# The black hole of logistics costs of digitizing commodity money

Boliang Linabc ∗, Ruixi Lind a School of Traffic and Transportation, Beijing
Jiaotong University, Beijing 100044, China
b Sino-UK Blockchain Industry Research Institute, Guangxi University; Nanning
530004, China
c Beijing Laboratory of National Economic Security Early-warning Engineering,
Beijing 100044, China
d School of Computing, National University of Singapore, Singapore, 117416,
Singapore ††footnotetext:  ∗Corresponding autohr<EMAIL_ADDRESS>
###### Abstract

In this paper, we reveal the depreciation mechanism of representative money
(banknotes) from the perspective of logistics warehousing costs. Although it
has long been the dream of economists to stabilize the buying power of the
monetary units, the goal we have honest money always broken since the central
bank depreciate the currency without limit. From the point of view of modern
logistics, the key functions of money are the store of value and low logistics
(circulation and warehouse) cost. Although commodity money (such as gold and
silver) has the advantages of a wealth store, its disadvantage is the high
logistics cost. In comparison to commodity money, credit currency and digital
currency cannot protect wealth from loss over a long period while their
logistics costs are negligible. We proved that there is not such honest money
from the perspective of logistics costs, which is both the store of value like
precious metal and without logistics costs in circulation like digital
currency. The reason hidden in the back of the depreciation of banknotes is
the black hole of storage charge of the anchor overtime after digitizing
commodity money. Accordingly, it is not difficult to infer the inevitable
collapse of the Bretton woods system. Therefore, we introduce a brand-new
currency named honest devalued stable-coin and built a attenuation model of
intrinsic value of the honest money based on the change mechanism of storage
cost of anchor assets, like gold, which will lay the theoretical foundation
for a stable monetary system.

###### keywords:

Monetary anchor; Devaluation; Logistics cost; Commodity money; Stable-money;
Digital currency.

##  1 Introduction

Without sound money, there is no protection for savings and property, nor
capital accumulation, nor long-term investment, nor entrepreneurship, nor
social advance. Although it has long been the dream of economists to stabilize
the buying power of the monetary units, the goal we have honest money always
broken since the central bank depreciate the currency without limit( Ebeling,
2015)[1]. The reason hidden in the back of the depreciation is the black hole
of storage charge of anchor over time.

Generally, commodity is a labor product that is used for exchange. Obviously,
the basic property of commodity is values and use values. Therefore, commodity
also has the property of finance. According to the common definition,
commodity money is money whose value comes from a commodity of which it is
made. i.e., commodity money consists of objects that have value in themselves
as well as value in their use as money (Sullivan et al., 2003)[2]. It mainly
includes physical money and metal money in money-shape. Physical money whose
value as money is equal to its value as a commodity is the primal money-form
produced in the long-term development process of commodity exchange. At the
early stage of human society, it was fixed on some specific kinds of
commodities, for example, cattle and sheep, shells and so on.

From the perspective of logistics, the transportation and storage of commodity
will incur logistics costs. Although the physical money has an advantage of
stable intrinsic value, it has an obvious drawback of high logistics cost. In
comparison, the logistics cost of metal money is much lower. Therefore, metal
money gradually replace other physical money in the process of the development
of human beings.

In order to further reduce the logistics cost of physical money, there was a
time when people used precious metals as a major commodity money. However, due
to the limited resources of precious metals, the growth of precious metals is
far slower than the accumulation of human wealth. In addition, people’s
expectations that precious metals will appreciate often lead to the behaviors
of hoarding. This kind of phenomenon will inevitably result in liquidity
shortage in the money market.

The emergence of representative money is a milestone to reduce logistics cost
of commodity money. Generally, representative money, as the receipt for
circulated metal money, is those paper money or banknotes issued by the
government or banks, which replaces metal money in circulation. In theory, the
representative money is equivalent to commodity money. In fact, the value of
representative money is often lower than its anchor value represented by the
goods. The hidden reason is to be discussed later in this paper. Compared with
metal money, representative money not only has the advantages of low printing
cost and low logistics cost, but also can overcome the weight loss caused by
metal money in circulation.

The evolution of the representative money is credit currency, which completely
bid farewell to the logistics cost incurred by commodity money. But the
inherent defect of credit currency is the risk of unrestrained over-issue. In
recent years, people are anxious to inflation of fiat money and mistrust of
the central bank.

Hence, some decentralized digital currencies, for example, Bitcoin, have
emerged. Actually, the virtual currencies do not correspond to real wealth
since their supply is only controlled by algorithms. Virtual currencies are a
type of digital currency, typically controlled by its creators and used and
accepted among the members of a specific virtual community (Rastogi et al.,
2019)[3]. Moreover, their prices have fluctuated significantly in recent
years. Stablecoin is an approach to address this problem of high price
volatility, which is for example defined as a digital currency that is pegged
to another stable asset like gold, or to major fiat currencies like Euros,
Pounds or the US dollar (Mita et al, 2015)[4].

However, all these money with zero logistics cost, namely modern money, is
basically token money. Therefore, it is irrelevant to its intrinsic value and
not a currency of "stable value". In this background, those credit currency
holders will be the victims of inflation. Therefore, it is an important
research topic on how to reveal formation mechanism of the cost of symbolized
or certificated commodity money from the perspective of logistics costs, and
how to design a new currency of "stable value" to integrate the advantages
that credit currency has no logistics cost and that commodity money can store
wealth.

This paper aims to reveal the depreciation mechanism of representative money
(banknotes) from the perspective of logistics warehousing costs. The
contributions of this paper can be summarized as follows:
$\bullet$ We proved that there is not such honest money from the perspective
of logistics costs, which is both the store of value like precious metal and
without logistics costs in circulation like digital currency.
$\bullet$ A brand-new currency named honest devalued stable-coin is
introduced.
$\bullet$ A attenuation model of intrinsic value of the honest money based on
the change mechanism of storage cost of anchor assets is built.

The remainder of this paper is organized as follows. Section 2, we review the
evolution of money form from the perspective of logistics cost. In Section 3,
a technique route for a currency of stable value is described. Section 4, from
the perspective of a goldsmith is the warehouse night watchman, we analyzed
the phenomenon which inventory cost of mortgage assets were intentionally hide
in the process of signifying commodity money. In Section 5, we put forward the
paradox of the existence of a currency of "stable value". A honest currency of
“stable devalued” model based on “gold” standard is proposed in Section 6.
Finally, conclusions are drawn and future research directions are discussed in
Section 7.

##  2 Review the evolution of money from the perspective of logistics cost

Early trade took the form of barter that goods are directly exchanged for
other goods without using a medium of exchange. For example, a sheep can be
exchanged for a stone axe. However, the goods exchanged sometimes are not what
the other party needs. Therefore, it is necessary to find an object that can
be acceptable to both in exchange, which is the primitive money. As a result,
some items that are not easy to be obtained a large quantities, such as rare
shells, fabrics, feathers of rare birds, precious stones, alluvial gold, etc.,
are assumed to act as the universal equivalent, namely primitive commodity
money, at different times in different regions. On average, the logistics cost
of primitive commodity money is lower than barter. However, this kind of
equivalent commodity still has fatal disadvantages such as difficulty in
carrying and storing. That is to say, it has high logistics cost.

Universal equivalent, as the medium of exchange, needs to frequently circulate
among commodity producers. Obviously, it will be touched by countless people.
What’s more, money usually can be saved to store value for a long time, which
retains purchasing power into the future. However, it is impractical for some
commodity money, such as shells, fabrics, cocoa beans, to store wealth for the
future.

With the second great division of labor in society, handicraft industry was
separated from agriculture. Due to the inventions in melting technology, metal
gradually become the mainstream of universal equivalent in trading, which made
metals as coin materials. Generally, metals, such as gold, silver and copper
etc., have the advantages of stable value, divisibility and easy to carry. As
a result, they played the role of money in a long time. Obviously, the
logistics cost of metal money has been reduced significantly.

In the early days of commodity economy, most countries and regions used base
metals as money, for example, copper. Base metals are compatible with the
initial commodity economy. However, there was a problem later that monetary
materials competed for raw materials to used for manufacturing. Moreover, base
metals lost their suitability as media of exchange when their value per pound
became too low. For example, the copper money of seventeenth-century in Sweden
was notoriously cumbersome. Individual pieces of copper "plate money"
eventually weighed up to 20 kilograms (44 pounds). Strong young men had to be
employed to carry the copper to make an ordinary-sized commercial purchase,
which made the logistics cost extremely high. Finally, Swedes stopped using
copper, except in some small trading (White, 1999)[5]. In the 19th century,
many countries in the world joined the Latin Monetary Union (LMU) and adhered
to bimetallism (Bae et al., 2011)[6].

Paper money emerged after metal money, also known as credit currency, has
almost no logistics cost. Actually, paper money is a promise or liability
which represents physical assets by a piece of paper that circulates as medium
of exchange (Battilossi et al, 2018)[7]. Of course, in a serious inflation
period, people need to use a lot of money to buy daily necessities. When the
value of paper money is similar to its cost of production, there is still high
logistics cost.

After entering the Internet era, electronic money has been widely used.
Electronic money will inevitably reduce the time and space disposal of
expenses of payment and settlement transactions, which increases the volume of
transactions by promoting transaction convenience (Mohamad et al., 2002)[8].
In this case, people can realize the long-distance transmission and payment of
money in a short time which makes the transactions convenient. Therefore, the
circulation of money has truly entered the era of no logistics cost.

The logistics cost of money in various historical periods are shown in Fig.1.
Among them, cattle and sheep are the representative of barter, and shells are
the representative of the primitive commodity money.

Figure 1: Logistics cost for each stage of monetary development

In the process of monetary evolution, human beings always tend to choose money
with lower logistics cost. Obviously, as a medium of exchange, the
minimization of logistics cost is one of the goals pursued in the process of
monetary development.

##  3 A technology framework to design a currency of stable value based on the
trade-offs between store of value and storage cost of anchor

The first function of money is measure of values. Just as a weight used on a
balance itself has weight, obviously, money used to measure the value of a
commodity itself is also a commodity and has intrinsic value. Therefore,
commodity money can serve as a measure of value.

After the seller converts goods into money in the trading process, the money
will be deposited for a period of time, and then be used to buy other goods.
In these processes, there will be logistics costs for carrying and storing
metal money. Therefore, in order to reduce the cost in exchange of goods and
money, it is not difficult to understand that people choose the precious metal
material with the highest intrinsic value per unit weight or volume to cast
specie. In fact, it is the embodiment of minimizing the logistics cost of
commodity money.

On the one hand, specie is constantly being worn out in circulation, on the
other hand, considering that the function of money as a medium of circulation
is only a transient medium. Therefore, either devalued specie or even a
currency symbol with no intrinsic value at all, can also replace metal money
in circulation. From this point of view, to symbolize commodity money is the
best way to prevent it from being worn and tore in circulation.

As a store of value and a universal representative of asset or material
wealth, money should have the function to be directly convertible into any
other commodity. In other words, it must be full-bodied commodity money, such
as gold and silver specie or bullion. Generally, only full-bodied metal money,
namely honest money that its value is honestly established in the marketplace
without bankers, government, politicians, or the Federal Reserve manipulating
its value to serve special interests (Paul, 2008)[9], can be saved and serves
as a store of value. On the contrary, it is not stable for the wealth
represented by hoarding paper money. Obviously, storage cost of paper money is
much lower than that of the metal money. However, the devaluation rate of
credit currency is unpredictable, which renders it hard to store wealth. It is
a basic fact that since credit currency dominated the Global Financial System,
Western developed countries have been fighting against inflation, and the harm
caused by hyperinflation has been obvious to all.

In a nutshell, honest money (physical money) is the best choice considering
the functions of a measure of value and a store of value. Nonetheless, the
main drawbacks are as follows: first, logistics cost is high in circulation;
second, the weight of the metal loss is not easy to be controlled; third, it
is hard to avoid hoarding of money, especially precious metals. From the
perspective of a medium of circulation, paper money and digital money with
zero logistics cost are the best choices.

Based on what has been discussed above, from the perspective of logistics
cost, the design approach of future new money should satisfy the following
constraint conditions: (1) it has almost no logistics cost including
transportation or carrying cost in circulation and safekeeping cost in
storage; (2) It has no weight loss in circulation; (3) It has the function of
storing wealth; (4) Hoarding of money can be avoided which will not result in
a shortage of market liquidity;(5) It contains the property of scarcity
resource, such as precious metal money (commodity money), and over-issue is
not easy.

The above characteristics of the new currency actually are a combination of
physical money and credit currency. According to these analyses, the best
design approach for future money is the digitization of physical money.

##  4 Inventory cost of mortgage assets were intentionally hide in the process
of signifying commodity money

About a thousand years ago, base metal money, mainly iron and copper coins,
was circulated as currency in Sichuan, China. When merchants faced with large
transactions, carrying heavy metal money will significantly increase logistics
costs. To reduce the carrying cost of specie in circulation, some businessmen
set up deposit shops named “jiaozi” shops to specialize in safekeeping of
metal money for merchants with large sums of money. In this case, the
depositors hands over their money to the shop, and then were given a slip of
special paper named “jiaozi” that made from mulberry leaves, recording the
amount of cash they had with that shop. If the “jiaozi” holders show the paper
to that shop, they could redeem on demand in metal money after paying a
safekeeping fee of 3% (Xue, 2015)[10]. Actually, “jiaozi” is regarded as the
first paper money used in China and even in the world. Afterwards, many
merchants jointly established the deposit shops specializing in the issuance
and exchange of “jiaozi”, and set up branches in other places. Since the
deposit shops abide by their credit and keep the promise, “jiaozi” could be
converted into money at any time. Eventually, “jiaozi” were served as currency
for decades in the region (Battilossi et al., 2018)[7].

In the middle of the 17th century, a lot of goldsmiths engaged in the
production of gold jewelry. Some civilians got rich through business, and they
put their gold stored in the goldsmith’s shops, then goldsmith wrote a receipt
for the depositors. Depositors can withdraw their gold at any time with the
receipt, at that time, goldsmiths needed to be paid safekeeping fees and
handling fees. The further development of the business, goldsmiths can also
transfer gold and silver from the depositor A to the customer B upon the
written request of depositor A. From the perspective of modern logistics, the
early goldsmith in England is equivalent to the current third-party logistics,
and the goldsmiths were the leading financiers in England (Milevsky,
2017)[11].

Later, the receipt of safekeeping gold coins evolved into a format
certificate. The depositors or certificate holders found that when they needed
money to buy goods, they did not have to withdraw the gold at all and just
gave the certificate to the supplier. And then later, goldsmiths realized that
the certificates they had issued could be used as money. Therefore, they began
to issue “fake certificates” for lending and reaped the benefits. As long as
all depositors do not come to withdraw gold on the same day, “fake
certificates” are equivalent to “real certificates”. This shows the origin of
the “deposit reserve system” in modern banks. In a nutshell, physical money
was replaced by “fake certificates”, and the goldsmiths, as third-party
logistics, evolved into banks. So, goldsmiths not only are no longer charged
the storage fee but also paid some fees to depositors. Actually, this method
was adopted by ancient Chinese banks, generally called qianzhuang, whose
certificates were called “yinpiao”, a bank notes or receipt of storage silver
(Yang et al, 2019)[12]. In this way, the safekeeping fee of gold and silver
magically disappear in the black hole of the certificate market.

As the safekeeping receipts evolved into bank notes, transferring certificates
evolved into bank checks, and full reserves turned into fractional reserves
system, the goldsmith industry gradually developed into a banking industry
with main business on money. The essential practice of modern banks is still
to lend out the depositors’ assets to obtain profits, which will cover
safekeeping fee (inventory costs) and interest expenditure for depositors.

From the above analysis on the origin of banks and credit money, we can find
that as an honest money with the function of a store of wealth must be a
commodity money, and any bank note will enter a devaluation channel if they
can’t redeem on demand in gold or other assets of anchor. In order not to
reduce the monetary function of a store of wealth, only to restore the
goldsmith as the warehouse night watchman. In this way, we can put the
logistics cost of commodity money back into people’s sight from the
disappearing black hole. And this cost would be clearly reflected on the bank
notes or certificates of anchor goods.

##  5 The paradox of the existence of a currency of "stable value"

Stablecoin is a cryptocurrency that can keep a stable exchange rate with its
anchor. It is designed to be price stable with respect to some anchor (Moin et
al., 2020)[14].

The stablecoin can be divided into the following several types according to
the different anchors. (1) Fiat Stablecoins, backed by fiat money as
collateral; (2) Digital stablecoins, backed by crypto-assets like Bitcoin as
collateral; (3) Commodity Stablecoins, backed by commodities like precious
metal as collateral; (4) Algorithmic Stablecoins without collateral, backed by
users’ expectations about the future purchasing power of their holding.

Among them, commodity stablecoin is the most expected choice. In theory, the
anchor goods of stablecoins can be precious metals, steel, real estate, etc.
For instance, AnthemGold, a Texas-based blockchain company, launched its gold-
backed asset token AGLD (Business Wire, 2019)[14]. Each token is backed by one
gram of gold. Evidently, it is a stablecoin that anchors physical assets.

Up to now, there is no strict definition of stablecoins. In the following
text, we will define a stablecoin as one kind of certificate that can be
converted into mortgage assets at any time. It can be considered as a currency
of "stable value". Next, we will prove that it is impossible for the currency
to exist.

We assume that the customer $k$ buys $n_{k}$ tokens of AGLD at time $t_{k}$
with $n_{k}$ grams of gold (or equivalent fiat money, like US dollars at the
same time and place). After a period of time, the customer or the person who
is in possession of tokens redeems gold at time $t_{k}^{\prime}$ . The
customer will pay the processing fee to the AnthemGold company is $\beta$ per
token, thus the gross profit issuer can obtain is formulated as follows:

$C^{\mbox{profit }}=\sum_{k}\beta\times n_{k}$ (1)

The logistic cost of the issuer can be formulated as follows:

$C^{\mbox{warehouse }}=\sum_{k}\alpha\times
n_{k}\times\left(t_{k}^{\prime}-t_{k}\right)$ (2)

Where, $\alpha$ is warehouse cost of saving one gram of gold per day, which
consists of transportation cost, settlement cost, storage cost, management
cost, etc.
If the gross profit of issuer can’t cover logistic cost, i.e., the follow
condition will be met,

$C^{\mbox{profit }}<C^{\mbox{warehouse }}$ (3)

then the issuer will go bankrupt. Obviously, there exist always such a day
when condition (3) is met. Without loss of generality, assuming that the whole
system has only one customer, formula (3) can be simplified as $\beta\times
n<\alpha\times n\times\left(t^{\prime}-t\right)$. We can still find the buying
time $t$ and selling time $t^{\prime}$ of the stablecoin AGLD, which makes the
following formula (4) work.

$t^{\prime}-t>\frac{\beta}{\alpha}$ (4)

In order not to go bankrupt, after collecting the user’s collateral, the
issuer invests the collateral during the user holds the stablecoin, which will
earn interest for issuer. In this case, investment risk will be generated.
Therefore, stablecoins will be unstable. AGLD is similar to the U.S dollar
during the Bretton Woods system, except that there was no function to convert
gold to individual holders of US dollars. The Bretton Woods system priced an
ounce of gold at $35.2, therein $0.2 was for transportation fee. According to
formula (4), the accumulation of its warehouse cost will eventually consume
all the gold. Hence, the Bretton Woods system is bound to collapse, which
means that the decoupling of the dollar from gold is a historical necessity.

In the same way, "a 100 Percent Gold Dollar" proposed by Rothbard[15] in the
last century cannot exist stably, because he did not propose a gold redemption
route that face value devalues over time.

In conclusion, for any currency anchored by 100% commodities, as long as it
does not have a timestamp and its face value does not devalue over time, then
the currency cannot become a stablecoin or as a currency of "stable value".

##  6 A honest currency of "stable devalued" model based on "gold" standard

We have proven that an absolute currency of stable value is impossible to
become a reality, except for commodity money. Although the logistical costs of
digital currency and banknotes can be negligible, they hardly fulfill the
function of money as a store of value. While commodity money such as precious
metals can store wealth, the logistical costs of circulation are too high.
Taking the advantages of both, we innovatively design an honest currency of
“stable devalued”, a brand-new currency named (DSC, similar to DCM in
reference [16]) and built a attenuation model of intrinsic value of the honest
money based on storage cost of anchor assets. Obviously, a SDC issuer must
adopt full reserve system, and the anchor of the SDC should be some physical
commodities rather than a credit currency.

###  6.1 The Design Principle of An honest stable devalued coin

Supposing a currency issuing institution (a bank or a finance company) $B$
issues a type of SDC at time $t$ (usually in the New Year’s day of a certain
year such as January 1, 2035). Each SDC contains a gram of precious metal $m$
as a mortgage assets. Issue number is $N_{B}^{m}(t)$. Let
$M_{B}^{SDC}(t,m,W,\rho,\theta,E,\Delta W)$ denote the certificate of a SDC,
where $t$ is the date of issue, and $m$ stands for the mortgage assets, $W$
for the weight of anchor goods each SDC, $\rho$ for purity of the the metal
materials as anchor assets, $\theta$ for the attenuation coefficient of the
weight of anchor goods, $E$ for the expiry date of SDC and $\lambda$ is the
delivery fee rate for SDC holder to redeem for collateral. Take gold as a
case, for example, $m$ is gold, $W=1$ , $\rho=0.9999$ , $E$ is fifty years,
and the volume of issuing is 2 billion shares (2,000 tons) , $\Delta W=3\times
w^{\mbox{remaining }}\left(t^{\mbox{redemption }}\right)/1000$ ,
$t^{\mbox{redemption }}$ is the redemption time and $w^{\mbox{remaining
}}\left(t^{\mbox{remaining }}\right)$ is the residual weight of a SDC. The
redemption fee equals to 3‰of the weight of the residual value, i.e.,
$\lambda$= 3‰.

Thus, the residual weight of a SDC at date $t+\Delta t^{\prime}$ is

$W\left(t+\Delta t^{\prime}\right)=W\times\theta^{\Delta t^{\prime}}$ (5)

Let $P_{B}^{m}\left(t+\Delta t^{\prime}\right)$ denote the price of the
precious metal $m$ with purity $\rho$ , where the price is set according to
the local currency. Then, a customer needs to pay $P_{B}^{m}\left(t+\Delta
t^{\prime}\right)\times W\times\theta^{\Delta t^{\prime}}$ for a SDC. In
practice, the customer can give the issuer $W\left(t+\Delta t^{\prime}\right)$
units of the precious metal $m$ for a SDC. In this case, the issuing
institution $B$ will inspect whether the precious metal submitted by the
customer meets the purity standards, and this will incur an inspection fee of
$\Delta H$. Considering that the local currency is not stable, $\Delta H$
could differ at different times, and the issuing institution $B$ will have to
announce $\Delta H$ in advance.

When a SDC holder needs to redeem the collateral of a SDC at time $t+\Delta
t^{\prime\prime}$ , the quantity of precious metal available to the customer
is

$W_{mB}^{\mbox{Redemption
}}\left(t+t^{\prime\prime}\right)=\theta^{t^{\prime\prime}}\times
W-\lambda\times\theta^{t^{\prime\prime}}\times
W=(1-\lambda)\theta^{t^{\prime\prime}}W$ (6)

The second item in the formula (6) is fees arising from such delivery at
redemption.

Of course, the issuer can require that the amount of the precious metal $m$
redeemed must be an integer multiple of certain units (for example, one
kilogram of gold is the minimum unit). In any case, SDC holders have a
relatively clear expectation of the future wealth.

###  6.2 A Numerical Examples of SDC

To further illustrate the innovative principle of SDC, we design an honest
stable devalued coin named SDC_AU999, issued by LIN on January 1, 2030, with a
circulation of one billion coins. Each coin is backed by one-gram of gold with
a fineness of 99.9%. As mortgage assets, one thousand tons of gold were
entrusted to a warehousing company in Switzerland to be stored in caves in the
Alps. Besides, the marking information for each SDC_AU999 includes : the
issuing date is on January 1, 2030, the mortgage asset is 99.9% gold, the
weight of associated asset is 1 gram, the daily attenuation coefficient is
$\theta=99.996\%$, the delivery fee is 3‰of the actual delivery weight, the
minimum delivery weight is 1000g and the delivery point is appointed by LIN.
and the validity is 50 years, i.e. December 31, 2079 (see notes for
redemptions beyond validity).

When a client want to buy 2000 coins, i.e., certificate of SDC_AU999, on July
1, 2030 in New York, the actual weight of mortgage assets for each coin after
183 days will be:

$W(183)=W\times\theta^{183}=1\times 0.99996^{183}=0.9927(\mathrm{~{}g})$ (7)

If the global gold price on that day is $1500 /OZ and the selling price in New
York is 101% of that, the money that the client needs to pay will be:

$\displaystyle P_{mB}^{\mathrm{Sell}}(183)$ $\displaystyle=(1500\times
1.01)\times W\times\theta^{183}$ (8) $\displaystyle=1515\times
0.9927/31.1035=48.35(\mathrm{USD})$

Thus, the client should pay 96705.55 USD for 2000 coins of SDC_AU999 actually.

The opposite is the SDC holders to redeem the mortgage assets. When a SDC
holder wants to redeem for gold on January 1, 2031, the residual weight of
2000 coins of SDC_AU999 will be:

$W(365)=2000\times 0.99996^{365}\times(1-0.003)=1965.0986(\mathrm{~{}g})$ (9)

Considering that the minimum unit of delivery weight is 1000g, the client can
make up for the payment for goods according to the gold price of the day, and
then can get 2000 grams of gold with purity of 99.9%.

If the client wants to convert SDC into the currency of the country, one way
is to sell DCM-SDC on the market; and another is to sell SDC back to issuer.
Assuming that the repo rate of the issuer recycle a SDC is 2‰of the residuary
weight, and then the chargeable weight will be:

$W(365)=2000\times 0.99996^{365}\times(1-0.002)=1967.0698(\mathrm{~{}g})$ (10)

Assume the gold price is $1600 / OZ on that day, the charge that issuer should
pay to the client will be:

$P_{mB}^{\mbox{buy-back }}(365)=1967.0698\times
1600/31.1035=101188.36(\mathrm{USD})$ (11)

The mode of SDC circulation can be similar to the paper money or digital
currency, or to Bitcoin’s mode which is through an open management account
transfer mechanisms. In order to prevent SDC over issue by some authorized
banks, the SDC’s mortgage assets which are stored by third-party logistics
service provider need to be over sighted by the third-party needs to receive a
third party must be supervised by relevant international organizations like
IMF.

Of course, banks can also accept SDC deposits, similar to the rules for fiat
deposits. Obviously, the devalued stablecoin is a good money that can store
wealth well. Moreover, due to the SDC own attenuation function, it cannot be
widely hoarded by people, which can avoid the risk of a shortage of liquidity.

###  6.3 The Model for determining the attenuation coefficient of SDC

For example, the financial institution $B$ issues $N$ certificates of SDC
anchored with precious metal $m$ at the time of $t$. If the initial weight of
each SDC is $W$, the total initial weight of mortgage assets is $N\times W$ .
Assuming the validity period of the SDC is $E$, we can split $E$ into $D$
intervals $\\{1,2,\cdots,d,\cdots,D\\}$. Let $w^{\mbox{remaining }}(d)$ denote
the residual weight and $\Delta w(d)$ is the extracted weight from a SDC in
the intervals $d$ (at the end of the period of time), we have the expression
as follows:

$\Delta w(d)=w^{\mbox{remaining }}(d)-w^{\mbox{remaining }}(d-1)=\mu(d)\times
w^{\mbox{remaining }}(d-1)$ (12)

where $\mu(d)$ is the attenuation coefficient of SDC in the intervals $d$.

Let $c^{\mbox{storage }}(d)$ denotes the storage charge to store a unit weight
of the metal $m$ in the intervals $d$, which including warehouse rent,
management staff salary, etc., and $P_{m}^{\mbox{precious\\_metal }}(d)$
denotes the price of the precious metal $m$ at that time, the condition that
the issuer does not lose money is:

$P_{m}^{\mbox{precious\\_metal }}(d)\times\Delta w(d)\geq c^{\mbox{storage
}}(d)\times w^{\mbox{remaining }}(d-1)$ (13) $\qquad P_{m}^{\mbox{precious
}_{\mbox{metal }}}(d)\times\mu(d)\geq c^{\mbox{storage }}(d)$ (14)

So, we can get the condition:

$\mu(d)\geq\frac{c^{\mbox{storage }}(d)}{P_{m}^{\mbox{precious\\_metal }}(d)}$
(15)

A simple way to calculate the attenuation coefficient is to take the average
of all $\mu(d)$ :

$\bar{\theta}=\frac{1}{D}\sum_{d=1}^{D}\mu(d)=\frac{1}{D}\sum_{d=1}^{D}\frac{c^{\mbox{storage
}}(d)}{P_{m}^{\mbox{precious\\_metal }}(d)}$ (16)

It can be seen that the attenuation coefficient depends on the predicted price
and storage costs of the precious metal $m$ for every intervals of time.

During the expiry date $E$, some SDC holders may redeem their mortgage assets.
The issuer can resold these SDCs or destroy it.

In fact, there are always some SDCs backlog in the issuer’s hand, which are in
a state of for sale and will incur the cost of capital tied up. Therefore, the
attenuation coefficient need to have a small correction as follow:

$\theta=\bar{\theta}+\Delta\theta$ (17)

The size of parameter $\Delta\theta$ should be determined by issuer according
to the estimate speed of the SDC sales.

###  6.4 An approach to redemption of SDC over expiry date

If the SDC holder still does not redeem the mortgage assets of SDC from the
issuer $B$ in expiry date $E$ with the version, the issuer shall have the
right to set new attenuation coefficient for the expired certificates.

We can cope with this problem in two different ways in regards to the
conditions. First, if the issuer $B$ has recently issued a version of SDC’
before the expiry date $E$ and its expiry date $E^{\prime}>E$, the default
attenuation coefficient is equal to version SDC’. The second case is the above
condition is not met. In this case, the issuer $B$ need to refer the
attenuation coefficient which of the similar SDC issued by other issuers.

Supposing that there are $N^{\mbox{bank }}$ banks issued the SDC with precious
metal $m$ as mortgage assets during the period of time $(E-\Delta E,E)$, the
corresponding attenuation coefficients are
$\left\\{\theta_{1},\quad\theta_{2},\cdots,\quad\theta_{N_{m}^{bank}}\right\\}$
respectively. The mean value $\bar{\theta}$ is:

$\bar{\theta}=\frac{1}{N_{m}^{bank}}\sum_{k=1}^{N_{m}^{bank}}\theta_{k}$ (18)

The maximum one of these attenuation coefficients is as follows:

$\theta^{\mathrm{max}}=\max\left\\{\theta_{1},\quad\theta_{2},\cdots,\quad\theta_{N_{m}^{bank}}\right\\}$
(19)

Considering that SDC holders should the blame bear since they did not redeemed
within the prescribed time limit, the determination of the attenuation
coefficient of some overdue SDC can be higher than the average value of the
market as follow:

$\theta^{\mbox{overdue }}=\bar{\theta}+\alpha\times\theta^{\max}$ (20)

where the coefficient can take a certain value of $\alpha\in\\{0,0.5\\}$.

##  7 Conclusions

Strictly speaking, for any currency anchored by 100 % commodities, as long as
it does not have a timestamp and its face value does not devalue over time,
then the currency cannot become a stablecoin or as a currency of "stable
value". Although commodity money itself, such as precious metal money, has its
inherent basic value, a major drawback of physical money is high logistics
costs in circulation. When representative money comes into use, such as silver
certificate issued by private financial institutions in Shanxi one or two
hundred years ago, in theory, the logistics cost reduces to nearly zero.
However, this is based on the assumption that banks, as the third-party
logistics, provide customers with physical currency custody and exchange it
for physical goods without compensation. In fact, we cannot assume that free
storage always exists. Hence, financial institutions that keep anchor goods of
representative money generally lack the integrity owned by third-party
logistics companies. They would inevitably appropriate anchor goods for other
uses or set up obstacles to conversion, such as inconvertibility, to gain
profits and pay storage fees. In history, the cost of safekeeping anchor goods
is basically realized through the risk transfer of lending, while credit money
transfers its risks through the devaluation. Therefore, there is no absolute
stablecoin whose value does not decay in proportion to time.

Due to the progress of technology and the cost of access to resources in the
fall, it is difficult to try to stabilize the buying absolutely power of a
monetary units. One of the feasible ways to build an honest money system is to
symbolize commodity money as a certificate which can redeem mortgage assets on
demand. A difficult problem to solve is how to pay issuer who is as the
warehouse night watchman the safekeeping fee. How fast is a rational rate for
devaluation of denomination of certificate, which is an acceptable solution to
both the issuer and holders of certificate? In addition, in consideration of
the dramatical price fluctuation of the current virtual currencies, such as
Bitcoin, we also can set an attenuation coefficient for them in order to
increase stability.

## Acknowledgments

This research is supported by the Program of the Co-Construction with Beijing
Municipal Commission of Education of China (Grant No. B20H100020, B19H100010).
The authors wish to thank Prof. Ning Wang of Mathematical Institute,
University of Oxford , Prof. Xiaojun Jia of Beijing Laboratory of National
Economic Security Early-warning Engineering and Mr. Xiaohong Zhao of Beijing
Jiaotong University for their valuable comments and suggestions.

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$\lambda\in(-1,1).$ Only the coefficient of equation (5.3) is needed to prove
that there is no almost rectifiable basis. The written polynomial coefficient
is proportional to $\lambda_{1}^{2}$ except for the cases
$2\mathfrak{n}_{1,1}$ and $\mathfrak{s}_{5,43}$, whose coefficients are
proportional to the polynomials $\lambda_{2}^{2}+\lambda_{3}^{2}$ and
$\lambda_{5}^{2}$.

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