As the world economy heads further into uncharted territory with commodity deflation, negative interest rates abroad, The Brexit, and the economic turmoil in Venezuela, one notable economist and former U.S. Treasury Secretary, Larry Summers, has proposed a radical solution to curb criminal activity, drug and human trafficking, tax evasion, and money laundering by eliminating large denominational notes in both the U.S and Europe through either legal tender laws or by legislation. His proposal is based off of a working paper by Peter Sands from the Mossavar Rahmani Center for Business and Government.

This policy would include the 500 Euro note and the $100 bill. By 2018 , the European Central Bank will no longer be producing the 500 Euro(although it will still be considered legal tender) and it will be slowly phased out. At first glance, this may seem like a harmless policy change. After all, as Summers states, “There is little if any legitimate use for €500 notes. Carrying out a transaction with 20 €50 notes hardly seems burdensome — and this would represent more than $1,000 in purchasing power.”

Kenneth Rogoff, the Thomas D. Cabot Professor of Public Policy at Harvard University and former chief economist of the International Monetary Fund, has echoed Summers in a recent essay for the Wall Street Journal. His claim is that the use of cash in general not only gives rise to the same criminal activity that Summers has stated, but also enables illegal immigration by allowing these workers to be paid off the books in cash. The difference between Summers and Rogoff is a matter of degree, in which Summers only targets eliminating the $100 bill, while Rogoff suggests that the $20 bill and $50 bill are be phased out as well.

To be fair, phasing out the largest of these denominational bills would prevent virtually no day-to-day transactions, for the lone reason that this note is the equivalent of a $600 bill. However, in this article, I will discuss why I believe that this potential future policy (particularly in the U.S.) creates a unique opportunity for investors,savers, and businesses.

An important addition to this policy that is mentioned by Rogoff is that interest rates must go into negative territory in order to stimulate spending and borrowing so that the increased economic activity will induce businesses and investors to spend and invest to combat the low economic growth the U.S. has seen in recent years. In what economists call the zero lower bound, where effective interest rates go below zero, businesses should theoretically be induced to borrow with such low borrowing costs, and consumers should be more willing to spend instead of save due to such low rates. As Rogoff states:

In principle, cutting interest rates below zero ought to stimulate consumption and investment in the same way as normal monetary policy, by encouraging borrowing. Unfortunately, the existence of cash gums up the works. If you are a saver, you will simply withdraw your funds, turning them into cash, rather than watch them shrink too rapidly. Enormous sums might be withdrawn to avoid these loses, which could make it difficult for banks to make loans—thus defeating the whole purpose of the policy.

Take cash away, however, or make the cost of hoarding high enough, and central banks would be free to drive rates as deep into negative territory as they needed in a severe recession. People could still hoard small bills, but the costs would likely be prohibitive for any realistic negative interest rate. If necessary, central banks could also slap temporary fees on any large withdrawals and deposits of paper currency.

My analysis will be limited to the $100 bill in particular, although if smaller denominations are eliminated afterward then this will also apply to them to a lesser extent due to the higher rates of inflation that are likely to follow such policies including negative interest rates charged on checking deposits and savings accounts. While real interest rates in the U.S. are currently negative due to price inflation exceeding the rates that banks are paying to customers, I will be focusing on negative nominal rates from this point on(unless otherwise stated). I will also ignore the moral and ethical arguments against this policy which have been stated already.

According to recent estimates by the Federal Reserve, the total amount of money in the U.S. economy(known as M2) is currently about $12.7 trillion. However, most of this money is digital, with only $1.4 trillion, or 11 percent, consisting of physical cash(approximately half of which is held abroad). The rest is contained digitally in checking and savings accounts among others. Of this $1.4 trillion, $1.08 trillion are composed of $100 bills. So over 78% of all the value of physical currency in circulation is from these large notes.


Assuming that negative interest rates will be combined with both the halt in production of such large denominational notes and the elimination of their legal tender status(or them being outright outlawed), it can be safely assumed that there will be one of two outcomes. Either 1) $100 bills will be hoarded or 2) they will still exchange and circulate at a “premium” to digital dollars. For it to be determined which of these is the likely outcome, it is necessary to understand a concept known as Gresham’s Law.



In its most basic form, Gresham’s Law states that “bad money drives out good money”. But this is not complete. For this to theoretically hold true, the exchange rate between the “good” money and the “bad” money must be equal. Or to be even more precise, the legal exchange rate at which these two monies exchange must differ from the market(non-par) price. In that case, debts and transactions will be paid with the bad(overvalued) money, while the good(undervalued money) will be hoarded.

A Federal Reserve research paper by Rolnick and Weber questions the theoretical and historical validity of Gresham’s Law, providing substantial evidence that undervalued money doesn’t always disappear from circulation. They found several examples in the U.S. of undervalued money (alternating between gold and silver at different periods) actually circulating at a premium beside the overvalued money dictated as legal tender by the federal government. For example, between 1793 and 1846, when gold was undervalued at the mint(1793-1833), 25% of the money in circulation consisted of gold; when silver was undervalued at the mint(1834-1846), almost half of the money in circulation was silver. They make this observation, as well as others, and base it on the existence of fixed transaction costs, rather than fixed exchange rates(between these monies) which, according to their research, have never actually existed:

If such a rate were ever managed-through a mint policy or a legal tender law, for example-it would imply potentially unbound profits for currency traders at the expense of a very ephemeral mint or a very naive public.

It is my contention that a similar version of Gresham’s Law will apply with the abolishment of cash, particularly higher denominational bills previously mentioned, being combined with negative nominal interest rates. There are several differences between my version and the one proposed by Rolnick and Weber. While their work is based almost entirely on gold and silver as monies at different time periods, I will be concentrating on physical cash versus digital dollars. But before it can be seen why real dollars will circulate with digital dollars at a premium instead of being hoarded, it must be understood why the idea of a significant general price deflation, or a rise in the purchasing power of the dollar(whether digital or real) in the U.S. economy, is extremely improbable without negative interest rates and legal tender laws.



First, while the banking system, operationally known as fractional reserve banking, allows for both an expansion and contraction of the money supply, the incentives for an expansionary monetary policy greatly outweigh the latter. This is in spite to the fact that deflation, while good for creditors(i.e. banks), is bad for debtors(individuals). However, if deflation is significant this relationship only holds true up until the moment of default on the part of the debtors, who cannot repay the loans to the creditors due to the increasing nominal value of debt. Default is the instantaneous transfer of wealth from the creditor to the debtor. If this were to happen on a large enough scale, the banking system would be heavily crippled. It can also be ascertained that while the government can gather revenue from taxes on capital gains and especially rising nominal incomes, the same cannot be said in a deflationary world. With the prices of goods and services falling, real incomes and wealth are increased, even though nominal incomes stay the same or fall less than prices. The difference is, the government has yet to figure out a way to tax the increase in real wealth with deflation. They can only do so with inflation and the inevitable rise in nominal wages that accompanies it. And in a serious deflationary recession the federal government will be hard-pressed to collect tax revenue if GDP falls, unemployment rises, and the banking system falters. It should be said that it is conceptually possible for the government to do this in a similar manner to which they do it with rising nominal incomes. The problem would be using a price index that is accurate in estimating falling prices. While it is possible, it can be ignored for the purpose of this analysis.

Second, due to the digitalization of monetary exchanges in our economy, consumers are becoming less inclined to carry physical cash around with them. This is primarily due to the existence of credit cards, debit cards, and EBT cards. These “substitutes” for cash, along with other clearing systems, have reduced the demand to hold cash balances, thus artificially raising relative prices more than what they otherwise would have been over time(when coupled with low rates). Other digital payment systems such as Paypal and Venmo link directly to your bank account, reducing the need to exchange real dollars. This also reduces the demand to hold physical cash(balances).

Third, and most importantly, due to the nature of fractional reserve banking, a significant fall in prices in our economy rests solely on money being “idle”, or not spent. In other words, if, generally speaking, cash balances are lower than they otherwise would be due to the previous reasons given, then the possibility for deflation is virtually eliminated. The last time the U.S had any real deflationary pressure was during the first years of the Great Depression. This is primarily due to consumers taking money out of their respective banks and “hoarding” it. While this is certainly possible for consumers to do today, it cannot be maintained in the aggregate. As economist Gary North states:

…it is not possible for depositors to take sufficient money in paper currency notes out of banks and keep these notes out, thereby reversing the fractional reserve process, thereby deflating the money supply. That was what happened in the USA from 1930 to 1933. If hoarders spend the notes, businesses will re-deposit them in their banks. Only if they deal exclusively with other hoarders can they keep money out of banks. But the vast majority of all money transactions are based on digital money, not paper currency.

Today, large depositors can pull digital money out of bank A, but only by transferring it to bank B. Digits must be in a bank account at all times. There can be no decrease in the money supply for as long as money is digital. Hence, there can be no decrease in prices unless it is FED policy to decrease prices. This was not true, 1930 to 1933.

Consumers, while currently having the power to hoard physical cash, don’t have the means to prevent this money from being stored digitally while they still use it, to any extent, as a medium of exchange.



Now, let’s explore a scenario where the Federal Reserve lowers nominal interest rates below zero, thus causing banks to do the same to their depositors(to maintain profit margins). This could be due to inflation slowing(disinflation), a significant correction in the stock market, or some international economic disturbance such as Brexit. If the Fed gave markets significant notice of this policy change, consumers would merely begin to withdraw their money from banks and acquire cash to escape the negative rates, which is essentially the same as saying that they would be paying the banks to hold onto their money. But what if the government changed the law so that large notes over $50 were no longer considered legal tender(coupled with the the U.S. Treasury no longer printing $100 bills) or were made illegal as money as proposed by Summers? While the outcome would be similar if not the same for either policy, we will look at both separately.

Let’s take the circumstance of a change in the legal tender status of the $100 bill first. Most would respond that those still possessing $100 bills would simply hoard them, transforming them from a medium of exchange to an asset to be held as a buffer against uncertainty or inflation, as they(and gold were) during the Great Depression. This, however, would most likely not be the case. Legal Tender laws are often confused with the idea that only legal tender can be used in both private and business transactions. But this is not true. From the Federal Reserve’s official website:

Section 31 U.S.C. 5103, entitled “Legal tender,” states: “United States coins and currency [including Federal reserve notes and circulating notes of Federal reserve banks and national banks] are legal tender for all debts, public charges, taxes, and dues.”

This statute means that all United States money as identified above is a valid and legal offer of payment for debts when tendered to a creditor. There is, however, no Federal statute mandating that a private business, a person, or an organization must accept currency or coins as payment for goods or services. Private businesses are free to develop their own policies on whether to accept cash unless there is a state law which says otherwise.

In other words, there is no reason why a consumer cannot pay for a product with another type of money other than dollars. This can be seen with the creation of Bitcoin and others “crypto” or purely digital currencies. Websites such as and Expedia, along with many brick-and-mortar businesses accept Bitcoin as the means of final payment for their goods and services. While these payments are most likely eventually exchanged for dollars, this is beside the point. Economist Bob Murphy makes this clear:

Even though the US government can tell Americans which pieces of paper are dollars, it cannot tell Americans that dollars are the money that they will use economically. The existence of legal-tender laws and other regulations complicates the issue, but nonetheless it is possible that next Tuesday, nobody will want to hold US dollars anymore and so their purchasing power will collapse, with prices quoted in US dollars skyrocketing upward without limit. This has happened with various fiat currencies throughout history, and these episodes did not occur because the State in question repealed a regulation that had previously ensured its currency would be the money of the region. Instead, the people using that currency simply abandoned it in spite of the government’s desires, resorting either to barter or adopting an alternative money.

In a world of negative interest rates, consumers would be induced to withdraw their money from banks due to the opportunity cost of paying a “fee” for having the banks holding their deposits. In essence, if the $100 bill were no longer legal tender according to law, these large notes would still be used as a medium of exchange. This is especially true if price inflation is increasing which is a likely scenario in a negative rate environment, which would cause digital money to be exchanged at a discount(and physical dollars including the $100 bill at a premium).

In addition to negative nominal interest rates charging a percentage to customers’ digital accounts, there would likely be an increase in bank fees. These would include, but not be limited to, debit card fees, overdraft fees, user fees, and ATM fees(for withdrawing small bills), not to mention hidden fees. For example, according the Wall Street Journal, out-of-network ATM fees have risen over 50% in just the last ten years. While these fees already exist, there is considerable reason to believe they would be expanded or increased as such due to the fact that the majority of U.S. citizens would be discouraged from using larger denominational notes, and hence would do a larger percentage of their transactions with real money. While taxes on wages cannot be avoided due to the infamous withholding tax, a policy that eliminates $100 bills as legal tender would only further encourage holders of real dollars to use them in exchange. This is because all official purchases with digital money would be more easily tracked than if they were used with tangible money. This would make it easier for the state and local governments to levy bigger consumption taxes on all purchases of goods and services. In fact, in September 2012, the government of Argentina introduced a 15 percent tax surcharge for every time a purchase was made outside the country using a credit card issued by an Argentine bank. In addition, taxes on investments will encompass more of the economy. While today most investments are made electronically such as bonds, stocks, and real estate(most of which incur capital gains taxes upon liquidation), there are still investments that are made “off the books” and thus are not subject to taxes. This would most likely expand(along with similar consumer purchases) if such a policy were implemented, but with holders of real dollars possessing the advantage over non-holders.



Now let’s introduce a law that completely eliminates the use (economically) and production of $100 bills(during a period of negative interest rates). This is the extreme version of the proposal of Summers, Rogoff, and a few others. At first glance, it would seem unlikely that anyone would be willing to use or exchange something that has been completely outlawed by the government. However, there are numerous examples throughout U.S. history that have shown this to be false including prohibition and the “War on Drugs”. Assuming a large enough percentage of consumers will either ignore or purposefully disobey this new law, a case can be made that the holders of these $100 bills at the time of it being implemented will see windfall gains.

Under our assumptions thus far it seems that there will be a meaningful amount of consumers and market participants who not only foresee the ability to gain from these extreme policies, but they’ll also be willing and able, to a large extent, to avoid these laws due to the amount of anonymity that comes with using real cash (more on that later). This will solve the problem of network effects. Network effects exist when the desirability of an object or objects is dependent on the amount of people using it in a given area. The result will be a catallactic nexus of market participants, composed of wage earners and entrepreneurs, who interpret this transitory period as an opportunity to obtain premiums on exchanging their holdings of the now illegal $100 bills for goods and services from others who also use and accept these bills. This will occur instead of consumers merely hoarding these larger bills for several reasons.

With the cessation of the production of $100 bills, a law prohibiting the use and exchange of said currency would allow for an increase of the value of each note relative to the total physical supply(with a given demand). This stabilization of the supply of large notes would cause a significant price deflation, particularly in relation to the price of the same goods in terms of digital money(and smaller denominational notes). While the supply of $100 bills will most likely remain the same and circulate outside of the “digital” economy, there will be a tendency for the supply to decrease over time for two reasons.

First, physical pieces of paper that are used as money deteriorate over time as they’re handled by a multitude of people in countless situations. It’s only natural that the wear and tear to these large notes will at some point become too severe for them to be accepted at par with newer, fresher looking dollars(or to be accepted at all). And since the treasury is no longer printing these specific dollar bills, the supply will fall. Second, as professor North stated, there will be a tendency, albeit a small one in this case, for users of the $100 bills to either deposit their bill in a bank account themselves, or to initiate an exchange with a market participant who, for whatever reason, may decide it to be advantageous or convenient to hold his money in digital form(perhaps he feels there is less risk of theft of storing money in his bank than in his wallet or under his mattress).

This is in contrast to digital dollars, which will almost certainly see an increase in supply due to the incentives banks have to loan more money out. This is due to the fact that in a negative rate environment, banks that keep their reserves at the Federal Reserve will pay a fee to have them held there, rather than be paid a small percentage on the reserves as has been the case historically. On the other hand, it could be argued that the demand to use digital dollars in exchange could vastly exceed real dollars, especially in a inflationary period. As economist Finbar Feehan-Fitzgerald claims:

A currency experiencing more inflation than substitute currencies would be used in trade as often as possible. This would serve dual purposes. First, the owner of the substandard currency would prefer to use it in trade in order to keep their more stable and more robust currency in hand. Second, an individual in possession of the value-losing currency would rush to exchange it in order to obtain goods losing value less rapidly than the said currency.

Laws and policies aside, we have seen that historically this doesn’t hold true however. Moreover, as Nobel laureate F.A. Hayek states:

Beyond the desire to use his regular receipts for his ordinary
expenditure, the wage- and salary-earner would probably be
interested chiefly in stability. And although in his mortgage
and instalment payments he might for a while profit from a
depreciating currency, his wage or salary contract would
incline his wishes towards an appreciating currency.

As mentioned earlier, deflation tends to favor wage-earners and creditors and inflation tends to favor debtors. During a period of negative interest rates, while digital money is losing value relative to physical dollars(particularly the $100 bill), the opportunity cost of paying off debt using digital money falls relative to real large notes. This means that digital money will be more advantageous to use in paying off debts and fixed installment payments. But consumers and wage-earners will no doubt prefer an appreciating currency to acquire more goods and services with a given amount of labor. While these market participants won’t be able to acquire these appreciating $100 bills(except in exchange with someone willing to part with them) through their banks or paychecks, the owners of $100 bills who possessed them the moment these policies were implemented will see their currencies stabilize and even decrease in supply, and rise in purchasing power relative to digital money, which will increase in supply(due to increase in lending and inflation), and decrease in purchasing power(due to fees and negative rates on bank accounts). Hence, these real dollars will command a premium over digital money, which will inversely exchange at a discount.

Another reason market participants will be encouraged to use physical currency in trade instead of digital currency is the likely price controls enacted by the government due to any significant amount of inflation in the economy, most likely caused, in part, by negative interest rates. As I stated earlier, digital money can easily tracked by the banking system and a nation’s government. Every transaction using a smartphone, credit card, or Paypal can be recorded in a digital ledger that the issuing bank, phone application, or clearing house can keep in it’s database so that the government can have easy access to where people’s money is going. This makes it virtually impossible for anyone to buy products whose prices are fixed by law to acquire said goods at any other price as long as they use digital money. On the other hand, transactions using physical dollars are completely anonymous, and while purchasing goods at below the government-mandated prices would be technically illegal, anyone who would be willing to take advantage of the premiums that real dollars have over digital money would be able to do so in the likely scenario that producers would be participating in the black market.



Economist Robert Wenzel has suggested in a recent article that in a scenario where ATM withdrawals are restricted for any reason, as little as ten thousand dollars under the bed could possibly equal $100,000 in buying power during such a period and “those who have cash are going to be in a very strong position in terms of buying power.” While he does not go into detail about why this is so, it can be deduced that it is a lack of real dollars that would cause this discrepancy in value. This falls in line directly with our analysis that a lack of supply of real dollars, including other factors, relative to other currencies will raise the purchasing power of the limited currency when measured against the unlimited currency.

A more realistic example has been made by University of Michigan professor of economics Miles Kimball. He proposes that central banks proactively eliminate the exchange rate between electronic money and physical money. Instead of depositing $100 into your bank account and it being credited with an equal amount, you would be credited with $98 for example, which would equate to negative two percent on deposits. This would instantly create a scenario in which physical dollars exchanged at a premium against digital dollars. Simultaneously the government could sever the ties in value between deposits and cash by not requiring banks to accept cash as legal tender. Whether the federal government makes cash illegal or not is immaterial. Anyone who uses cash would be at an advantage. Professor Kimball adds:

“Businesses have got to start planning for this. Any lawyer who writes a debt contract without stipulating what happens if the market price of a paper dollar is not equal to an electronic dollar has to wake up… There’s going to be some central bank that does what I’m suggesting, and the companies who didn’t prepare for it are going to be disadvantaged.”

He makes the claim that what we have stated about individual holders of $100 bills also holds true for businesses as well. While physical currency would be exchanged at a premium, it would be advantageous for them to transact with it. In addition, since both types of currency would be legal to use, any business or corporation could float bonds to raise capital. However, in this negative rate environment, lenders( larger businesses) would pay borrowers(citizens) to borrow money. In his example, he says that the government could make it legal to accept both cash and digital money as payment, which is significantly different from the scenario I’m presenting in my analysis. It seems more than likely that the government will instead outlaw cash entirely so central banks can get past the problem of the zero lower bound. Yet this scenario that Kimball presents as being probable only strengthens my analysis by demonstrating the desire for market participants that are aware of such policies to secure profits rather than incur losses.

We have seen that policies of negative interest rates combined with the elimination of high denominational notes will cause those notes to be exchanged at a premium versus digital money, rather than disappear from circulation as is claimed by proponents of Gresham’s Law. Given that there will be a substantial amount of market participants who anticipate these policies and their effects, they will be at an advantage when their physical notes climb in purchasing power while simultaneously digital money begins losing its purchasing power. To the extent that this holds true, it will be seen that there is an inherent economies of scale in terms of money through reduced transaction costs(fees and taxes) by the limitation of their supply. Those who attempt to withdrawal money from banks to acquire real dollars such as the $100 bill will not be permitted through law to do so. This will create a “grey economy” where those who seek alternatives to digital money will be able to do so through network effects. In addition, there are several recent real world examples that support our position.



Since Argentina defaulted on its foreign debt in 2001, it’s currency, the peso, has collapsed in value by over 75%. While the government has tried to raise it’s value on the regulated official exchange rate using its foreign reserves, Argentinians have been attempting to pay large premiums for higher valued currencies such as dollars which are traded on the black market as “blue dollars” at prices far exceeding the official exchange rate. For example, according to The Economist, in late 2015 citizens exchanged pesos on this “blue dollar” rate at a rate of over 14 pesos for one dollar, compared to an official exchange rate just under 10 pesos for one dollar. That is an over 40% premium for a more stable and trusted currency. Even more interesting is the fact that in September 2012, the official exchange rate was 4.63 pesos for one dollar, while unofficial rate was 6.39 pesos for one dollar. In essence, in 2012 dollars held a premium of roughly 27% over pesos, while 3 years later, in 2015, they held a premium of more than 40% over pesos. Thus it is obvious that Gresham’s Law does not hold true regardless of the effective exchange rate maintained by the government. This in fact shows that policies that devalue currencies can have effects that last for years.

In Venezuela, price inflation was over 150% for fiscal year 2015. At the time of this writing it has increased to 500%. It is estimated by the International Monetary Fund that inflation will be over 1600% in the coming year. As of February 2016, there are four different exchange rates used to trade bolivars, the official currency of Venezuela, for dollars. The official exchange is called CENCOEX, in which one dollar can be acquired for 6.3 bolivars. The other two exchanges are SICAD 1 and SICAD 2, which require 12 and 50 bolivars, respectively. The newest exchange is called SIMADI, which requires around 200 bolivars in exchange for one dollar. While each of these 4 exchanges has different uses for different market participants, they all have one thing in common. It is considered to be quite difficult to acquire dollars at these more favorable exchange rates for reasons such as fraud, lack of trust in both the stability of the bolivar and the process of acquiring other currencies, capital controls, transaction costs, and the overall bureaucracy that no doubt inflicts monetary costs to users that wish to make these exchanges at the going rate(s).

As a result, Venezuelans have relied on the black market to acquire foreign currencies like the dollar. While it is possibly easier to acquire dollars at the black market exchange rate, it is much more expensive to do so. For example in early 2016, the black market exchange rate was 900 bolivars for one dollar. This is more than a 400% premium for dollars than the highest official rate. The vast majority of citizens that can acquire dollars at the black market rate are only the wealthy and higher-income earners. And these citizens primarily hoard the cash as a means of saving. Unfortunately in the case of both Venezuela and Argentina, there isn’t much data on the use and hoarding of high denominational dollars in these countries. Peter Sands states:

…it is hard to imagine that Argentina’s persistent mismanagement of monetary policy and banking would have continued so long if the elite did not have the dollar alternative. Through access to US $100 bills, elites secure insulation from domestic monetary and banking disasters, which weakens their incentive to seek change. Whilst there is no data to prove this, we would suspect that in most such countries, access to and holdings of foreign currency high denomination notes is highly concentrated.

So these dollars are seen as more of an asset than a medium of exchange to the wealthy and high-income earners. However, it has been observed by some economists such as professor Steve Hanke of Johns Hopkins University, that citizens of Venezuela have begun abandoning bolivars and started using dollars in trade when he states:

Facing this inflationary theft, Venezuelan’s have voted with their wallets. Indeed, they have unofficially begun to dollarize the economy.

Companies such as American Airlines and Ford Motor Co. have stopped accepting bolivars as payment for their products. This “partial dollarization” seems to be spreading with a lag along with the massive inflation that has decimated the bolivar. In fact, while most real estate contracts are calculated in bolivars, in higher income areas, many owners do business outside the law and accept payments and rents in dollars only.

The difference between the scenario in Argentina and Venezuela, and the one of negative rates in the U.S. is that in those examples, the more stable currency that held a large premium over the inflationary currency was a foreign currency. This implies that once citizens of these countries realized how devastating the devaluation of their currencies would be, it became either too expensive or too difficult for many to import dollars or euros in order to acquire necessary domestic goods and services. Because of this, the ability of a more stable currency, despite its exchange premium over the depreciating currency, to circulate in the black market is significantly hampered by the lack of network effects(though not completely eliminated).

This is in contrast to the U.S. where both real dollars and digital dollars are both domestic. This means that international transaction costs are essentially eliminated and many market participants will already possess the requisite amount of physical dollars to create the network effects necessary for them to take advantage of the premiums their dollars will have in exchange over digital dollars.


In a working paper previously mentioned titled, “Making it Harder for the Bad Guys: The Case for Eliminating High Denomination Notes”, Peter Sands makes the argument that high denominational notes such as the $100 bill should be eliminated from circulation. His reasoning isn’t important for the purpose of our analysis but there are several points to be made in relation to our claim that in a negative interest rate environment with the abolishment of cash, it will be advantageous to use physical currency in trade.

According to Sands, cash is the preferred proxy that criminals use whether in high denominational notes such as the $100 bill or in lower denominational notes. The difference, he claims, is that lower denominational notes play an important role in everyday exchange in the economy while higher denominational notes have very little impact. Criminals involved in illegal activity could still very easily conduct illicit activity using $5, $10, or $20 bills, but it would increase transaction costs and transportation costs, particularly with cross-border exchanges. And even with domestic or local transactions, the ability to exchange with anonymity would be more difficult due to the larger amount of smaller denominational notes that would be required to conduct a transaction of the same value in $100 bills. He states:

Criminals are not going to stop being criminals simply because we eliminate high denominations. So they are going to look for other ways to make payments and move and store value surreptiously. The issue is whether the substitutes are more expensive, less convenient and carry greater detection risk. The most obvious substitutes are lower denomination notes of the same currency. Yet using these would raise the cost of doing business for criminals, since they are bulkier and heavier.

Thus it easy to see why in the same paper, Sands finds that $100 bills exchange at a premium with smaller U.S. dollar denominations in many emerging markets.
Cash premiums for Paper


This discovery seems to somewhat reflect the analysis of the paper by Rolnick and Weber on a different version of Gresham’s Law. They argue that the determining factor of whether a currency circulates at a premium is based on the costs of paying such premiums. Legal tender laws can explain what is used as the unit of account, but cannot predict when a money will circulate at a premium and when it will be hoarded. For example, during the years of 1792-1833 only the large denominations of the undervalued currency, which was gold and Spanish dollars, circulated. Most of the gold was exported, but for several years the Spanish dollar, which contained more silver than the U.S. dollar, circulated at a premium. More important is the fact that small denominational coins of the undervalued money in this period did not circulate:

The small change available during this period consisted of U.S.
silver coins and a substantial amount of Spanish coins.
The small-denomination Spanish coins contained less
silver than the U. S. coins (just the opposite relationship to
that between the Spanish and U.S. dollars), and, as our
hypothesis predicts, the undervalued small U.S. coins
had trouble circulating.

The reason for this has to do with the costs incurred from paying for premiums on smaller denominational coins which are usually higher than on larger denominational coins. This causes citizens to bundle the smaller denominational coins together to complete transactions and they disappear:

Generally, the smaller the denomination, the more costly it is to pay the fractional part of a premium. Because of this additional cost, traders are not likely to pay premiums on individual small-denomination coins. Thus the public is not likely to use these coins as a medium of exchange and is, rather, likely to collect them into large quantities that will exchange at a full premium; that is, individual units of small-denomination currency will tend to be bundled and taken out of circulation.

Similar reasoning can be used to support our position that large denomination notes such as the $100 bill will circulate at a premium, particularly against lower denominational notes and digital dollars. While it has already been seen that the fees, taxes, and negative interest rates that will be levied on digital money will cause physical dollars to exchange at a premium, it should be emphasized that this will also be the case when compared to lower denominational notes. As the Wall Street Journal states:

A million dollars in $100 bills weighs approximately 22 pounds and can fit comfortably into a large shopping bag. With $10 bills, it isn’t so easy. Think of lugging around 220 pounds in a giant chest. Hoarders and tax evaders would find small notes proportionately costlier to count, verify, handle and store. The use of cash could be further discouraged by putting restrictions on the maximum size of cash payments allowed in retail sales.

This implies that costs, particularly transportation and transaction costs, will be much higher for lower denominational notes than larger notes. Since banks cannot be trusted to store $100 bills by market participants who wish to exchange these notes, holders of them will prefer to keep them stored with as little cost as possible. Thus it is easy to see that $100 bills will be the preferred denomination in terms of storage. Counting notes will also pose a considerable cost if extremely small denominational notes such as $1, 5$, and $10 bills are used, especially for larger purchases. The same logic applies to verifying the authenticity of physical cash, as well as handling and transporting it. This will hold true for market participants wishing to take advantage of their holdings of $100 bills because we can see the same results when applied to criminals using $100 for illegal activities. Peter Sands makes this clear:

High denomination notes are the preferred form of cash for conducting illicit activities where significant values have to be transferred, stored, or moved. As an indicator of the incremental value provided by larger denominations, criminals will pay a premium for €500 notes and US$100 bills often attract an exchange rate premium relative to smaller US$ denominations in many emerging markets.

It has been seen that due to costs incurred by holding and exchanging digital dollars and lower denominational notes in an economy consisting of negative nominal interest rates and legal tender laws, it will be advantageous for holders of larger denominational notes such as the $100 bill to use them due to the premium they will command because of these transaction costs, as well as inflation. Gresham’s Law in its popular form does not hold true, as the historical evidence and theory demonstrate. Instead of one currency disappearing from circulation, the undervalued currency will likely be traded at a premium unless the costs of using that money in exchange are too high.