DIGITAL MONEY: REVIEW OF LITERATURE AND SIMULATION OF WELFARE IMPROVEMENT OF THIS TECHNOLOGICAL ADVANCE

DIGITAL MONEY: REVIEW OF LITERATURE AND SIMULATION OF
WELFARE IMPROVEMENT OF THIS TECHNOLOGICAL ADVANCE


Joilson Dias
Department of Economics
State University of Maringa, BRAZIL
jdias@uem.br





Abstract

The objective of this paper is to discuss the overall role of digital money
and its impact on welfare and monetary policy. The role of digital money is
discussed under a review of literature and through a simple theoretical model
that captures technological advances. In this model the representative
consumer decide over two key elements: consumption and leisure. Here, the
leisure are affected by transaction costs and the amount of money available.
To simulate the model’s result, I use data for Brazil. As general result, I
predict that digital means of payment will improve welfare and increase the
overall demand for money.

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1. Introduction
In my view digital money, sometimes mentioned in the literature as e-
money or e-cash, is any form of electronic payment mechanism. This
definition is very much compatible with the ones proposed by Dias, Dias &
Silva (2000) and Wan (1999).
As a mechanism of payment it is supposed to impact the economy on
two grounds. First, on the monetary policy aspect where its widespread use by
consumers lead to paper money substitution on the day by day transaction.
Second, on the welfare of the consumers. If society’s welfare improves it will
stay longer; otherwise it will not be used. Seeking to see the impact of digital
on both variables, I start the paper with a brief review of literature on digital
money.

2. Review of Literature
This review of literature is drawn extensively on Dias, Dias & Silva
(2000). Therefore, for a more detailed discussion I recommend to look that
paper.
Digital payment system coupled with safe cryptographic resources
according to the American Banks Association (1996) has the lowest
transaction cost. It has an estimated cost of US$ 0.01. When compare that with
traditional one make at the banks which is US$ 1.075. This overwhelming cost
reduction will make without doubt digital money a serious candidate to
substitute paper money.
North (1994), showed that the changes in money’s form along the
history were done exclusively based on transaction cost reduction to final
users. So, history is keeping its pattern on today modern society.
The digital money literature can be divided into two groups. The first
composed by those that argue in favor of maintaining digital money as inside
money, keeping its parity on paper money [Konvisser (1994), Bernkopf
(1996) and Greespan (1996)]. Here, the monopoly of issuing paper money or
digital money should in the hands of the central bank. The second, composed
by those that defend more competition [Chaum (1995), Montanis (1995), Ely
(1996), England (1996) and White (1996)]. According to them, digital money
is an outside money -- notes issued by private banks. Here the supervision cost
of the private is transferred to consumers.
The centerpiece of the discussion between the two groups is about the
seigniorage. The seigniorage is between 1.5% - 3% of government revenue for
developed countries, according to Cukierman, Edwards and Tabellini (1992).

The introduction of digital money will certainly move some of the
revenue if not all to issuing companies of digital means of payment, even

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though the money is inside. In our view, the monetary policy will still be
valid.
In our view, the digital money as an outside money will not become a
reality. As an outside money it increases consumers transaction costs, since it
demands constant supervision by consumers. Therefore, it goes against the
history of money and the theory to be developed next section.

3. The Model
It is important to have in mind the focus of the model. Here, the very
important aspect is the welfare of the society. The changes proportioned by
technological advances must reflect in the welfare improvement of the society.
Otherwise, it will not become a permanent technological mechanism to be
used by society.
On the economical aspects, the technology advances are in last instance
simple transaction cost reduction and time saver. The effect of technological
advances on the society’s welfare can be seen in the following graph.

Figure 2: The Transaction Costs Effect
The welfare function (W) is composed of two variables: total
consumption (TC) and leisure (L). A technological shock (S? S’) that reduces
transaction costs and is time saver would increase the total leisure from L to
L’ and the total consumption from TC to TC’. Bringing a welfare
improvement from W to W’. This welfare improvement will be brought by a
lower transaction cost.
Santomero-Seater (1994) and Berentsen (1998) studied the demand for
digital money. Dias, Silva & Dias (1999) besides deriving a more complete
demand function, they also analyzed the impact on the demand for money due

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to the adoption of digital money. Here, I advance in relation to Dias, Dias &
Silva (2000) by building a theoretical model that enable me to verify the
welfare impact caused by technological advances that lowers transaction costs.
The verification will be done through simulation using Brazilian data. These
are the two objectives of the model to be developed henceforth.
The representative consumer has the following welfare function (W):

c
(
W
,l )
? c ?
?
l
,




(1)
t
t
=E ?? t
0
{ ?1 t + t}
t=0

where: W is the consumer’s welfare function and ct is the consumption and l
t
is the leisure, both at time t; Eo is the expected operator; ? is the discount rate.
The leisure function is represented by the following equation:

?a
a
U(s , m ) = l = s m ,






(2)
t
t
t

where st is the transaction cost 0 < s < 1. The variable s captures technological
advances like the digital money. A lower s means that more transactions can
be made with the same amount of money, mt. Therefore, leisure will increase
because more money will be available at the cost already incurred by the
consumer.
The consumer’s budget constraint is given by the following function:

P y + M ? + 1
( ? R
)B
?
? = P c + M + B .



(3)
t
t 1
t 1
t 1
t
t
t
t


Where Pt is the price index; Mt is the nominal money at time t; Rt is the
nominal interest rate; Bt is the amount bonds (or debits) at time t; ct is the
consumption in period t.
The model’s solution consist of equating through time the utility from
extra time leisure from a incremental unit of money with the utility of extra
money times the interest forgone by this same unit of money.1 The
mathematical solution of the system consists of maximizing equations (1) and
(2) subject the constraint of the equation (3). This is equivalent to solve the
following equation:

?W ?U
? R
?? W
W
U
t
?
?
? ?
=
?
+
?
?
?
?
?





(4)
?l
m
1
R
c
l
s
t ?
t
? + t ?? ? t
? t ? t ?

1 For those interested in the details of the solution see for example McCallum (1989).

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Where ? ’s represents the derivatives of the functions with respect to the
variables and Rt is the interest rate. The solution can be easily found by taking
the derivatives of equations (1) and (2).

?W
??
?a
a
?
= W = 1
( ?






(5)
1
? )c (s m )
c
?
?W
1??
?a
a
? ?1
= W = c
?
(s m )






(6)
2
?l
?U
?a?1
a
= U = ??s
m






(7)
1
?s
U
?
?a
a 1
= U = s
? m ?






(8)
2
?m


Now, I substitute equations (5)-(8) into equation (4). After
simplifications, I get the following:

?
?
?
?
?1
?ac
? 1+ R ?
?
t
?
t
m =





(9)
t
?
c ? ??
?
?
t
R
?
t
?
1 ? ? ? a
?
?
?
?
?
s
?
t ?


The above equation shows that a reduction in transaction cost caused by
a technological advance, like the digital money, equivalent to a lower st in
equation (9), will increase the overall demand for money. However, paper
money is the one being substituted here. Thus, digital money will reduce the
government revenue made from seigniorage.
Over the long the run policy makers in order to keep a compatible
monetary policy must be attempt to this demand increase. The general form
for the equation (7) would be the following:

Mt
? + ? ?
= L c ,R ,s





(10)
t
t
t ?
?
?
Pt
?
?


The demand for money will increase with consumption, technological
advances -- smaller st, and with interest rate decrease.

4. Simulation for the Brazilian Economy

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In this section I will use the Brazilian data to analyze the impact of
technological advances on welfare and monetary policy. The baseline line data
for December of 1999 was obtained from Conjuntura Econômica (2000). The
idea is to simulate the impact of 1% reduction in transaction cost due to the
use of digital money through equation (9).

The baseline data for Brazil are the following:
GDP = US$ 775.50 billions;
M1 = US$ 50.88 billions;
? = 0.02;2
s = 1;

First, I use equation (9) to obtain the value for a at the baseline year.
The result gave is a = 0.069142. This is the elasticity of leisure with respect to
technological advances. The total welfare is W=563.7451, equation (1).
Now, I use these numbers to simulate a technological advance that lead
to a 1% transaction cost reduction or equivalent to make s=0.99. The impact
on the overall money demand is of 8.21%, therefore reaching US$ 55.41
billions and the rate of total welfare improvement is 0.0104% or W=563.804.
Although this impact on the total welfare seems so dismal it is not in
economic terms, since this is an overall welfare improvement. I simulate a
welfare improvement on the same size through the use of the interest rate as a
policy instrument. To obtain the same welfare improvement, the interest rate
in Brazil must be reduced in 1.6%.

The digital money impact on monetary policy is done through an
overall demand increase for money and by suppressing the need of paper
money. As it can be seen from above, a 1% transaction cost reduction increase
the demand for money by as much as 8.21%. This huge impact captures the
new aspect of the digital money that is making more of it for transaction at
lower cost. However, more studies need to be done in this field in order to
drawn a precise conclusion on the magnitude of the impact on the money
demand.


5. Conclusion
From the review of literature I learn that there is not much chance for
outside money to happen. The transaction cost that comes with outside money
is a high price to be paid by consumers. Therefore, it goes against the money
development history. In sum, money will be inside which means controlled by
government.

2 From Dias (2000).

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The welfare and monetary impact to be caused by the use of digital
money will be in three fronts. First, it will reduce the need for paper money
and consequently reduces government revenue from seigniorage; second, it
will increase the overall demand for money, third, it will improve the overall
welfare of society.
As mentioned before any means of payment mechanism must bring
with it welfare improvement in order to be accepted by society. The digital
money seems to fulfill very well this condition.



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6. BIBLIOGRAPHICAL REFERENCES


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