Theoretical Economics Letters, 2013, 3, 226-228
http://dx.doi.org/10.4236/tel.2013.34038 Published Online August 2013 (http://www.scirp.org/journal/tel)
Inseparability of Transaction Medium and Store of Value
in the Role of Money
Masayuki Otaki
Institute of Social Science, University of Tokyo, Tokyo, Japan
Email: ohtaki@iss.u-tokyo.ac.jp
Received April 27, 2013; revised May 27, 2013; accepted June 27, 2013
Copyright © 2013 Masayuki Otaki. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
We analyze whether or not money can be circulated as a purely transaction medium in the search theory. We obtain the
following result: unless the role of a store of value added to the function of money, money does not circulate and the
economy degenerates into a barter economy.
Keywords: Search Theory of Money; Degeneration of Monetary Economy into Barter Economy; Inseparability of
Transaction Medium and Store of Value
1. Introduction
The paper explores the function of money in the search
model. There exist two main functions of money: trans-
action demand for clearing and demand for store of value.
Kiyotaki and Wright [1], which is the seminal work on
the search money model, insist that money can be circu-
lated solely by the motive of transaction even though it
does not operate as a store of value.
However, if money is perishable while differentiated
goods are durable, some advantage exists on the side of
goods. Namely, the visiting opportunities of exchange in
a barter economy are more frequent those in a monetary
economy. This leads us to the following hypothesis:
unless money possesses both of the above properties, it is
unable to circulate. Based on Kiyotaki and Wright [1],
we ascertain the validity of this hypothesis.
This paper is organized as follows. In Section 2, we
construct a simple model based on Kiyotaki and Wright
[1], and exhibit that money never circulates only as a
transaction medium. Section 3 proves that money does
not circulate until being attached by the function as a
store of value. Section 4 contains brief concluding re-
marks.
2. Model and Its Properties
2.1. Structure of the Model
Our model entirely depends on Kiyotaki and Wright [1].
The individuals are classified into three: producers, com-
modity traders, and money traders. A producer possesses
nothing and is searching for the opportunity of produc-
tion. A commodity trader has already finish ed pr oduction
and is searching for a counterpart of exchange. The
counterpart is admissible regardless of whether he/she is
a commodity trader or a money trader. To become a
money trader, it is necessary to first become a commod-
ity trader. A money trader seeks a commodity trader for
consumption. Money is assumed to be accepted with
probability one by any trader, whereas there never exists
such a guarantee in barter trade.
2.2. Assumptions
We now state the assumptions of the model.
i) A unit good produced by each producer is differen-
tiated in the interval
0,1z. The good is more
preferable when approaches 0. Namely, the utility
derived from the consumption of a unit good ,
z
z
z
uz,
is a decreasing function of . This implies that indi-
viduals are uniformly distributed around a circle of di-
ameter 2 and that prefer goods produced at nearer dis-
tance.
z
ii) Money is perishable. Namely, a money trader can
stay in its position only within and returns to a
producer thereafter. This means that money serves only
as a transaction medium and not as a store of value.
0
iii) The opportunity of production follows the Poisson
process with mean
. Further, the opportunity of ex-
change also follows the Poisson process with mean
.
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