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New Ideas in Currency Systems: Z Dollars
by jcr13Tuesday, May 24, 2005 [10:50 am]

Back in the fall of 2003, I came up with a novel paper currency system that would solve many of the problems associated with traditional currency systems. This system was elegant, simple, and beautiful---perhaps one of my best inventions so far.

My wife and I played a game of Monopoly (classic Parker Brothers board game) using this new system instead of Monopoly's default money system, and it worked. I discussed my idea with Jason Adaska during his Thanksgiving visit to Potsdam in November of 2003. He and my wife can both serve as witnesses that I indeed formulated these ideas a year and a half ago.

Of course, I was caught up in full-steam MUTE development back then, and I never had a chance to write my idea down (at least not that I can find in all of my electronic archives), let alone develop a real-world currency project based on the idea. This idea has been sitting on the back burner for too long now: it's time to write it down.

Background -- The Money Creation Problem

Most people (including me before the fall of 2003) do not think very much about where money comes from. If you think about the US economy today and compare it to the economy of fifty years ago, you see obvious growth. There are more people involved and there is more money in the pool than ever before. If the money pool is growing over time as our economy grows, then someone, or something, must be injecting new money into our economy.

So where does this new money come from? The government prints it, right? If they print too much, we get inflation, right? Even if this simplistic explanation was correct, it still does not explain how these freshly printed bills make their way from the presses into the wallets of ordinary citizens.

In our modern economy, the money pool is almost completely divorced from its physical manifestation as paper bills. Bank accounts hold most of the money, and this money is represented only as numbers in computer databases (or formerly as numbers in paper ledger books). Paying someone by check, Automated Clearing House transaction (ACH, in other words, direct deposit and debit), or credit card involves subtracting a number from one database record and adding it to another. So, if anything were to discount the theory that the government prints money to grow our economy, the diminishing importance of paper money to modern society would be it.

In fact, banks create money, not governments. New money is created every time a bank makes a loan, and that extra money is destroyed as the loan is paid back.

Every bank has a certain amount of money available---the total sum of all deposits in all accounts in the bank. By law, a bank must keep a fraction of this money on hand: this is called a reserve ratio. The rest of the deposited money can be made available for loan. In the US, the minimum reserve ratio for a bank is between zero and ten percent, depending on the size of the bank (see the Federal Reserve for more information).

What does this mean, in practice? As an example, we can assume a very conservative reserve ratio of ten percent (10%). If Alice deposits $100 into her bank, the bank must keep $10 of that deposit in reserve, but it is free to lend out the other $90. Suppose Bob takes out a loan of $90---at this point, the bank cannot give out any more loans. Bob uses the $90 to pay a carpenter, Eve, for house repairs. Suppose Eve has no expenses, aside from her own labor, from the carpentry work: she receives $90 of pure profit. Eve then deposits this $90 into the same bank as Alice and Bob. Whoa! The bank now has a total deposit of $190 instead of only $100. The bank effectively created $90 out of thin air, just by making a loan. Of course, the bank needs to keep $9 of that new $90 on reserve, but it can loan out the remaining $81 to someone else. This is a simple example, though it certainly could happen in real life. The situation becomes more difficult to visualize when multiple banks are involved, but the underlying mechanism---a mechanism of money creation from loans---is the same.

So what stops this system from spiraling out of control toward massive inflation? Each of these loans has an interest rate associated with it. Higher interest rates discourage people from taking out loans, while lower rates encourage loans---high and low rates effectively discourage and encourage the creation of more money. The Federal Reserve adjusts the interest rate at which it will lend money to control inflation rates and otherwise steer the economy.

But what happens in our example when it comes time for Bob pay back the loan, including interest? Suppose the interest rate is ten percent. Thus, Bob owes the bank $99 instead of $90. But in a closed system, with only $100 on deposit and $10 of that in reserve, where could Bob possibly get $99? Suppose the carpentry work has been done, and we now have $190 on deposit, with $19 in reserve and $90 already loaned out. $81, as mentioned before, are still available for loan. Bob could take out another loan for that $81, leaving him in search of $18 additional dollars (though he would be foolish to take out a loan to pay off a loan, since he would only spiral deeper into debt). No matter what Bob does, in our closed system, he is still stuck and unable to pay back his loan.

In reality, we are indeed operating in a closed system, but it is much bigger than a single bank with only a $100 deposit. Thus, Bob could do work and get paid $99 from someone else to pay back his loan. We still are not sure about where that $99 is really coming from, since it includes a demand for $9 of interest that were not part of the original money pool.

Every time money is created through a loan, effectively inflating the money pool, the interest on that loan effectively demands payment of money that does not exist yet, not even in the pool in its inflated state. Thus, additional money must be created somewhere to pay back the interest on each loan. Since money is only created through loans, we are all depending on new loans to pay back our old loans. Our monetary system can never fully pay itself back for the money that it creates---eternal debt is inevitable.

Returning to our example, suppose Bob takes out a loan for $99 from another bank and pays back his bank. $90 of this payment is "destroyed," as it cancels the outstanding loan. Thus, the bank again has all $100 of Alice's money on hand, and still has $90 from Eve on hand. It is now ready to make a loan of $171, keeping $19, or ten percent, on reserve. What about the $9 of interest? That is profit for the bank, and the bank will deposit this money into its own account. Our three-person, one-bank system now has $199 in total deposits. Of course, $99 of this came from a loan at another bank, and it will eventually need to be paid back by Bob.

So, all of the "new" money entering our economy each year is effectively debt money that must eventually be paid back. This is the way our money system works, and the situation it creates certainly does not seem ideal . However, there is a deeper problem with money that goes beyond the specifics of our money system---I call it the "Money Creation Problem."

Money serves to lubricate an economic system by enabling abstract trading. Without money, or a sufficient supply of money, an economy grinds to a halt. As an economy grows, say from 10 people to 100 people, more money is needed to enable to same amount of abstract trading. If members of your 10-person economy are each accustomed to having $10 on hand for abstract trading, you must somehow create 900 additional dollars if your 100-person economy is going to be trading at the same level. But where does this money come from? Any of the mechanisms used in standard monetary systems, such as printing more paper bills or making loans, are deeply unsatisfying.

Economists respond to these fundamental questions by fanning the flames: it obviously works in practice, so we should all keep using it. If we think about it too much, it may stop working. Traditional money systems depend on faith and general ignorance to stay afloat.

The same problems plague alternative currency systems like Ithaca Hours. The North Country Notes project effectively passes the buck by making local bills exchangeable for US dollars and keeping a 100% reserve of US dollars for all local bills that are in circulation, but it does nothing to solve the underlying problem.

A Net Sum of Zero Dollars

What if we avoided the money creation problem by never creating money? How could we do this in a way that still lubricates our economy?

We can start from first principles: our foundation is a system with no money at all. In such a system, each person obviously has zero dollars, and the net sum of dollars in the system in also zero. If we never create money, the system must always have a net sum of zero dollars. Note that traditional money systems do not have this property---instead, they always a net positive sum of dollars.

How can we maintain a net sum of zero dollars while still facilitating abstract trading? Traditional money systems only use dollars to represent abstract credit: you do a service for someone or give someone goods, so society "owes" you something in return, and the $100 in your pocket represents how much society owes you. Note that traditional dollars are abstract credit, since they do not track who owes you something---dollars are much different from concrete, person-to-person loans (where you give me corn, and I owe you something in the future). The key to supporting a zero sum of dollars is to also track abstract debt, and we can do this by explicitly allowing negative dollar balances. Traditional money systems support abstract credit, but only allow concrete debt (in the form of direct loans that must be paid back to the lender).

Returning to our earlier example, we can now suppose that Bob and Eve each have a balance of $0. Bob needs $90 worth of carpentry work from Eve. After the work is done, Bob has a balance of -$90, while Eve has a balance of +$90, and our net sum is still $0. If Alice, who also starts with $0, buys $110 worth of corn from Bob, she then has a balance of -$110, while Bob then has a balance of +$20. Our net sum is still $0.

Note how this system is effectively tracking net credit and debt for each member. Bob is initially in debt for $90, but after "giving" corn to Alice, that debt shifts to Alice. Eve has thus far given carpentry work but gotten nothing in return. Suppose that Eve buys a bicycle from Alice for $95. Now Eve's balance is -$5, while Alice's balance is -$15. Alice is still in debt, because the corn she received is worth more than the bicycle she gave, and Eve is also in debt because the bicycle was worth a bit more than the carpentry work that she did for Bob.

We have not actually created any dollars, yet we still have enabled abstract trading (in this case, a trade triangle). This system lets the participants effectively "create" dollars as they are needed at the time of a trade and just as easily "destroy" dollars once credits are spent and debts are paid back.

But what would stop a participant, say Dave, from running his balance more and more negative? What happens when someone receives indefinitely without ever giving back? The solution to this problem is to make the balances of all participants publicly available. If Dave has a public balance of -$5000, very few people will be willing to sell anything more to him, though they would certainly be willing to buy from him.

The key mechanism is the explicit representation of negative dollar balances, and this particular idea is not new. The LETS System, which was designed by Michael Linton in 1982, pioneered the negative balance mechanism.

In a LETS system, each participant has a publicly-visible account that starts at $0 and can go either positive or negative. Each exchange between participants is associated with a dollar value that is added to the giver's account and subtracted from the receiver's account. In Linton's original conception, and in all of the LETS systems that have sprung up around the world since then, a central authority tracks account balances for each participant. This "authority" can be as low-tech as a ledger book kept in a public location or as high-tech as an web-accessible database. Several pieces of software have been developed over the years to facilitate centralized account tracking.

Though the LETS System solves the money creation problem in an elegant way, its implementation has a fundamental flaw. When an exchange happens out in the real world (say you go to a farm stand and buy $10 worth of strawberries), the transaction is not truly "complete" until it has been recorded in the central registry. In a retail situation (such as a farm stand), many exchanges will happen throughout the day, and it will not be practical for the merchant to record each exchange with the registry as it happens. Thus, there will be a back log of transactions, and the posted account balances will lag behind the actual balances.

Thus, we go from the convenience of a paper currency (with all of its money creation problems) to the hurdles associated with checking accounts. In fact, some LETS systems, such as the Brisbane LETS, use paper slips to record transactions. These slips must be delivered to a central bookkeeper so they can be entered into the database.

My invention builds on the LETS model to solve this fundamental flaw.

Positive Dollars, Negative Dollars

In a LETS system, we are tracking both positive and negative balances. Since these balances must be recorded in a central registry, the system is rather inconvenient to use in the real world. It would be great if we could build the properties of LETS into a paper currency in a way that somehow avoids the money creation problem.

To do this, we need a way to represent negative balances with paper bills. The first thing that comes to mind is some kind of "negative" dollar bill. If you have a positive balance, you would have a wallet full of positive bills; if your balance is negative, your wallet would contain negative bills. But the other property of a LETS system is that everyone starts out with a balance of $0. If everyone starts out with an empty wallet (neither positive nor negative bills), where does the money come from for the first exchange? We are back to the money creation problem.

After thinking about this problem for a while, I came up with a beautiful solution, what I call Z Dollars. We use both positive and negative bills, but everyone in the system has some of each. Each participant starts out with an equal number of positive and negative bills for a net balance of $0. During an exchange, the seller receives positive bills from the buyer and gives an equal number of negative bills to the buyer in return. Thus, the buyer's balance becomes more negative, while the seller's balance becomes more positive---this is exactly what we want.

Bob may start out with 100 positive bills and 100 negative bills (written here as [-$100, +$100]) and a balance of $0. Alice might also start out with [-$100, +$100]. Bob then might buy $25 worth of corn from Alice, giving her 25 positive bills and receiving 25 negative bills from her. He would then have [-$125, +$75], while Alice would have [-$75, +$125]. To convert either of these wallet states to an equivalent LETS balance, we subtract the negative bill count from the positive bill count and divide by two. Thus, Bob has a balance of -$25, while Alice has a balance of +$25. This conversion-to-balance calculation is only carried out to compare Z Dollars to a LETS system---the bills themselves are effective as a credit and debt tracking mechanism, even though they store this information in a different form than a LETS system does.

We actually have an additional conservation property here---not only is the net, system-wide sum always zero, but each participant always has the same number of bills. So, if Bob starts out with [-$100, +$100], he will always have 200 total bills. If he sells a lot, he may end up with [-$50, +$150] or even [-$0, +$200]---regardless, he still has 200 bills.

What about cheating? If Bob has [-$150, +$50], for a total balance of -$50 (50 - 150, divided by two), he might try to destroy some of his negative bills to increase his apparent balance. For example, he might destroy all of his negative bills to get [-$0, +$50], or a total balance of +$25. Two mechanisms would prevent this kind of cheating. First, anyone inspecting Bob's wallet would notice that he does not have the 200 total bills that he should have. Second, when Bob destroys his negative bills, he loses his ability to sell anything, since negative bills are necessary to participate in an exchange as a seller. This is an interesting property of Z Dollars: negative bills are just as valuable as positive bills, since they enable to sell something to gain more positive bills. Without negative bills, you cannot acquire more positive bills.

This leads us to another interesting property: both maximum debt and maximum credit are capped by the number of bills in the initial, starting-balance state. Thus, if Bob starts out with [-$100, +$100], he cannot go more than $100 into debt or have more than $100 of credit. This effectively limits how "wealthy" or "poor" Bob can become.

Once he hits his maximum debt, Bob has no positive bills left, so he cannot buy anything else. He must give back to the community, receiving positive bills and unloading negative bills, before he can buy more from the community. Likewise, if he has given too much to the community, he must take something (thus acquiring negative bills and dispensing positive bills) before he can give any more.

By adjusting the number of bills in the "starter" kit that is given to each participant, we can effectively control this debt and credit cap to suit the needs of a given community.

What about transparency? One important property of a LETS system was that all balances are publicly known---people then can avoid selling to participants who have not given a fair share back. With the paper currency that I have presented above, each person is carrying a natural balance indicator with them: the contents of his or her wallet. Especially if the negative and positive bills are given distinct colors, a quick glimpse at the content of a participant's wallet will let you know if that person is either too rich to sell more or too poor to buy more.

Though Z Dollars avoid much of the centralized tracking issues associated with a LETS system, there is still some central administration involved in a Z Dollar system: paper bills must be printed and starter kits containing these bills must be given to each participant. Furthermore, measures must be taken to ensure that each participant acquires only one starter kit to prevent cheating.

Though Z Dollar administrators are printing dollars, they are not actually creating money, since they alway print an equal number of negative and positive bills. Thus, Z Dollars solves the fundamental money creation problem, while still being as convenient to use as a traditional paper currency.

Note: the "Z" in "Z Dollars" should be formatted as the mathematical symbol for integers, with two bars on the diagonal. Thus, the "Z" refers to the fact that balances can be either positive or negative. The Z also refers to the number "zero", which is the system-wide balance of a Z Dollar system.

A similar idea has been proposed by Eric Harris-Braun: Paper Based Mutual Credit.

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by TobyThursday, October 20, 2005 [11:25 am]

Here's a neat CSS trick to format the "Z" in "Z Dollars" as the mathematical symbol for integers.

Basic idea:

<span style="position:absolute">Z</span> Z

The same quoted, in case the comment system here needs it:

<span style="position:absolute">Z</span>&nbsp;Z


Here is *one* of the possible ways to display it on Firefox (with an appropriate sans-serif font) and instead fall back on a single "Z" on browsers which don't understand CSS:

<style>
.z1, .z2 { font-family: sans-serif }
.z1 { position: absolute }
.z1:before { content: "Z" }
.z2:before { content: "." }
</style>

Look! It's the
<span class=z1></span><span class=z2>Z</span>
Dollars!

The same quoted, just in case:

<style>
.z1, .z2 { font-family: sans-serif }
.z1 { position: absolute }
.z1:before { content: "Z" }
.z2:before { content: "." }
</style>

Look! It's the
<span class=z1></span><span class=z2>Z</span>
Dollars!

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by Benjamin NewmanSunday, February 4, 2007 [2:52 am]

Fascinating...

From your reading list, it looks like you know a lot more about alternative currencies that I do, but I was fascinated by your idea of Z dollars and have a few comments. I've tried to consider which of the problems I see with it are due to my perhaps insufficiently revolutionary outlook, and which are actual problems with the system.

Having a limited number of positive and negative dollars, and using this limit on liquidity to discourage people from simply burying their negative dollars, raises a numer of issues. First, you have the fundamental problem of a limit on liquidity. How do you buy a house with this money, if your liquidity is capped at a sensible-for-petty-cash level?

The liquidity limit also makes trouble for people who do their selling on a less-than-regular basis — farmers who grow primarily summer crops and thus do little selling in winter, for example, or people who make a living making and selling discrete, expensive objects, and thus have a small number of large sales, are going to have a serious problem with running out of negative dollars. (This is the mirror image of the first problem).

I was thinking about the Z dollar <i>economy</i> (as distinct from the implementation) in terms of the existing banking system as you described it, and I think it's formally equivalent to the following system: There is a central bank, which holds <i>no</i> principal, and can lend as much money as it likes <i>at zero interest</i>. Your "starter kit" is an interest-free loan for $100 from the central bank.

With the Z dollar economy expressed in terms of a more conventional banking system, we can use some of the convenient features of the conventional system, while avoiding its faults (because the is no principal and no interest). The central bank can extend additional credit if someone needs to make a large purchase like a house. People can write checks against their credit, or can withdraw it as a cash advance (in positive Z-dollars — the negative ones are held in your name by the bank in the form of interest-free debt).

I can think of two ways to make sure that the money keeps flowing in this system. One is to have cash expire. You can't put cash under your pillow because it will become worthless — not gradually, but suddenly, say 90 days from the date of issue — <i>and the debt associated with that cash will be forgiven at the same time</i> (this makes "cash" equivalent in every way to a check drawn on the account of the person who originally withdrew it).

Another way to keep money moving is interest. I know, I said no interest, but I can think of a way to make the interest also sum to zero. One way to think of it is like this — each citizen of Zville is an equal shareholder in the central bank, so people pay interest to each other. But the most mathematically clear way to put it is this: You pay interest on the <i>difference</i> between your loan and the <i>average</i> loan.

Anyway, that's my idea. I think I would call the central bank in this system something else, though — I would call it a "credit union" ;-).

A further thought: Under current banking law (as you summarized it), this kind of credit union can't exist, because it doesn't hold any principal to lend against. <i>But</i>, this is the central banking institution of a community. There's no "money" to put in at the beginning in this system, but there is something of inherent value in the community — <i>land</i>. Local law would require that a share (depending on the desired level of liquidity) in the ownership of each parcel of land be deposited with the central credit union. This is starting to look like a pretty decent way to run a local monetary system. What do you think?

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