Tuesday, November 5, 2013

Interest, Growth, and Power

Compounding interest has the peculiar character of exponential growth that doesn’t fit well on a planet that has been steadily orbiting the same sun for billions of years. Since any sort of interest or return on investment should generally be capable of re-investment, which implies compounding, it seems logically that profit or return on investment or interest payments can only work in a world where unbounded growth is possible, i.e. some other world than the one we live in.

This understanding of interest and compounding, however, creates an illusory problem at the same time that it hides a real problem. Since finance and economics are such important mechanisms for structuring the way we live, it is worth looking carefully at these fundamentals.

A monetary system can be modeled quite simply. Each person has an account, a single number, their net monetary worth. Some people have positive net worth, other people have negative net worth. Perhaps Fred has a net worth of +10, Sally has +2, and Bill has -12. Adding up these three numbers, the total is zero. The net worth totaled across all people is always exactly zero.

Day to day transactions happen when people exchange goods or services for money. Bill might cut Sally’s hair, in exchange for which Sally pays Bill 3 monetary units. That payment moves from Sally’s account to Bill’s account. So now Sally’s net worth is -1, Bill’s is -9, and Fred’s remains at +10.

Interest payments occur at regular intervals. At the end of each interval, each person’s account is multiplied by some number. Let’s use an interest rate of 1% per time unit. Then when interest payments are made, Fred will have 10.1, Sally -1.01, and Bill -9.09. The sum of these three numbers remains zero.

If there are no other transactions, then interest will simply amplify the differences in net worth more and more over time. But people with negative net worth can also provide goods and services for those with positive net worth, in exchange for money. These exchanges reduce the differences in net worth. The combination of these two effects determines how account balances actually evolve.

It should be clear from this simple model that interest payments are entirely compatible with a steady state or even a shrinking economy. All that is required is that sufficient transactions occur that move money from those with large positive net worth to those with large negative net worth to counter the amplifying effect of interest payments.

This simple observation exposes the real problem with interest payments. What if these exchanges fail to occur? How might they fail to occur? To whose advantage would it be if they failed to occur? Could those who benefit by such failure influence affairs in a way to increase the likelihood of that failure? Could that chain, failure – benefit – influence – failure, then feed on itself to amplify the imbalances?

It is not the simple mathematics of interest payments that leads to accelerating imbalance. Putting the blame in the wrong place means that the blame is not being put in the right place!

It is important to see how money is power, and also how debt is powerlessness. Money gives a person options. Debt reduces a person’s options. The more options a person has, the more they can optimize their behavior and enhance their productivity, their profitability. The fewer options a person has, the less opportunity they have to find ways to be productive and to earn a profit. This connection between money and power is not a property of the simple monetary model presented above. What real monetary systems generally add are rules that restrict transactions for people with large negative balances.

The reality of the world is of course vastly more complex than any economic model. How are prices determined? If the power conferred by money gives a person influence over pricing, this can enable them to acquire more goods at lower prices, further concentrating wealth.


  1. The simple monetary system above allows for unlimited expansion of money. Fractional reserve requirements put a limit on that expansion. This reserve requirement is a simple adjustment to the simple model.

    Instead of the total of all balances being fixed at zero, let there be some initial capital C in the bank. Then, as transactions proceed, let the total of all positive balances be (C+L) and the total of all negative balances be -L so the total of all balances stays fixed at C. The initial capital doesn't earn interest in this model.

    The fractional reserve requirement says that f * L must stay smaller than C where f is some number like 10%. Transactions that would increase L beyond that limit are forbidden.

    With this limit, L can grown to C/f. L is essentially the money supply, so the money supply can expand tremendously as f gets small.

  2. Interestingly, the very simple model you talked about is similar to a mutual credit network. And coincidentally, the Hudson Valley Current is just now going into beta testing (for business-to-business users at first). In the case of an actual network of this kind, the money supply is constrained by, obviously, the number of users times the amount of credit they can use. In our case, at least for beta, we are using an account limit of C300 (maximum negative balance). Since everyone can't be 300 currents in debt, I guess the max theoretical money supply in such a system would be 1/2 of C300 x number of users. But I don't think that figure is a key indicator. We are looking at more dynamic indicators, such as some sort of a transaction rate overall, as well as the "balance" of activity on individual accounts and how that aggregates into a "system health" indicator of some sort.

  3. I think the theoretical maximum would be (n-1)*300, i.e. everybody but one has borrowed the max and that one last person has piled up all the chips. But yes, the money supply itself is not such a useful indicator.

    The problem with a simple volume of transactions is that it could just be two people passing a small amount back and forth, which wouldn't mean much.

    Ha, here is an idea. Look for a loops of people where e.g. A has a net flow of money to B, B to C, C to D, and D back to A. Such a loop could be characterized by two numbers: the number of people in the loop, and the smallest net flow along the loop. Look all all loops with three people and find the loop whose min-net-flow is largest. Do that for four person loops, five person loops, etc.

    Sorry... I get carried away! Here is a much simpler idea. Each person has a volume of transactions. Just look at that distribution. How many people move C10 a month, or C20, or C50, C100, C200, etc. Look at that graph. I think a single number or a few numbers are never going to carry enough information to really tell you what is going on. When you can plot a graph, some kind of distribution, it is a whole collection of numbers with well defined structural relationship among them, then you can start to get some insight.

  4. I think a problem with interest is its abstraction. Here is an idea for managing loans. One way to manage people going negative, spending money they don't have, is like a credit card... like a relationship between a person and the bank. I think this is too abstract.

    Instead, it could work better to view a loan as a relationship between two people. Probably the bank can maintain an abstract view of the relationship and let the people themselves work out the details. So e.g. if a tractor dealer wants to sell a tractor to a farmer, maybe the dealer lends the farmer the money to buy the tractor, and the farmer then agrees to make installment payments, perhaps in corn or in money or whatever.

    From a bank's point of view, some transactions could be marked as special and require sign-off by both parties. Suppose a tractor is C50000. The payment by the farmer for the tractor puts the farmer at -C50000 and the dealer at +C50000. The dealer agrees not to let his balance drop below +C50000 and the farmer agrees not to let his balance drop below -C50000. At any time, the farmer and the dealer can adjust these matching limits, depending on the details of their agreement that the bank doesn't really need to know about. If they both agree to adjust the limits, the bank just adjusts the limits.

    Each person could participate in multiple such arrangements. The person's actual balance limit is just the sum of all those individual commitments. E.g. maybe the tractor dealer wants to get a new roof for her house. The tractor dealer could borrow C20000 from the roofer. So the roofer promises to keep +C20000 minimum balance, and the tractor dealer agrees to keep a -C20000 balance. But the tractor dealer also has the agreement with the farmer. So the net position of the tractor dealer is +C30000, the farmer is at -C50000, and the roofer is at C20000.

    Yeah it makes good sense to have some initial capital in the system or some ability to borrow a small amount, so there is some fluidity and people have something to spend without a two party agreement. But the two party agreements could really give the system vast room to expand with simple accounting and still great flexibility.