Modern Economy, 2012, 3, 671-674 Published Online September 2012 (
A Local Currency in a Dollarized Economy
Sokchea Lim1,2
1Department of Economics, Southern Illinois University Carbondale, Carbondale, USA
2Cambodian Institute for Cooperation and Peace, Phnom Penh, Cambodia
Received July 3, 2012; revised August 2, 2012; accepted August 10, 2012
The paper uses a dual-currency search theoretic approach to demonstrate that it is possible to induce the acceptance of a
local currency in a dollarized economy. In the model, we assume that a foreign currency is in full circulation and the
government policy tool is the convertibility of the local currency to the foreign currency. We show that the economy
can achieve equilibria where two monies are in circulation if the government can raise a sufficiently high probability of
exchange between the two currencies.
Keywords: Dual-Currency Search Theoretic Approach; Dollarized Economy
1. Introduction
Curtis and Waller [1] explore the coexistence of two cur-
rencies, domestic as a legal tender and foreign as an ille-
gal one. Assume that the legal currency is always accepted,
the government uses several enforcement policies to drive
the illegal currency out of circulation. Dutu [2] constructs
a one-country search-theoretic model of two monies with
different rates of return and bargaining powers. The results
show that the weakening of the domestic currency’s bar-
gaining power can invite strong foreign currency while
its lower rate of return drives out the foreign one. Lotz
and Recheteau [3] use the search-theoretic approach to
determine how the government can replace an old currency
with a new one. Different from the above papers, we in-
troduce the convertibility between the two monies in the
model. We want to show that the government can induce
the acceptance of a local currency in an economy in which
a foreign currency is fully accepted.
The purpose of the paper is to determine under which
conditions a local currency can be accepted in a dollar-
ized economy where a foreign currency is in full circula-
tion. The policy tool of the government is to link the lo-
cal currency to the fully established foreign currency by
easing the convertibility between the two. Using search-
theoretical approach of money, we show that the econ-
omy can achieve equilibria where two monies are in cir-
culation if the government can raise a sufficiently high
probability of exchange between the two currencies.
2. The Simple Model
The model is related to the dual-currency search-theoretic
model of Kiyotaki and Wright [4]. In this model, the dou-
ble coincidence of wants between a given pair of agents
is ruled out; hence, there exist two fiat monies which play
an important role as media of exchange. The economy is
populated by a continuum of infinitely-lived agents with
total population normalized to unity. Time is continuous.
There are also a large number of consumption goods which
are indivisible and non-storable, and they come in units
of size one. Each agent is specialized in both consump-
tion and production. All agents are assumed to be homoge-
nous in their preferences. An agent gets zero utility (U =
0) from consuming her own production good or not con-
suming any goods and she gets a positive utility (U > 0)
from consuming a good that she likes. A type j consumer
consumes good j and produces good j + 1 (modulo N), for
j = 1, 2, ···, N and N 3. So, the probability that, for a
given agent, a would-be trading partner can produce her
desired good is x = 1/N (a single coincidence of wants).
The assumption is essential to rule out the double coin-
cidence of wants. For simplicity, it is assumed that there
is no labor cost of production of goods. Once consuming,
an agent can enter the production process and produce an-
other unit of consumption goods to trade in the next period.
There are two currencies in the model, local and for-
eign currencies which are denoted by subscripts of L and
F, respectively. Both monies are indivisible, costlessly stor-
able and cannot be produced by any private agents. An
agent stores only one unit of one type of money at a time.
At the beginning of period 0, a fraction of M agents is
chosen at random and endowed with one unit of money
each. Since there are two currencies in this economy, mL
denotes a fraction of private agents who are endowed with
opyright © 2012 SciRes. ME
a local currency and mF denotes a fraction of private agents
who are endowed with a foreign currency. So it follows
that M = mL + mF. mG is the fraction of agents who are
goods producers. Hence, at any point in time, the total po-
pulation can be written as:
Lt Ft
max π
Gt (1)
A key feature of the model is that the government has
a policy tool in the exchange market. There is a fraction
of money changers which are set up by the government
in the market so that private agents can exchange their
currency from one to another. We can think of this as the
government establishes exchange booths throughout the
economy or the government licenses exchange businesses
which will operate in a perfectly competitive market. We
assume that the exchange spread between the two curren-
cies is zero1. That is, the two currencies are exchanged
one for one with no extra cost incurred by the private agents.
F is the fraction of money changers who hold foreign
currency and exchange for local currency.
L is the faction
of local currency changers. Once exchange occurs, a for-
eign currency changer becomes a local one and, vice versa.
We also can think of these fractions as the probabilities
that a private agent can get her currency converted so 0
i 1 where i = L, F. Assume that money changers do not
enter the goods market, so they do not trade with the goods
History of each agent is private information. Informa-
tion that a good holder values a local or foreign currency
is private to the money holders; therefore, currency ex-
changes do not take place before the matching process.
On the other hand, because of the availability of instant
exchange with no cost in the market, it is deemed unnec-
essary for a money holder to exchange his currency be-
fore the matching process. The matching process follows
Poisson with constant arrival rate of α.
The acceptability of currency is determined endogenou-
sly. Π where 0 Π 1 is probability that a random goods
holder accept the foreign currency in trade and π repre-
sents the best response of individual goods holder to an
offer of the foreign currency. Φ where 0 Φ 1 is prob-
ability that a random goods holder accepts the local cur-
rency in trade and
represent the best response of indi-
vidual goods holder to an offer of the local currency. Given
symmetry, the Nash equilibrium is π = Π and
= Φ.
The analysis focused here is restricted to steady-state
equilibria where strategies and all aggregate variables are
constant over time. In such equilibria, all agents are hold-
ing either one unit of money or nothing (i.e. being able to
produce one unit of consumption goods), at the end of each
period. Let Vi where i = G, L, F be the value functions for
a goods holder, a local currency holder and a foreign cur-
rency holder, respectively, and they measure the expected
present discounted value of utility from trading in the fu-
ture, given the current trading position. Thus, the Bellman’s
equations specifying the steady-state returns to searching
rVxmV V
rVxmU VV
xm ΠUV V
rVxm ΠUV V
where r is the real interest rate.
Equation (2), the expected flow return to a goods
holder is equal to the sum of the surpluses (payoffs) from
trade with a local currency holder or with a foreign cur-
rency holder. αxmi, i = L, F, is the probability that the
goods holder is matched with a money holder holding
local or foreign currency and is able to provide her with
the desired goods. The former chooses
and π optimally
to maximize the payoff (VLVG) or (VFVG) gained
from trade with the latter.
Equations (3) and (4) have a similar interpretation. The
right hand sides denote the sum of surpluses from trade
with a goods holder who values either local or foreign cur-
rency. Note that the money holder has no information about
which currency is valued by the good holder before the
meeting. The first term is the payoff from trading with a
goods holder who values the currency she holds and swit-
ching from a money holder to a goods holder. The sec-
ond term is the payoff from trading with a goods holder
who values a different currency than the one held by a mon-
ey holder; hence, the currency needs to be exchanged with
i in the same period and then traded. The
payoff (U + VG Vi where i = L, F) is the sum of the util-
ity gained from consuming the desired goods and surplus
from switching her position from a money holder to a goods
According to the set of Equations from (2) to (4), the
acceptability of both currencies will depend on the com-
parison of value functions of monies (VL and VF) with the
value function of goods (VG). If a representative goods
holder expects a positive payoff from becoming a local
currency holder in the next period, VL > VG, her best re-
sponse is to choose to completely accept the local cur-
= 1. If the negative payoff is expected, VL < VG,
= 0, i.e. the representative goods holder chooses
not to accept the local currency. And, if the representa-
tive goods holder is indifferent between holding the local
1On Nov. 19, 2010, the buy-sell spread between Cambodian riel and US
dollar is 7 basis points which equivalent to 0.0017 dollar. Also, men-
tioned in Craig and Waller [5], the spread between Ukrainian hryvna
and US dollar was 0.5 cent per dollar exchanged.
Copyright © 2012 SciRes. ME
Copyright © 2012 SciRes. ME
currency and remaining as a goods holder in the next pe-
riod, VL = VG, she will choose
= where 0 < < 1, i.e.
the currency is partially accepted. The explanation is the
same for foreign currency acceptability.
Now, there are potentially nine types of steady-state
equilibria. Each type is characterized by a pair of the best
responses of an individual goods holder to both local and
foreign currencies. Confine to the purpose of this paper,
we only look at the equilibria in which the foreign cur-
rency is completely accepted by the goods holder (π =
= 1) which requires that VF > VG while the local currency
acceptability may fall in either of three cases. Solving the
system of Equations (2) to (4) gives the reduced-form
mU (5)
xm αxm ΓU
rV rαxm
xm αxm ΞU
rV rαxm
Πμ Ψ
Using Equations (5) and (7) and setting VF VG, the
sufficient condition for having the foreign currency ac-
cepted in the economy is to have2:
When the goods holder meets with a foreign currency
holder, she must decide whether to accept the currency or
wait until she meets with a local currency holder and trade.
From Equation (11), the left hand side is the acceptability
of the foreign currency plus the probability that it can be
converted into the acceptable local currency. The right hand
side is the probability of waiting to meet with a local cur-
rency holder and trade; then, acquiring the desired goods,
or the probability of hoping to consume a desired good in
the next period and not accepting the foreign currency
now. The intuition here is that the goods holder accepts
the foreign currency if she expects that it will help her
acquire her desired goods faster. And, if everyone com-
pletely accepts the foreign currency, exchanging it for the
local one may not be needed at all (
L = 0).Then, it fol-
lows that < 1.
Using (5) and (6), we can derive the sufficient condi-
tions for the acceptability of the local currency (see Ap-
pendix for derivation). The three equilibria to be discussed
in this paper are given in Table 1. In column (1), we pro-
vide the necessary conditions for the acceptability of a local
currency and column (2) presents the symmetric Nash equi-
libria and the sufficient conditions are detailed in column
(3). Please note that the explanation of column (1) and (2)
is provided above and we will discuss the last column and
government policy tool to move from an equilibrium where
the local currency is not accepted to the one where it is
partially or completely accepted in the economy. Under
the sufficient conditions, the right side is the same term
as interpreted in the condition for foreign currency ac-
ceptability and determined to be less than one ( < 1).
The left hand side is the probability that a goods holder
can obtain her desired goods after trading with a local cur-
rency holder. The three conditions state that whether or
not the local currency can be accepted depends on the ag-
gregate acceptability and its convertibility into a widely
accepted currency, the foreign currency.
From Table 1, it is clear from the sufficient conditions
that the government can raise the probability of exchange
of a local currency into a widely accepted foreign currency
to a sufficient level such that the local currency will be
accepted in the economy. From the mixed strategy equi-
librium (partial acceptability of local currency), the equi-
librium value of the aggregate acceptability is associated
with the level of convertibility of the local currency. The
association between the two variables is important in de-
termining the optimal level of convertibility that could put
the local currency in circulation. If the association is very
elastic, then we may see a low optimal value of
L; oth-
erwise, a high value. The intuition here is that if people
have little trust in the value of the local currency, the gov-
ernment has to pour in big amount of a trusted foreign
currency to ensure that every unit of the local currency is
backed by every unit of a trusted value, hence raising the
liquidity. Finally, the government can also move to the
best optimal equilibrium where the local is fully accepted
in the economy if
L gets so large that a representative
agent can get her desired good by using either currency.
Table 1. Characterization of symmetric nash equilibria.
Symmetric Nash
VL > VG ϕ = Φ = 1 +
VL = VG 0 < ϕ = Φ < 1 +
VL < VG ϕ = Φ = 0 +
 
αxm Γrαxm Ξαxm ΠΞ rαxm Γ
rαxm Γrαxm Ξαxm Παxmr αxm
 
2The derivation is provided in the appendix.
Therefore, in this economy, the convertibility from a local
currency to a foreign currency (
L) is an important policy
tool to move from a dollarized economy where foreign
currencies are fully accepted to an economy with both local
and foreign currencies.
3. Conclusions
The paper examines a fully-dollarized economy where the
government tries to introduce a local currency. The model
is a dual-currency theoretic approach in which one cur-
rency (foreign currency) is in full circulation. The policy
instrument of the government is the probability of exchange
between the local and foreign currencies. The result is that
the economy can achieve equilibria where two monies are
in circulation if the probability of exchange between the
two currencies is sufficiently high.
The paper does not examine the case where the gov-
ernment is in short supply of foreign currencies. This would
constrain the ability of the government to raise a suffi-
cient high value of
L. Hence, the government may not
be able to achieve the equilibria with two monies in cir-
culation. However, the game theory approach such as cred-
ible announcement by the government to back the local
currency can be introduced and the interaction between the
government and the representative agents can be analyzed.
This would go beyond the extent of this paper. Moreover,
the welfare analysis is not done in this paper.
[1] E. S. Curtis and C. Waller, “A Search-Theoretic Model of
Legal and Illegal Currency,” Journal of Monetary Eco-
nomics, Vol. 45, 2000, pp. 155-184.
[2] R. Dutu, “Strong and Weak Currencies in a Search-
Theoretic Model of Money,” Research Paper, 2001.
[3] S. Lotz and G. Rocheteau, “On the Launching of a New
Currency,” Journal of Money, Credit and Banking, Vol.
34, No. 3, 2002, pp. 563-588.
[4] N. Kiyotaki and R. Wright, “A Search-Theoretic Ap-
proach to Monetary Economics,” American Economic
Review, Vol. 83, No. 1, 1993, pp. 63-77.
[5] B. Craig and C. Waller, “Dual Currency Economies as
Multiple Payment Systems,” Economic Review, Federal
Reserve Bank of Cleveland, Cleveland, 2000.
Subtracting Equation (5) from (7) yields:
rVrVxm ΠμU
Ψαxm U
 
Simplifying the equation further gives:
αxm U
 
VF VG requires that:
Similarly, from Equations (5) and (6) we get,
αxm U
VL VG requires that:
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