarette money, described by Radford (1945), took place in the
P.OW. camp during WW2. Nevertheless, the case of Germany just after WW2 seems to
be very important, involving more people and having more economic consequences than
the one of the P.O.W. camp.
2Steiger (1992) proposed a brief presentation of this episode.
2
coffee) and the third consists of goods only used in direct barter trade (like
ßour, potatoes...).
Everyone familiar with search models can easily understand the differ-
ence between direct barter goods and all the other goods. A good is used
only in direct barter if nobody has interest to used it as an intermediary of
exchange. Hence, partial intermediary of exchange and commodity money
shared the features that they were both used as money: Both consumers
and non consumers accepts commodity moneys and partial intermediary
of exchanges in payments. But there existed two main differences between
these: First, a partial intermediary of exchange is used by only a part of
the population as a mean of payment while the other part used it only as
consumption goods while cigarette circulates as money in the whole popula-
tion, implying that smokers partially renounced to its consumption. Second
and consequently, the size of the stock of a good used as partial intermedi-
ary of exchange has to be lower than the one of a good used as commodity
money3. This gives us an explanation of why external observers of this mon-
etary crisis often mentioned cigarette money but rarely partial intermediary
of exchanges: To know the difference between these two types of means of
payment, one have to deal with German archives on black market exchanges.
This brief sketch of the historical situation entails that there exists a
difference between intermediary of exchange as modelled in Kiyotaki and
Wright (1989) and the one modelled in Kiyotaki and Wright (1993). In
Kiyotaki and Wright (1989), the medium of exchange is close to our notion of
"partial intermediary of exchanges" in that just one subset of the population
use it as money while in Kiyotaki and Wright (1993), the Þat money can be
used by the whole population of traders. Burdett, Trejos and Wright (2001)
constructed a commodity money model based on Kiyotaki-Wright 1993 in
whichcigarettecanbeacceptedorconsumedbythewholepopulationor
not. Note that there exist a mixed strategy equilibrium in Burdett et alii
model, but this equilibrium cannot be interpreted as a situation in which just
one part of the population used cigarette as money (see Wright, 1999 and
Shevshenko-Wright, 2003). Hence, as we want to study how the introduction
of a sub-population of non-consumers of the cigarette affect the emergence of
the monetary equilibrium, we introduce three heterogeneous types of agents
in our model: suppliers of cigarette4,andapopulationofGermandivided
into smokers and non-smokers (to account for the facts that just one part
3This difference between commodity money and intermediary of exchange seems to
have been Þrst noticed by Menger (1909, p. 90).
4Corresponding in the historical case to the Allied soldiers that import cigarette from
their own country to Germany in order to sell them to German people.
3
of the population smoked). We also do not assume a random probability
of disappearance of a unit of cigarette as we think of cigarette as a typical
durable good. Then, at the monetary equilibrium, the only way to ensure
a steady state equilibrium, smokers has to smoke. This implies that the
only cigarette money equilibrium is the one in which smokers play in mixed
strategy regarding smoking or trading cigarette bought. This does not come
form a addiction of smokers to cigarette but simply to a comparison of the
utility to smoke with the utility to use it as a medium of exchange (which
is endogenous) and then foregoing its consumption.
In our model, the use of cigarette money is analyzed regarding two key
parameters: the size of the German smoker population (i.e. the size of the
demand for cigarette in the barter equilibrium) and the utility derived by
smokers when they smoke. The Þrst parameter can explain the appearance
of the partial monetary equilibrium (i.e. the one in which non smokers are
middlemen between the sellers and the smokers, their ’bid and ask’ coming
from the increased probability of obtaining their consumption good) while
the utility derived from smoking explains the use of cigarette as money by
the whole population. More precisely, the use of cigarette money by all sub-
populations implies that smokers forego the consumption of this good. This
could be the case only if the expected gain for trading cigarette is at least
equal to the utility of its consumption. This condition is fulÞlled if smoking
provides a relatively low utility compared to the one as a consumer good.
Hence, the historical record can be explained in that model because 1/ the
consumption of cigarette is not necessary for surviving and 2/ there exists a
prior demand for this good (i.e. smokers) and if this demand is sufficiently
large, people could have interest to use it as money just because its use
increases the probability of succeeding in a trade. Moreover, the model gives
us a theory of the difference in goods used as means of payment in post WW
2Germany.
The paper is organized as follows: the following section presents the
historical background of this cigarette money episode and match it with the
search assumptions. Section 3 describes the basic environment of the model
while section 4 studies equilibria. Section 5 concludes.
2 Historical background
The German monetary crisis can be characterized by huge changes in the
medium of exchange used for everyday purchases by the German population.
This process converged toward a refusal of Þat money and the emergence
4
of barter relationships and commodity moneys. The symptoms of this crisis
strongly differ from an hyperinßationary one, mostly because of the relative
stability of prices. Although we don’t have any national statistics5, the path
increase of regional price indexes between the end of WW II and June 1948
seems to have no common range with hyperinßationary one6. For example,
inthecaseofBavaria,the”official price index” increased by only 60% in
3 years following the war. The understanding of this situation, qualiÞed
as repressed inßation by Ropke (1947), implied to change the basic story
driving exchange behaviors: the consumer does not want to escape from
the effects of quick price changes but rather try to Þnd the goods he needs
without using Þat money. In this section, we present the basic environment
of German exchange economy during the period of the monetary crisis. The
Þrst sub-section deals with the period relevant with the way we study this
historicalepisode.Thereasonswhypeoplecametoexchangegoodsforgoods
in that economy are explained in the second sub-section. Finally, the last
sub-section presents the basic characteristics of cigarette money.
2.1 The process towards the barter economy
The demonetization of the German economy has roots in the monetary pol-
icy conducted by the Nazi regime to Þnance war. Between 1939 and 1945,
most of the governmental expenses were Þnanced through banks which sub-
scribed to almost all the public loans, thanks to deposits from the German
population. In 1945, this lead to a money stock that was 8 times bigger7
than the one of 1938. After WW II, the Þrst decisions taken by the 4 Allies
tended to decrease the total money supply, but it still remained 4 times big-
ger than the one of 1938 (at the same time, the industrial production of the
country had decrease to half of its 1938 level). Despite this huge increase,
no inßation appeared. The reaction of the Germans have rather consisted in
changes of their exchange behavior: Reichsmark tended to be ignored either
as a unit of account or as a way to pay purchases, as the following report of
the American military governor stated:
” Germany’s inßation today is a stagnant inßation. Instead
5After the defeat, the German state has collapsed and hence, there does not exist any
broader price index than the one constructed at the regional level.
6Remenber that the currently used deÞnition of an hyperinßationnary crisis was given
by Cagan (1956). He proposed the following criteria : a country experiences hyperinßation
when the rate of price increase is greater than 50% per month.
7300 billions of Reischmark as compared to 38,7 on the 31th of december, 1938, cf.
Samuelson (1972).
5
of rapidly rising prices destroying the value of money, a money
without value has tended to destroy the function of prices. To
an increasing degree the Reichsmark prices of good have become
subsidiary and formal appendages of purchase and sale transac-
tions or have even been eliminated entirely from transactions in
favor of a variety of direct barter ratios between goods, especially
between cigarettes and other goods ”
Monthly Report of the Military Governor 8n◦21
The German exchange economy did not became a barter economy overnight.
Moreover, the moment from which people renounce to Þat money is still an
open question. On the one hand, some historians, such as Brackman (1993),
sustain the view that the German monetary crisis began around 1942 and
1943, with the Þrst defeats experienced by the Nazi regime. On the other
hand, most of the contemporaries of this crisis, either German or Ameri-
can, thought that the refusal of the Reichsmark and the emergence of barter
transactions began late in 1945. Although our purpose is not to deal with
the starting point of this crisis, it could be interesting to note that, in No-
vember 1945, an official report of the US army gauge that the proportion of
illegal exchanges of foodstuffamounts to 20 % of the whole number of that
kind of exchange9. During spring 1946, 6 month later, this share has grown
to 50 % and the barter of luxury goods or clothes against food has tended
to be replaced by the one implying industrial goods against food10.Mostof
American officers who served in the economic division of the Office of Mili-
tary Government of United States (the military government that drove the
occupation of Germany, also called OMGUS) indicates that this proportion
seemstobestablefrom1946to1948.
Hence, the history of the German monetary crisis is better described
by dividing the events into two sub-periods. The Þrst one consists of the
process conducting the German population in the refusal of its Þat money,
with barter transactions emerging as an alternative way to carry on exchange
relationships.Thisprocessbeginswiththeendofworldwar2andendsin
1946. During the second period, from 1946 until the end of the German mon-
etary crisis, the basic environment of exchanges seems to be stationary: The
8Monthly Report of the Military Governor n◦21, feb-march 1947, section Price control,
p. 19 (Institut für Zeitgeschichte, Munchen, Germany).
9Cf. Monthly Report of the Military Governor of the US Army in Germany, report n◦5,
december 1945, section ”Trade and Commerce”. This report can be read at the Institut
für Zeitsgeschichte, Munchen, Germany.
10Cf. Monthly Report of the Military Governor n◦11, This report can be read at the
Institut für Zeitsgeschichte, Munchen, Germany.
6
1946
20th of June 1948
Monetary Reform that
replace the Reichsma rk
by the Deutsche Mark
May, 1945
End of WW2
The Reichsmark tend to be
less and less acceptable as
money,
Barter transactions emerged
Barter is used in half of all
transa ctions,
Stationnarity of strategies
regarding exchange
tec
hn
o
l
og
i
es
used
Barter disappeared,
the Deutsche Mark
is the only medium
of exchange us ed
Figure1:TimelineofeventsinpostWWIIGermany
share of barter trade in all transaction is estimated as constant by American
economic occupation staffand it seems there had been no great change in
the strategies of agents regarding barter or the use of commodity moneys.
This second period ends with the introduction of a new Þat currency on
the 20th of June, 1948 and the suppression of the old one (the Reichsmark).
Broadly speaking, the main point of this monetary reform was the exchange
of ten Reichsmark for one Deutsche Mark and the scaling down of all claims
in the same ratio. This sole change induced the disappearance of both all
barter transactions and commodity moneys. Figure 1 draws this sequence
of events in summary.
In this paper, we focus our historical study on the second period of this
monetary crisis. We take as given the fact that Germans have renounced
their Þat money before adopting the cigarette money. As showed by Bur-
dett, Trejos and Wright, this renouncement is a necessary condition to the
adoption of a commodity money. The following sub-sections present 1/ the
institutional framework surrounding and inßuencing the exchange strate-
gies chosen by German people and 2/ some basic facts regarding the way
cigarettes were used as means of payments.
2.2 What has driven the need for illegal exchanges ?
At that time, Germany was mostly an industrial economy and most of the
population consisted of workers selling their labor for money. The resurgence
of barter relationships is then very surprising as most of the population did
not have access to goods directly but rather by an intermediated system
delivering these through shops against the money earned. The establishment
and the generalization of barter have then entailed change in the way wages
7
were paid (with a growing part paid with goods) but also an increasing
share of direct exchange relations: many workers used their pay in kind to
transact directly with other workers or with farmers. Here, we review Þrst
the institutional (and legal) framework of exchanges. We then presents the
organization of the illegal exchange and Þnally discuss the way workers have
came to have access to goods.
2.2.1 The institutional framework of exchanges: The (in)efficiency
of the rationing system leads agents to conduct illegal ex-
changes
From the war, the Allied occupation Authorities inherited from a very highly
developed system of monitoring both the allocation and the prices of goods.
This system — created by War Economy Ordinance of the 1st of September,
1939 and usually called the rationing system — fulÞlled two functions, the
authorization of price increases and a centralized system of allocation of civil
goods11. People must work for some Þrms for a wage paid in Reichsmarks.
On the side of consumption, they received a monthly food and textile ration
that has to be paid with the RM and some ration ticket. The quantity of
goods delivered by the rationing system is decided monthly by an authority
takingintoaccounttheamountproducedbytheeconomy.
The aim of such a system was to regulate the economic life such that
all efforts have been directed towards the continuation of the war. In this
context, the rationing system had to guarantee the population a minimum
standard of living and a minimal disturbance of their economic life in a
context of an always growing money supply. The expected return for the
government was low disturbance in the labor supply and as a result the
production of weapons in a private property economy.
When Germany experienced the defeat — on the 8th of May, 1945 — the
disorganization of the economic system, mainly the transportation system
and the labor supply, was so great that production had been dramatically
reduced. This breakdown of the economy, documented by Botting (1985),
entailed major changes in the food supply and motivated an increase in
the number of illegal exchanges12 . Allies feared the risk of starvation and
11The delivery of goods is ensured by private shoppers but clients can make a purchase
only if they possess a rationning card composed of many coupons that are, together with
the Reischmark, necessary for the purchase of the quantity of food allowed by the card.
There exist many types of cards to discriminate the food ration between male and female,
workers, pensionners and young people. For a theoretical explanation of the rationning
system at that time, see Tobin (1952).
12see, e.g the report on ”price control, rationning and black market in Bavaria for
8
decided to continue the system of rationing the allocation of goods, with
some minor changes in the price policy of the administrative bodies in charge
of monitoring prices changes. The policy is clear from a proclamation of that
time ”All price regulation and management regulations which were effective
before the entrance of the American troops will continue to be valid”13.
But the efficiency of the rationing system, from the point of view of the
consumer, had been dramatically reduced with the end of the war. The daily
ration delivered to a normal consumer decreased from 1900 Calories per day
in 1944 to less than one thousand in June, 1945 (Backer, 1971). This gave
incentives to agents to Þnd some ways to supplement the daily ration. Some
decided to convert gardens to produces vegetables, others decided to carry on
illegal trades, i.e. exchange outside the rationing system. As indicate in the
report on ”Black Market operations in the American occupied zone” from
the 30th of July, 1945: ”In several of the areas where a black market exists,
it is primarily at the result of the urban dwells descending in mass upon the
surrounding countryside and purchasing food direct from the farmers without
beneÞt of price control or ration coupons”14.In the fall, 1945, ”the whole
Germany went offin search for calories” (Botting, 1985, p. 180). Of course,
the breakdown of the economy following the destruction of cities explains
part of the change in agents’ strategy. But, this change also had spillover
effects, due to the diversion of food entailed by illegal exchanges:
” There has been a noticeable loss of food from the normal
market channels due to the people from the city going to nearby
farms and buying on the spot. In Frankfurt, the local Pubic
Safety and Food and Agriculture Officer ordered the Regional
Food Office Director to combat the problem. (...) This has re-
duced the food available in the normal distribution channels to an
alarming degree and in one instance, Kreis Schültern, via Frank-
furt, an estimated 50 % of the dairy products failed to reach the
legal market. ”
”Black market operations in the American occupied zone”
(07/30/1945)15
the week ending the 22 of june, 1945” from the OMGUS (available at the Institut für
Zeitgeschichte, Munchen, document number 1/177 3/8, mark BICO C+J).
13Proclamation of the Allies, see document of the OMGB marked FOD, branch B,
Eichstätt, 9/138 1/7. Held by the Bayerische Hauptstaatsarchiv,Munchen,Germany.
14Document marked 1/177 3/8 BICO C+J available at the Institut für Zeitgeschichte
(Munchen, Germany).
15Document marked 1/177 3/8 BICO C+J available at the Institut für Zeitgeschichte
(Munchen, Germany).
9
2.2.2 The police Þght against the black market leads to the de-
velopment of disorganized illegal exchanges
To fulÞll this need for calories, German people could went to a black market,
i.e. a public place where sellers and buyers meet and exchange their goods.
This type of market did exist in post WW II Germany, it took place in the
most prominent locations in German cities. But it was not commonly used
by the population. People preferred searching for partners alone, without
meeting at established black market place. This kind of exchange was called
the ”grey market”. It was a very disorganized way to exchange goods either
because one needs to travel to the place of production ( in the case of urbans
going to the countryside to exchange with farmers) or because one needs to
meet someone randomly in a city. This counter intuitive choice (in favor of
the grey market) done by most of the Germans can be explained by the
action of the police against the black market.
Indeed,fromtheendofthewartilthemonetaryreformofJune,1948,
the police and the MP strongly fought all types of illegal exchanges. For
example, records of the police from Munich16 indicate that early in the
summer of 1945 police descended each day to prevent the establishment of
a black market in a well known place of Munich (i.e. Viktualen Markt).
This strong activity prevented the appearance of such a market place in all
cities of Bavaria17 — except Munich — for all the summer and fall of 1945.
After the winter of 1945/1946, black markets were established in strong
connection with some maÞa organizations [3, p. 82] but as noted earlier,
they saw very little activity. Although the police were successful in their
Þght against any well known market places, they did not have success in the
Þght against other kind of illegal exchanges. The intuition runs as follows:
Black markets were held mostly in the street of the city and consisted of
a crowd concentrated at a central point. Hence, it was very easy to Þght
against this form of illegal exchange simply by conducting a police raid at
that place. The nature of the grey market make it difficult to Þght because
it consisted of people moving independently to try to Þnd other people that
would exchange with them.
But the police activity did not prevent the carrying out of all illegal
16See documents marked 1/177 3/8, BICO C+J of OMGUS (Institut für Zeitgeschichte,
Munich), or those marked FOD, branch B, Bayreuth, 9/127 - 3/10 (Bayerische Haupt-
staatsarchiv, Munich) but also the records of the police marked MInn 72571 or MInn 72628
(Bayerische Hauptstaatsarchiv, Munich).
17From 1946 on, all cities in Bavaria had his own local black market. But the activities
of these markets were very limited. Menderhauser (1949) estimates their share in the total
number of transactions to less than 2%.
10
exchanges by the German population. This comes from the fact that the in-
efficiency of the rationing system gave incentives to achieve illegal exchanges.
Hence, anticipating the cost of being caught by the police on the black mar-
ket, Germans directed their search for suitable partners towards the grey
market because
” Only very few individuals or Þrms, however, Þnd it possible
to survive without engaging in barter. It is characteristic that the
practice has grown up as a self-help reaction without any public
or governmental program, and that the same people who reject the
principle — manufacturers, work-councils representatives, etc. —
have begun to trade along these lines. It has become axiomatic
for German business that production and the inßow of goods and
services depend on the provision of goods and services in direct
exchange. ”
Note on price control (06/18/1947)18
This induces a huge difference in the size of each market: The black mar-
ket activity is estimated to be about 2% of all the transaction of consumer
goods in post WW II Germany whereas the grey market represented about
half of the transaction of consumer goods19. This also induces a very unique
way to carry on illegal exchange as the Þght of the police against all types
of illegal exchanges had also consequences on the meeting technology used
by agents. On one hand, this entailed an incentive to exchange with family
member. But, as the goods searched were often not possess by relatives,
transactions had also to be carried on in anonymous meeting to lower the
probability of being denounced to the police. By the way, this kind of ex-
change had excluded the use of credit. The next sub-section presents the
activity on the grey market.
2.2.3 Decentralized trading and the rise of barter relationships
between specialized agents
On the ”grey market”, people really met according to a random matching
technology for them trying to exchange goods they possess against goods
18Available at the Institut für Zeitgeschichte, Munich under the mark 4/77 2-1 econ
Trade & Commerce, blatt 4/5 (OMGUS records).
19This is ascertain either by the economic report of the US army authorities (e.g.
Monthly Report of the Military Governor which can be read at the Institut für Zeit-
geschichte, Munich Germany) or by all of the observer (e.g. Menderhauser (1949) or Lutz
(1949)).
11
they want. The use of the grey market had entailed anonymous relationship
among sellers. Moreover, its very form has excluded the use of the Reichs-
mark as ”there is so desperately little goods available that those in possession
will not give anything up for mere money, on the chance that they can buy
what they need with the money”.
Given this ”good psychology”20,Þrms decided to pay part of the wage
in kind in order to keep their workers at work. Hence, although, legally, all
wages have to be paid in Reischmark, in fact quite all Þrms supplement the
monetary wage by adding some of the good produced. This payment took
various forms, as noted by Menderhauser (1949):
”Bilateralism in the employer-employee relationship took the
form of factory meals more substantial than the turned-in ration
coupons of the workers warranted, the sale of consumers’ goods to
the workers at legal prices but without permits (...). Naturally fa-
vored were the employers producing foods of general usefulness to
consumers. But where the productions was not suitable, or could
not be made so by the addition of special lines, goods for dis-
tribution to workers were obtained from other producers through
”compensation trade” or the workers were given factory products
that could be taken out to the peasants and bartered for food. In
this way, even a steel mill could satisfy its workers by giving them
Thomas fertilizer and steel bands for the wheels of peasant carts”
Menderhauser, 1949, p. 657
As a consequence, each worker have a continuous access to goods he
can bartered on the grey market. This change of Þrms’ behavior is obvi-
ous from 1946. This goods’ endowment by employers replace the selling of
personal items that wages owners have done during 1945 when they paid
their purchases to farmers with their jewelry, radio or clothes. But Þrms
were specialized in the type of goods they produce and workers had to com-
plete the ration for all their family to survive. This gives rise to a search for
suitable medium of exchange that would increase the probability to succeed
in making an illegal exchange with a randomly selected agents. Among all
the goods, cigarette was the most famous and the most used medium of
exchange. But chocolate or alcohol also fulÞlled such goals together with
barter, as noted by the following report:
20report ”InßationandtheBMinGermany”,document of the OMGUS marked FIN
17/5, BICO FIN group. Available at the Institut fur Zeitgeschichte, Munich.
12
”Detachment A-250 Bad Kissingen and Det. E-237 Ingolstadt
call attention to the fact that it is customary in the British zone
for employees to receive part of their wage in industrial goods
in order to barter these items against food in Bavaria and other
lands. Over 300 pounds of fat were recently conÞscated by the
local police of Ingolstadt from people working in the British zone.
Another large catch in Landeskreis [canton] Ingolstadt consisted
of 1100 pounds of canned meat, which was to be shipped to
a railroad trade union in the British zone, admittedly acquired
through unauthorized barter transaction.”
Intelligence Report of the 02/11/194821
2.3 Cigarette money and means of payment in post WW II
Germany
In this section, we Þrst present the three types of means of payment in good
used during the monetary crisis and then concentrate on cigarette money by
presenting the reasons that could have driven the use of cigarette money
and the characteristics of the ”market” for cigarettes.
2.3.1 Supply and demand of commodity moneys’ goods in the
German barter economy
Three types of means of payments were used during the monetary crisis. The
Þrst one implied a direct barter exchange. In that kind of meetings, agents
matched exchanged their good without needing to exchange. The next two
sub-sections presents the reasons that can explained the use of cigarettes as
money and the characteristics of the ”market” for cigarettes.
The following table resumes these three types, give examples and de-
scribes their main characteristics.
There are reasons to think that cigarettes, chocolate or alcohol were
more acceptable than other goods. First, all of these goods are demanded
by the population while the supply of these good were very low. Let us
take the example of the cigarette. The newspaper Die Welt (05/08/1947,
cited by Ruland, 1968, p. 58-59) estimated the demand for cigarettes22 in
21see record of the Office of military government Land Bavaria marked ODI 7/36-2/4
p. 2/17 (available at the Institut für Zeitgschichte, Munich).
22Estimated from the average consumption of 1938 time the population of Germany
after WW II.
13
Means of payments Examples Main characteristics of exchanges and goods
Commodity mone ys
- cigarette,
- chocolate,
- alcohol, candy bar
- “Universal use as money” : each German used it as money
- consumption of these goods did not collapsed entirely
- A cigarette can be exchanged 100 times before being smoked
Partial Intermediary of
exchange (indirect
barter)
- Butter, coffee,
meat…
- tire, coal, gas
- Relatively scarcity of these goods : People value them a lot for
consumption
- This kind of good was not exchanged many times before being
consumed
Direct barter
shoes, saucepan,
cement, flour,
potatoes
To succeed in such a trade need either “chance” (random search) or
the help of someone who direct your search for partner
Figure2:ThethreetypesofmeansofpaymentinGermanbartereconomy
post WW II Germany to about 80 thousands of tons whereas the local pro-
duction amounted for only 30 thousands. Locally produced tobacco came
mainly from 2 regions of the south of Germany: Schwaben (for 50%) and
Pfalz (30%). The official imports of tobacco ceased with the entry of Allied
troops in Germany, as Allied government did not want to pay for the German
consumption of that good. Hence, despite the fact that the local production
had could grown up through the growing of new plants of tobacco by farm-
ers (Ruland, 1968), German smokers experienced a more difficult access to
cigarettes through the legal channel and especially rationing23.
In the same time, as indicated by Proctor (1999), the consumption of
cigarettes by Germans increased sharply during the war. We can then con-
clude that the demand for cigarette were high while, in the same time, this
good was less available to consumers. This situation entailed the emergence
of three new forms of tobacco supply, localized mostly in the cities. First,
traffics of cigarettes grew up with the establishment of illicit imports of ciga-
rette from Czechoslovakia, Hungary and Belgium24. Second, another type
of traffic emerged with the establishment of new "factories" of cigarettes
produced from cigarette ends25 (Botting, 1985). Third Allied soldiers had
23The cigarette delivery has been integrated to the rationning system around 1942, see
Singer (1943).
24See documents of the bavarian police at the Bayerische Haupstaatsarchiv in Mu-
nich (marked Innerministerium) or at the Institut für Zeitgeschichte (OMGUS documents
marked Black Market).
25The people who done that were called the ”Kippensamler”. Their work consist in
buying cigarette butts to barman and then to use these to produce new cigarettes. A
14
become dealers in cigarettes that they imported from their own country26.
These cigarettes were either sold by the soldiers against goods or they gave
them to their German "girlfriend". Most of these traffics were done on the
black market established mostly in cities. This indicates that the supply of
cigarettes was done by only few people while the demand for that good was
relatively important.
This situation entails the emergence of three new forms of tobacco sup-
ply. First, in few part of Germany, farmers had came to offer tobacco in sale.
Second, traffics grew up with the establishment of illicit imports of cigarette
from Czechoslovakia, Hungary and Belgium27.Anothertypeoftraffichas
consisted in the manufacture of new cigarettes from cigarette ends (Botting,
1985). The people who done that were called the ”Kippensamler”. Their
work consist in buying cigarette butts to barman and then to use these
to produce new cigarettes. A tumbler of cigarettes butts was paid 5$ to
the barman and 7 butts make 1 cigarette. With this cigarette, one could
obtained one meal in a restaurant. Third, and perhaps less anecdotal, al-
lied soldiers had became dealers in cigarettes they imported from their own
country. The US military government for Germany (cited by the New York
Herald Tribune, 05/17/1947) gauge to about one thousand tons per month
thequantityofcigarettesimportedbyAmericansoldiersin1947.
The supply of chocolate was quite inexistent in the rationing system
since the beginning of the war and, after the defeat, most of it consisted in
Allied soldiers selling chocolate bars on the black market. For alcohol, the
increase of taxes on beer and other alcohol28 together with the restriction
in the supply of good necessary to produce them induces a decrease of their
production and agents seemed not have stopped to consumed it. While some
of the production of alcohol was done by farmers themselves, part of the
selling also came from Allied soldiers (for imported alcohol like cognac which
was not produced in Germany). Hence, for these 3 goods, the two intuitive
conditions for them to be used as a medium of exchange are fulÞlled: they
are mostly sold in the cities and Germans farmers could not easily gained
tumbler of cigarettes butts was paid 5$ to the barman and 7 butts make 1 cigarette. With
this cigarette, one could obtained one meal in a restaurant.
26TheUSmilitarygovernmentforGermany(citedbytheNewYorkHeraldTribune,
05/17/1947) gauged to about one thousand tons per month the quantity of cigarettes
imported by American soldiers in 1947.
27see documents of the bavarian police at the Haupstaatsarchiv in Munich (mark Inner-
ministerium) or at the Institut für Zeitgeschichte for OMGUS documents.
28For example, taxes on beer increased of 50% in the Þrstyearofthewar(cf. Singer,
1941) and taxes on all types of alcohol increased of 22,45% in 1945, as one of the Þrst
decision of allied armies (cf. Guggenheim, 1965, p. 39).
15
access to them, except if they went to a black market in one of the city.
This indicates that the supply of cigarette (or other commodity moneys
but, for simplicity, we will use cigarette as the "representative" commod-
ity money) was done by only few people while the demand for that good
was relatively important. This could be used to address the question of why
cigarettes had been chosen as money in post WW II Germany. As the pro-
portionofsmokersunsatisÞed by the legal rationing system, it could be the
case that agents had came to buy cigarette simply to resell it to smoker. It
could also be the case that German smokers had came to renounce to the
consumption of this good because its utility in consumption was lower than
its utility as a medium of exchange. But in any case, as the proportion of
cigarettes sellers was relatively low, agents could also have interest to barter
directly their good. This could explain the coexistence of cigarette money
andbarterinpostWWIIGermany.
2.3.2 Explaining the use of commodity moneys: the example of
cigarette
Cigarette money had a universal acceptability in post WW II Germany
— everybody accept them for payment. However, contrary to exchanges in
modern exchanges economy with Þat money, the use of commodity money
did not have ruled out the use of barter, direct or indirect. In this section,
we give some historical pieces of information on the reasons that could have
drove the universal acceptability of commodity moneys.
Many reasons (or many frictions) can explain why agents had come to
use a commodity money rather than direct barter. One can think of three
main reasons: the divisibility of the good choose as commodity money, the
standardized character of this good and the difficulty of exchange. Here, we
argue that the Þrst and third reason can be thought as a key elements driving
the choice of good as commodity money in the German barter economy.
The second element is much more difficult to deal with as the quality of the
supply of good has to be endogenous in equilibrium (people can counterfeit
cigarettes). In this section, we concentrate on the advantage of cigarette
compared to other goods. But note that many advantages of cigarette were
also shared by chocolate and even alcohol.
Without doubt, the difficulty to Þnd a double coincidence of wants is a
driving force for using an intermediary of exchange. It’s harder to succeed in
a trade when you possess a good that are not highly demand. In such a situ-
ation, one can think to sell his speciÞc good against a more demanded good,
in order to increase the probability of a double coincidence of wants meeting.
16
Using the concepts used by the basic model of Kiyotaki and Wright (1993),
the use of a medium of exchange increases the probability of succeeding in a
trade simply because it entails to succeed in two single coincidence of wants
meeting rather than waiting for a partner that want what you have when
youwantwhathehave.WhenÞat money is not accepted as a medium of
exchange, agents has to Þnd another object that can fulÞll this role. In this
paper, we argue that, in a context in which barter was difficult (because of
the meeting technology), the choice of cigarette as money can be explained
by the fact that it was highly demanded by Germans whereas the supply of
cigarette was relatively small.
Another friction that could have drove the use of cigarette as money
is undoubtedly the divisibility character of cigarettes (compared to other
goods like saucepan or radio). The following statement made by the Herald
Tribune of the 28th of February, 1947 is one example:
”A lot of them [cigarettes] undoubtedly end up in the hands of
farmers because cigarettes are a way of getting food (...) In Ger-
many, cigarettes lubricate the trade. For instance, if a Berliner
has a large radio that he has decided to sell, he cannot conve-
niently lug it out into the country in search of a farmer willing
to give him butter for it. Instead, he trades it to a black marke-
teer for cigarettes and takes the cigarettes to the farmer. This
has had advantage that he can dispose of the cigarettes bit by
bit instead of having to accept a whole radio’s worth of butter at
one time. Meanwhile, the black marketeer takes the radio to an
American officer who gives him more cigarettes. With these he
can get another radio or butter or whatever he needs to carry on
his trade. Then he can sit down and smoke his proÞt — or a part
of it.”
Herald Tribune 02/28/1947
This argument of the advantage of cigarette over radio due to its divisi-
bility is closed to the one proposed by Berensten and Rocheteau (2002). This
search model of money construct an environment in which both money and
goods are divisible. By relaxing the assumption that each agent has to spend
all his money stock for buying a divisible goods, they address the question
of the effect of this assumption on the efficiency of a bargaining between two
agents. They Þnd that the divisibility of both goods and money generates
gains from trade compared to the case studies by Trejos and Wright (1995).
Despite its interest, we will not explore this reason in our explanation of the
cigarette money acceptance.
17
Finally, the standardized character of cigarette could help to its use as
money. We need to be very careful when considering this reason because
the historical records learn us that the counterfeiting of cigarette was very
common in post WW II Germany (Suddeutsche Zeitung, 08/09/1946) so
that there exist middlemen specialized in the inspection of both the weight
and the quality of cigarettes (Botting, 1985).
3 A model of cigarette money with heterogenous
populations
In this section, we use the historical informations given by the preceding
section to construct the basic environment of a model which can explain
why cigarette money had been accepted by the whole German population
during the monetary crisis. This model can also explain the differences in
means of payments used by the German population of that time (i.e. direct
barter, indirect barter and commodity moneys). The following sub-sections
match the historical situation with search models’ assumptions, construct an
environment to deal with this assumption, derive the corresponding Bellman
equations and solve the equilibria to know the conditions under which agents
decide to a good as money.
3.1 Matching the situation with search models’ assumptions
The preceding part of that paper has learned us that agents found few goods
in the rationing system, that they had incentives to carry on illegal exchanges
and that they did them in a very disorganized way, i.e. by searching ran-
domly in cities or in the countryside to exchange what they have against
what they want. As the size of the black market is negligible compared to
the one of the grey market, we will abstract from this feature. The inef-
Þciency of the rationing system in providing sufficient living conditions to
Germans is not explicitly modeled although this fact is used to motivate our
assumption on the need for illegal exchanges. These are equivalent to sup-
pose that there was no interdependence between the 3 main ways to conduct
exchanges at that time29 .
To know how the exchange strategy were chosen by the agents, we con-
struct a model that try to "reproduce" the environment of illegal exchanges
on the grey market. By this, we want to understand the exchange process
29This assumption is only made for simplicity but future research has to be made on
the interlinks between these markets.
18
during the crisis in order to 1/ underline the close link between the histor-
ical situation and the search-theoretic framework and 2/ understand why
many types of transaction technology have coexist on the grey market dur-
ing this crisis. Then, the model presented here must then be seen as a Þrst
step to clarify the many ways people used to Þnd the goods they want to
consume. Before describing the model, we want to emphasize the closeness
between the German monetary crisis and the search-theoretic framework30 .
The methodology used by the search-theoretic approach to monetary eco-
nomics consists in constructing an environment in which it is possible to
address the issue of the type of transaction technology used, in equilibrium,
by the agents. This distinctive feature of monetary search models has been
emphasized by Wallace (1998):
"As noted above, the proposed dictum is that money should
not be a primitive in monetary theory. It is easy to describe in
the abstract how to construct model that satisfy this dictum:
specify the physical environment and the equilibrium concept
of the model in a way that does not rely on the concept called
money or force the modeler at the outset to specify which objects
will play a special role in trade (...) Given such a speciÞcation,
the model determines — but in general, not uniquely because
there may be multiple equilibria — the values of the different
assets and their distinct roles, if any, in exchange."
Wallace, 1998, P. 22
In other words, the pattern of exchange observed in a situation is the
result of an equilibrium. The explanation of this pattern needs then to be
derived from a model that just described the environment in which agents
have to carry on their transactions. The environment mainly consists in
the 1/ the existence of agents endowed with preferences and a technology
of production, 2/ a meeting technology describing how agents get in touch
with each other and 3/ a spatial separation between agents so that there
does not exist a centralized market (because this assumption will entail that
there is no need for agents to used decentralized transaction technology such
as money...).
We then have to conclude that the matching between our historical case
and the search theoretic approach has to rely on a basic correspondence be-
tween what we observed in the environment of exchanges during the German
30For a presentation of the search-theoretic approach to monetary economics, see Rupert
et alii, 2000 and 2001.
19
monetary crisis and the basic assumptions of search models. This correspon-
dence can in no case be perfect, but there has to be some correspondence in
order to have the right to interpret the results of the model as informative
for understanding the historical case. A brief remember of the facts isolated
aboveindicatethat:
1. Germans were still specialized in the production of one good and this
production did not fulÞlled all their needs. Hence there existed a need
for exchanges, and, as part of the wage was paid in kind, Germans
had goods to barter. These imply that one of the main friction of the
exchange process was the search for a double coincidence of wants.
2. Germans people (contrary to Þrms) did not use some communica-
tion technology enabling them to overcome the problem associated
with Þnding a partner. Hence, agents could not overcome the double
coincidence problem by directing their search to some partners they
had contacted before entering the market. This creates a need for a
medium of exchanges that would increase the probability to succeed
in exchanging in a meeting.
3. There were no intermediation on the grey market: all meetings imply
two producers.
4. As there was no central place on which agents can meet on the grey
market, the search for suitable good can not be directed and we can
presumed that a lot of meeting did not entailed an exchange. Hence, as
agents have renounced to use the (organized) black market to buy the
food, meetings on the grey market were very disorganized,. The search
for partners (in the city or in the countryside) was then "random" and
conducted quite independently from the others. Moreover, the way
exchanges were carried on imply that there were few chances to have
contact with another agent while soon involved in a meeting. This
implies time search cost for an agents to get in touch with a partner.
This also indicates that the meeting technology assumed in the basic
search model (Poisson process) is relevant for our study.
To bridge the gap between history and search models of money, we have
to make an assumption on the goal/objective of Germans people when they
carried on exchanges on the grey market. In this model, we assume that
their objective was to Þnd consumption goods by the less costly way (i.e.
they try to Þnd the best way to acquire them, taking as given the type of
good they possess).
20
3.2 Basic environment
Time is inÞnite and continuous, that agents live forever and discount future
at a common rate r(>0).To encounter from the difficultytofoundapart-
ner and to the random search for partner on that market, we will suppose
that agents in our model meet randomly according to a Poisson Process of
parameter α. To take into account the way cigarettes were introduce in that
economy, we will suppose that the population is divided into 3 parts: sellers
of cigarette (Allied soldiers, proportion proportion aof the population),and
German (proportion G), who could be either smokers (µG)or non smokers
((1 −µ)G).For ease of simplicity, the whole population will be supposed to
consistofacontinuumofagentsofmass1.Hence
Ω=g+a=a+µg +(1−µ)g=1
To account for the differences between cigarette and industrial goods, we
assumethereexist2typesofgoodsthatdiffers regarding the population that
can produce them and regarding the utility they gave when consume. The
cigarette is supposed to give a utility sand the industrial good (hereafter
special good) a utility u. The specialization of agent in production is taken
into account by assuming that German can produce only one type of the set
of special goods although the allied soldiers can only sell cigarettes. This is
rationalize by assuming that sellers of cigarettes beneÞted from a technology
allowing them to import cigarette while Germans did not have access to this
technology.
The production of one special good is instantaneous and is made with
cost cin terms of utility. Allied soldiers are endowed with cigarette with the
same assumptions. Cigarette and special goods come in unit of size one and
cannot be divided (this ruled out the possibility that agents bargain over
the prices of the goods exchanged). All goods are storable without cost by
their producer31 andcigarettecanalsobestoredbyalltypesofagents.An
agent holding a stock cannot produce.
All agents have preferences over special goods, but they derive utility
only from consuming a part xof this type of goods. This proportion can be
seen as he probability of a double coincidence meeting. A proportion µof
the German population also derive a positive utility to consume cigarette
(i.e. the smokers). Preferences over special goods are modelled as in Rupert
et alii (2001): in each trade between agents iand j, there is a probability
31because of the way preferences are modelled, nobody has interested in that economy
to store a good he does not produce (see Rupert et al. (2001)).
21
xthat iwants to consume the special good produced by j(that is agent i
derives a utility u>cfrom consumption). The probability that jwants to
consume the special good produced by i, knowing that iwant to consume
the good produced by jis denoted by y. Then, a double coincidence meeting
occurs with probability xy.
Given the assumptions made, the exchange process is modelled as fol-
lows: Agents meet bilaterally according to a Poisson process with parameter
α. Upon meeting, agents trade if mutually agreeable, e.g. an exchange oc-
curs if each agent is no worse offafter trading. As goods and money are
indivisible, each trade is a one for one swap. Every trade is either a trade
of one special good for another special good, or a trade for one cigarette
against one special good (between one agent with 1 unit of cigarette and
one agent with 0 unit of cigarette).
We will use this basic environment to study when a special good holder
has interest in accepting a cigarette as payment of his special good, even if
there exists a difference between the utility to smoke and the one to consume
a special good. For that purpose, we will compare the net gain to be a special
good holder to the net gain to be a cigarette holder by using the Bellman
equation derived in the next subsection.
3.3 Bellman equations
Let Ui(i=0,1) be the value function of German non smoker and Vibe
the value function of German smoker. The value function of the seller of
cigarette is omitted because they doesn’t have to take any strategic choice.
Then the Bellman equation of this model are deÞned as follows:
rU0=αxyg (1 −C)(u−c)+αx (gC +a)π(U1−U0−c)(1)
rU1=αxg [µ(1 −m)+(1−µ)(1−n)Π](u+U0−U1)(2)
rV0=αxyg (1 −C)(u−c)
+αx (gC +a)max
φ∈[0,1] [φ(s−c)+(1−φ)(V1−V0−c)] (3)
rV1=αxg [µ(1 −m)+(1−µ)(1−n)Π](u+V0−V1)(4)
Such equations are now standard in the search literature. Let us give
an intuitive explanation of equation (1).U0indicates the expected gain of
an German agent who is non smoker. When holding his production goods
for exchange, he can Þrst meet, with probability α, another German agent
who also holds a good (proportion (1 −C)of all Germans and there is a
double coincidence of wants (with probability xy). In this case, exchange
22
takes place immediately, agents consumes and produces a new unit of his
production good. He can also meet, with probability α, either an Allied
soldier (probability a) or a German holding a cigarette (gC). If with one
of this 2 agents a single coincidence occur (i.e. the soldier or the German
holding cigarette wants to consume the special good, probability x), then a
trade occurs iffthe special good holder accept the cigarette as payment. This
decision is taken if the net gain of accepting cigarette is positive: he accepts
cigarette as payment if the gain associated to this decision is greater than
the one associated with staying a special good holder (∆π=U1−U0−c).
The strategy of this agent regarding cigarette is resumed by the strategic
variabl e π.
Equation ?? has a similar interpretation except that this agent has to
decide, when someone proposes him a cigarette as payment, if he wants to
consume the cigarette or to store it and then become a cigarette holder. He
takes his decision by comparing the gain associated to smoke the cigarette
and then stay a special good holder with the one associated to trade ciga-
rette in the future, in which case, his gain is resumed in 4. the strategic
variable associated with this decision is φwhich value is determined by the
sign of ∆φ=V1−V0−s. Note that when s<c, no one accept cigarette in
this economy and then cigarette cannot become a money. Hence, we assume,
for the rest of the paper that s>cwhich imply that smokers always accept
cigarette as payment for their special good. Their only strategic question
is whether they want to consume it or to store it (at no cost).The follow-
ing correspondences resume the decision taken by the non smoker and the
smoker:
∆π>0⇔πn=1
∆π=0⇔πn∈[0,1]
∆π<0⇔πn=0
and
∆φ>0⇔φ=0
∆φ=0⇔φ∈[0,1]
∆φ<0⇔φ=1
(5)
Using the above Bellman equation, solving for symmetric equilibria in
which π=Π,and after some algebra, we Þnd the following best response
conditions:
∆π=αxg (µ(1 −m)(1−y)+(1−µ)(1−n)(π−y)) (u−c)−rc
r+αx [Aπ +gµ [mπ +(1−m)] + g(1 −µ)π](6)
and
∆φ⇔µαxg [µ(1 −m)+(1−µ)(1−n)π](u−s)
−αxyg (1 −C)(u−c)−αx (gC +a)(s−c)−rs ¶
(r+αxa (1 −φ)−αxgCφ +αxgµ +αxg (1 −µ)[n+(1−n)π])
(7)
23
3.4 Steady State conditions on the stock of cigarettes
The stock of cigarette held by the Germans is C=µm+(1 −µ)nwith mthe
proportion of smoker holding cigarette compare to the population of smoker
and nthe proportion of non-smoker holding cigarette in the population of
non-smoker). The study of steady state equilibria implies that we have to
deÞne the ßow of cigarette held by the German population (i.e. úm, ún, ú
C).
Moreover, we need to determine úm=ún=ú
C=0.Ta ke the e x ampl e o f n:n
increaseseachtimeanonsmokerwithoutcigarette(g(1 −µ)(1−n)), who
accepts cigarette as money (πn), meets (α)1/anAmericanwhowantshis
good (xa) and each time he meets an smoker who like his good (xgC ). And n
decreases each time a non smoker who have 1 cigarette in stock (g(1 −µ)n)
Þnd a smoker without cigarette (gµ (1 −m)) and exchange is possible (x).
Hence, ún=0is deÞned by the following equation:
ún=0⇔(1 −n)(gµm +a)πn=n[gµ (1 −m)] (8)
The computation of the value of mfollows the same strategy: min-
creases each time a German smoker without stock (gµ (1 −m))meets(α)
an American (a)oraGermannonsmokerwithcigarette(g(1 −µ)n)who
likes his goods (x) and the smoker doesn’t consume it ((1 −φ)). Conversely,
mdecreases each time one smoker with cigarette (gµm)meetsanonsmoker
without cigarette (g(1 −µ)(1−n)) and exchange is feasible (xπn)andeach
time he meets a smoker without cigarette (gµ (1 −m)) and this one smokes
(φ) rather than stocks the cigarette exchanged when the exchange is feasible
(x). This gives us úm=0:
úm=0⇔(1 −m)(1−φ)(g(1 −µ)n+a)=m·gµ (1 −m)φ
+(g(1 −µ)(1−n)πn)¸
(9)
Cincreases when Americans (a) succeed in dealing cigarette against
goods (αx) with either 1 non smoker without cigarette (g(1 −µ)(1−n)πn)or
1 smoker without cigarette (gµ (1 −m)) who decides to stock this cigarette
((1 −φ)). Cdecreases each time a smoker without cigarette (gµ (1 −m))
smokes (φ) one cigarette he has acquired in exchange for good (αx), and
that cigarette comes from the existing stock held by the German people
(g(1 −µ)n+gµm =gC). Hence, we can write:
ú
C=0⇔a[g(1 −µ)(1−n)πn+gµ (1 −m)(1−φ)]=gµ (1 −m)φgC
(10)
24
4 Equilibria
We Þrst begin by deÞning a steady state equilibrium and then discuss about
the one interesting to solve for our purpose.
DeÞnition 1 A steady state equilibrium is a n-uplet (m, n, C, ∆π,∆φ)that
satisfy the best response conditions 5 — with ∆πdeÞned by 6 and ∆φby 7 —
andsuchthatm, n, C —asgivenbyequations8,9and10—∈[0,1]
There potentially exists 8 equilibria. However, this set of candidate equi-
libria can easily be reduced just by thinking about conditions they must
fulÞll. Take, for example the equilibria with πn=0and φ=0.The sole
inspection of the best response condition indicates that this could not be
an equilibrium because of the assumption that s>c(which is necessary
for the acceptation of cigarette by the German smokers). Moreover, the two
equilibria where φ=1(i.e. when German smoker play in pure strategy
and accepts cigarette only as money) cannot exist without the violation of
steady state condition on m, n and C. For now on, we use this model to
answer to the three following questions:
1. For what parameters values does the equilibria with cigarette money
be ruled out ? This conducts us to study the barter equilibria (πn=
0,φ=1)
2. For what parameters values do non-smokers decide to use cigarette as
money ? ⇒study of equilibria with (πn=1,φ =1)
3. What are the conditions under which the whole population use ciga-
rette as money ? ⇒study of equilibria with (πn=1and φ∈[0,1])
The following 3 subsections are devoted to the answer of these questions.
4.1 Existence of the barter equilibrium
The study of this equilibrium tells us the answer to the Þrst question because
at this equilibrium, nobody accepts the cigarette as money. Hence C, m and
nare equal to 0in equilibrium and (πn,φ)=(0,1) ⇒∆φ<0and ∆πn<
0.We then just have to check the best response conditions to characterize
the region of the parameter space in which this equilibrium exists. ∆πn<0
25
imply that
∆πn=αxg (µ(1 −y)−(1 −µ)y)(u−c)−rc
r+αx [Aπ +gµ [mπ +(1−m)] + g(1 −µ)π]<0
⇔µ<µ
1=y+rc
αxg (u−c)
ForGermansmoker,weobtain:
∆φ⇔(αxgµ (u−s)−αxyg (u−c)−αxa (s−c)−rs)
(r+αxA (1 −φ)−αxgCφ +αxgµ +αxg (1 −µ)[n+(1−n)Π]) <0
⇔s>s
1=gµu −(gy +a)c
gµ +a+r
αx
We then see that cigarette is not accepted in equilibrium by non smokers if
barter is too easy relative to the prior acceptability of money in the pop-
ulation and if ris too high. For smoker, the refusal of cigarette as money
depends on the same principal parameter except that their behavior also
depend on the utility of smoking. It is easy to show that the condition of
non-smokers is always higher than the one of smokers. This is ascertain by
the fact that (u−s)
(u−c)<1and rs > rc. Hence, the condition for this equilibrium
to exist is only y1.
4.2 "Partial intermediary of exchanges" equilibrium
At this equilibrium, cigarette is accepted in payments by the whole German
population, but not for the same reason. A smoker accepts cigarette because
he can then consumes it, which gives him a positive utility while a non-
smoker accepts it as a medium of exchange. Hence, cigarette is only used
partially as money, conducting us to say that it has a partial acceptability
as money. The strategy of a non-smoker implies that he acts as middleman
between the population of allied soldiers and the one of German smokers:
when one non-smoker meet a agent of population aand there is a single
coincidence,he accepts to sell his special good against cigarette because he
knows that this will increase his probability to succeed if he met another
German who accepts cigarette. This German could be either a smoker or a
non smoker who will use cigarette to increase the probability of succeeding
in a trade but, necessarily, all cigarettes introduced in the economy ends
up in the hand of smokers who smoke then. Then, we can say that non
smokers acts as middlemen between seller and consumer of cigarette (at this
equilibrium).
26
The existence of this equilibrium needs that the best response condition
of non smokers is positive (they accepts cigarette as payments) and the one
of smoker is negative (they prefer smoking rather than trading cigarette).
Moreover, at this equilibrium, no smoker must hold one cigarette in stock
and then m=0. The stock of cigarette held by German in this economy is
only due to the behavior of non-smokers. Hence, as m=0,C has to equal
to (1 −µ)n. We can compute the value of nfor this to be a steady state by
using condition
ú
C=0⇔ag (1 −µ)(1−n)=gµgC
After some algebra, we Þnd that
ú
C=0⇒n=a
gµ +a
Using ún=0allows us to verify that we obtain the same expression.
Then, the total stock of cigarette held by German is simply
C=(1−µ)a
gµ +aand (1 −C)= µ
gµ +a
We then just need to check the best response condition to know the
region of the parameter space where this equilibria exists. Non smokers
accept cigarette as money if ∆πn>0,i.e. if
∆πn=αxgµ (1 −y)(u−c)−r(gµ +a)c
(gµ +A)(r+αx)>0
Solving this inequality for µ, we Þnd that it is rational for a non smoker
to accept cigarette as payment iff:
µ>µ
2=αxyg (u−c)+rca
αxg (u−c)−rcg
Since (gµ +A)<1,it is also easy to show that y3<y
1.
We see that non smoker accept cigarette as money if the population of
smoker is large enough. In that case, it is rational for them to sell their good
to an agent afor selling it to either a smoker or a non-smoker.
At this equilibria, smokers don’t accept cigarette as money but rather
to consume it. Hence, ∆φhas to be negative, which is true iff:
∆φ<0⇔µαxg [µ+(1−µ)(1−n)] (u−s)−αxyg (1 −C)(u−c)
−αx (gC +a)(s−c)−r(gµ +a)s¶
r(gµ +a)+αxgµ <0
⇔s>s
2=αxgµ (1 −y)(u−c)
(r+αx)(gµ +a)+αxc
r+αx
27
This condition hold if sis sufficiently large, compared to the value of
y. We can then conclude that for German smokers not to resell the ciga-
rette bought (i.e. to use it as money), they must sufficiently value the
consumption of cigarette compare to other parameters. By this way, one
canunderstandthedifference we can observe between the two types of in-
termediary of exchange discussed above. The good that seems not to have
a role of "commodity money" are those which continue to be consumed by
their potential consumer. We arrive there to a partition of the population
regarding this kind of good: the one who don’t want to consume it have
an interest to use it as a medium of exchange but no consumer want to
renounce to the consumption of it. Goods that seems to belong to the set
of such intermediary of exchange are, e.g., foodstuffslikebutterormeat
or scarce industrial products like gas, tire (everything one had to have to
maintain his transportation ability).
4.3 The "commodity money" equilibrium (cigarette used as
money by the whole population)
We now turn to the study of an equilibrium in which the two types of
German agents choose to use the "general goods" as a medium of exchange.
In table 2 upside, we called these goods "commodity moneys" (following
here the contemporaries of this crisis).
At this equilibrium, the behavior of smoker constraints the size of the
money stock in terms of cigarette because smokers accepts cigarette as long
as the gain from trading them is at least equal to the gain of smoking them.
Hence, in steady state, for the 2 German populations to accept cigarette as
money (at least partially), the stock of cigarette has to be such that smokers
has a equal gain for the 2 uses of cigarettes. Then, the money stock is given
by ∆φ=0,i.e. the best response condition of smokers has to be such that
they played in mixed strategy. Computing ∆φ=0give us the following
expression of C:
∆φ=0when Πn=1⇒C=1−αx (s−c)+rs
αxg (1 −y)(u−c)
which can be used to compute the value of nand m. For this equilibrium
tobeasteadystate,wehavetobesurethattheproportionofcigarette
smoked in equilibrium is equal to the number of cigarettes sold by the Allied
soldiers to the German agents. This give us the value of φ.Itistheneasy
to check the best response condition of non smokers and then to prove the
existence of this equilibrium, which is summarizes in the next proposition.
28
Proposition 2 The cigarette is accepted as money, at least partly, by the
whole population of German if the utility of smoking is sufficiently small
and if the proportion of smoker is large enough compared to the population
of sellers of cigarette. At that equilibrium, the stock of cigarette is equal to:
C∗=1−αx (s−c)+rs
αxg (1 −y)(u−c)(11)
which is positive iff12 holds and is less than 1if ?? holds.Chas a steady
state value iffsmokers smoke with probability φ∗each time they sell a good
against a cigarette, with
φ∗=a
(gµ +a)gC∗
with CdeÞned in 11.φ∗is positive if 12 holds and is less than 1if 13
holds.The following conditions resume the conditions on the existence of
this equilibrium in which cigarette is accepted as money by the two sub-
populations of German
αxc
r+αx <s<
αxg (1 −y)(u−c)
r+αx +αxc
r+αx (12)
s<s
2=αxgµ (1 −y)(u−c)
(r+αx)(gµ +a)+αxc
r+αx (13)
These conditions tell us that for money to be accepted by the German
population, the utility derived from smoking cigarettes must be small enough
compared to the utility to consume special goods and that there must be a
sufficiently large population of smoker.
Proof. Cigarette is accepted as money in a steady state equilibrium by
the 2 German sub-populations iff∆πn>0and ∆φ=0.But the behavior of
German smokers acts as a constraint on the money stock (i.e. the amount
of cigarette held for exchange by agents) because, for this to be a steady state
equilibrium, smokers have to be indifferent between smoking and consuming
this good. Hence, we use ∆φ=0tocomputethevalueof Csuch that they
are indifferent between smoking and trading cigarettes
∆φ=0when Π=1⇒C∗=1−αx (s−c)+rs
αxg (1 −y)(u−c)
This gives us C∗thathastobelessthan1and positive (implying αxc
r+αx <
s<αxg(1−y)(u−c)
r+αx +αxc
r+αx ). Then rearrange ún=0,Þnd (1 −n)(gC +a)=
29
ng (1 −C)and compute the values of n∗and m∗:
ún=0⇔n∗=1−αx (s−c)+rs
αx (1 −y)(u−c)(14)
C=µm +(1−µ)n⇔m∗=1−µgµ +a
µ¶∗αx (s−c)+rs
αxg (1 −y)(u−c)(15)
Inserting C∗and m∗in the steady state condition on the stock of cigarettes
(ú
C=0) gives the value of φ∗:
ú
C=0⇔ag (1 −C)=(gC +a)gµ (1 −m)φ∗
⇔φ∗=a
(gµ +a)∗αx (1 −y)(u−c)
αxg (1 −y)(u−c)−αx (s−c)−rs =a
(gµ +a)gC∗
The study of this equilibrium is completed by checking the best reply condition
of non-smoker that must be positive (giving us s>c,which value is less than
the one isolated in condition 12 for any positive r).
5Conclusion
The aim of that paper was to make a Þrst step towards a better under-
standing of one of the most fascinating example of commodity money in
contemporary history. His goal was to explain the use of cigarette money by
the prior demand for consumption of this good. By the way, we’ve learned
that conditions on the demand of cigarette and also on its utility in con-
sumption are two key parameters for this explanation. But the historical
study of this episode has also learned us the diversity of means of payments
in that barter economy. We have isolated three types of exchanges:
•the Þrst one is direct barter. In the model, the barter equilibrium
correspond to that case: agents have no interest in selling their pro-
duction good if the candidate good to that function has a low demand
compared to the probability of a double coincidence of wants. In that
case, the means of payments were simply the goods produced by the
partners.
•The second type of means of payments isolated in the historical study
consists in what we’ve called "partial intermediary of exchange". Such
a medium of exchange correspond to the partial monetary equilibrium
of the model: some agents, those who derive no utility to consume the
"general good" choose to use it in payment with agents that derive a
30
positive utility from its consumption. They do so because such kind of
good increase the probability to succeed in Þnding their own consumer
good (i.e. in the model, the "special good"). On the side of consumer
of the general good, the utility they derive from the consumption of
such a good is so high compared to the utility to consume another
good that they don’t want to renounce to this consumption. The
"money stock" of such a good is relatively low because the size of the
setofagentsconsumingithastobehighforsuchagoodtobecomea
partial medium of exchange, which implied that one unit of this good
is consume very soon after having been introduced in the economy.
•This leaves us with the third type of medium of exchange, commodity
moneys used by the whole population use as a medium of exchange.
The existence of this equilibrium implies that smokers (consumers)
partially renounced to its consumption. Moreover, the deÞnition of
a stationary equilibrium imply that smokers have an equal utility to
consume this good and to use it as a medium of exchange (indirect
utility as a medium of exchange has to be equal to the direct utility to
consume it). In that case, the "money stock", which is also endogenous,
is drove by the utility to smoke and the exchange frictions. Hence one
of the key parameter for the emergence of this commodity money is the
utility to smoke which has to be low enough for smokers to renounce
to smoke.
Graph (3) resumes the parameter region in which the different equilibria
computed exists. To summarize, our model provide a simple theory of the
choice of medium of exchange by the a population. This theory can be
summarized by 2 key parameters: the utility of consumption and the size of
the population of consumer of the "general" good.
The Þrst parameter gives us the frontier between "partial intermediaries
of exchange" and commodity moneys. "Partial intermediaries of exchange"
(such as tire or butter) were much more valuable to Germans than cigarette
or alcohol because one needed that goods to survive, either for the calories
they gave or the transportation capacity they gave in an economy in which
purchases implied travelling. Goods used as commodity moneys were then
those that the whole population - consumers as well as non-consumers of
such goods - can choose to use it to lubricate theirs exchanges rather than
consuming it. Note that contrary to Menger’ intuition, the German case
leaves us with many commodity moneys and we cannot reconcile this fact
with the usual Mengerian theory of money. Our theory of the choice of
31
0.8 0.60.40.2
0
1
0.875
0.75
0.625
0.5
0.375
µ
s
Eq. “partial intermediary
of exchanges”
π = 1; ϕ = 1
Barter eq.
π = 0 ; ϕ = 1
Commodity money Eq.
π = 1 ; ϕ∈ ]0,1[
Figure 3: Existence of the different equilibria in the (µ, s)space (with u=
0.9,c=0.3,g=0.9,a=0.1,r=0.05,y=0.15,αx=1).
commodity money in that episode overcome this problem because it doesn’t
restrict apriorithe set of goods used as commodity moneys.
The other parameter, i.e. the size of the consumers population of ciga-
rette, gives us the difference between goods that were used as medium of
exchange and those only used in direct barter relationship. The argument is
very intuitive and now common in search theory: when exchanges are disor-
ganized, an agent chooses to buy a good in order to resell it only if that can
speed up the purchase of his desired good. In that case, the bigger is the size
of the consumer population, the more likely is the case of meeting someone
that accept this good in payment. Note that this is different from the usual
argument on the "bootstrap" nature of monetary acceptability (i.e. money
is accepted because others accepted it) in that there is no indeterminacy of
32
the monetary equilibrium in our model: the monetary equilibrium rules out
the barter one.
This paper can be extended in three major ways. First, it has to be
extended towards the study of the dynamics of this equilibrium, in order
to increase our knowledge on the stability of various equilibria. Second, the
integration of bargain prices can give interesting insights on the properties of
medium of exchange. Finally, we think it could be valuable to include in the
paper two types of quality of the medium of exchange. This would enable us
to discuss the difference between the two types of tobacco distinguish at that
time: German tobacco and American tobacco (the former being valued 40%
less than the later on the black market, as indicated by various historical
sources).
References
[1] Backer J. (1971), Priming the German Economy: American Occupa-
tional Policies, 1945—1948, Duke University Press, Durham, USA
[2] Berentsen A. and Rocheteau G. (2003), Money and the gains from
trade, International Economic Review,44, 263—297
[3] Boeckle W. (1988), Der Schwarze Markt 1945—1948,Westerman,
Stuttgart, Germany
[4] Botting D. (1985), In the Ruins of the Reich, George Allen and Unwin,
London, UK
[5] Brackman M. (1993), Vom Totalen Krieg zum Wirtschaftswunder, Klar-
texte verlag, Essen, Germany
[6] Burdett K., Trejos A. and Wright R. (2001), Cigarette Money, Journal
of Economic Theory,99(1/2), 117—142
[7] Friedman M. (1951), Commodity-reserve Currency, Journal of Political
Economy 59(3), 203—232
[8] Herald Tribune (02/28/1947), The Cigarette Standard, New York, USA
[9] Herald Tribune (05/17/1947), Cigarette is King in Frankfurt Black
Market, New York, USA
[10] Kiyotaki N. and Wright R. (1989), On Money as a Medium of Exchange,
Journal of Political Economy,97(4), 927—954
33
[11] Kiyotaki N. and Wright R. (1993), A Search-Theoretic Approach to
Monetary Economics, American Economic Review 83(1) 63—77
[12] Klein B. (1976), Competing Monies: Comment, Journal of Money,
Credit and Banking 8, 513—519
[13] Lutz F. A. (1949), The German Currency Reform and the Revival of
the German Economy, Economica, 122—142
[14] Menderhauser H. (1949), Money, Prices and the Distribution of Goods
in post-war Germany, American Economic Review 39, 646—672
[15] Menger K. , 1892, On the Origin of Money, Economic Journal,2,239—
255
[16] Milward A. (1977), War, Economy and Society, 1939-1945, Allen Lane,
London, UK
[17] Proctor R. N. (1999), The Nazi War on Cancer, Princeton University
Press, Princeton & Oxford, USA
[18] Radford R. A. (1945), The Economic Organization of a P.O.W. Camp,
Economica, 189—201
[19] Röpke W. (1947), Repressed Inßation, Kyklos 1(3), 242—253
[20] Ruland B. (1968), Geld wie Heu und Nichts zu Fressen: Karussel einer
Verrückter Zeit, Hestia Verlag, Bayreuth, Germany
[21] Samuelson, A. (1972), Le Mark: histoire de la monnaie allemande,
Didier, Paris, France
[22] Singer H. W. (1943), The German War Economy — 9, The Economic
Journal, 54(210/211), 243—259
[23] Suddeutsche Zeitung (08/09/1946), Schwarzhändler mit Kundendienst,
Munich, Germany
[24] Tagesspiegel (08/04/1947) Die ”Schwarze Mark”, by Walter Gong, Ger-
many
[25] Tobin, J. (1952), A Survey of the Theory of Rationing’, Econometrica
20(4), 521—553
[26] Trejos A. and Wright R. (1995) Search, Bargaining, Money and Prices,
Journal of Political Economy,103(1), 118—141
34
[27] Rupert P., Schindler M. et Wright R. (2001), Generalized Search-
Theoretic Models of Monetary Exchange, Journal of Monetary Eco-
nomics, 48, 605—622
[28] Schevchenko A. and Wright, R., 2003, Partially Acceptable Money,
forthcoming in Economic Theory
[29] Wallace N. (1998), A Dictum for Monetary Theory, Federal Reserve
Bank of Minneapolis Quarterly Review 22(1), 20-26
[30] Wright R., 1999, A Note on Asymmetric and Mixed Strategy Equilibria
in the Search-Theoretic Model of Fiat Money", Economic Theory, 14,
463-471
Historical archives locations
The historical records cited in that paper come from the Institut für Zeit-
geschichte (Leonrodstrasse, Munich) for part of the OMGUS documents,
from the Bayerische Hauptstaatarchiv (Ludwigstrasse, Munich) for docu-
ments of the Bavarian Government and of the OMGB (Office of Military
Government for Bavaria).
35
