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After exploring Ray Dalio’s model of the economic machine in a previous article I decided to get my note paper out again and have a look at a transaction-based economic model. I tried to come up with something before but never came to a satisfactory conclusion, nor did I feel that there was great insight from what I had found. This time round I managed to get much further in terms of insight and better understanding of how things (should) work. Although I’m writing this article now I actually did all the pen-and-paperwork months ago, or more precisely: two days after writing my article on Dalio’s model. I feared this will be a long article and hence my reluctance to expend great effort to force my ideas to be clear and concise.

I know that I am not the first to make such considerations but this is almost entirely derived by myself without a great deal of external input. That is to say that it is logically inductive yet based on my own knowledge experience. There are naturally biases but not crippling flaws (imho).

This article explores the nature of transactions, primarily when money is exchanged for items. While there is a tendency to list prices in terms of money (nominally) we could list prices relative to the quantity of other items: that is, one Apple may cost one dollar, but that could be equivalent to half a chicken or whatever. Money is a convenient means of exchange and essentially a proxy for value, that is to say that we will easily remember a list of prices when they are all denominated in the same currency.

A simple transaction

One of the simplest examples I could think of involves exchanging an apple for money. We don’t need a strict definition of money here so we can stick with our everyday understanding of it. Alice sells an apple to Bob: she passed the apple to Bob who, in return, gives her some money. This amount of money is the price. The maximum price that the apple can be is the maximum amount of money that Bob owns. This is a simplistic model but for any obligations that Bob would have in real life you can subtract those from his income or his total savings to derive a figure that we could call disposable income, disposable money, or similar.

Ultimately I am attempting to build up a model based upon simple principles that we will aggregate over many transactions in order to model an economy, and in doing so try to come up with appropriate metrics that will give us an indication of economic health (etc). It is worth noting that in Dalio’s model he takes the total supply of money in a ratio with the total supply of the item to arrive at a price; in the above example that ratio is equal to the maximum price. In practise when there are many people with different amounts of disposable income then it is far trickier to find the maximum price, although we are probably more interested in the rate of change of such extreme prices as well as the rate of change in the at-market (actual/ current) price.

Caveat: Initially I wondered if I should use disposable savings/ income as opposed to total savings/income. The difference is mostly theoretical or perhaps ideological. In this simplified set of scenarios I am assuming that all the money in the system can be used to buy a particular item. In theory this is fine however in real life we have to be concerned with meeting our needs. After some thinking on the subject I believe that limiting my consideration to disposable income was more cautious than necessary. If an income stream is balanced against a stream of costs then that amount of money can not (or should not?) reasonable be used to purchase other items. The aim is focus upon what money can actually be spent on a particular item(s).

A second transaction
Now if I introduce Carol who now wishes to purchase the apple from Bob. This is a subsequent event to the above transaction. If we assume that Bob is willing to exchange his apple for money at some price then this transaction is the same as above but the price could be different. The maximum price that the apple could trade for is the maximum amount of money that Carol has. Let’s assume Alice had no interest and concentrate only on Bob and Carol. The value that Alice sold the apple for we shall call X, and the value that Bob will sell the apple for we shall call Y. If Y is greater than X such that Bob receives more money from Carol than he paid to Alice, this is a price increase. Y is nominally greater than X, and I shall ignore concepts of fluctuating currency value for now. If Alice was interested in buying the apple back from Bob then she would have to offer a greater amount of money than Carol or give Bob some ‘incentive’ (this could be qualitative) to accept her offer.

If Bob is only interested in a higher price then he will accept Carol’s offer. When prices of items rise on aggregate we call this inflation in modern vernacular. What I think is a better definition of inflation is when the supply of money into the system increases rather than the increase of nominal prices. The tendency is that when the supply of money increases then prices also tend to rise (eventually), as we are beginning to see in this example with Carol. The total amount of money has increased when Carol is introduced to the system however there is a competition for buying the apple between the two females so the maximum price can only be the whichever amount is greater, X or Y. The maximum price cannot be X + Y. That is to say that we can’t find the maximum price by taking the ratio of the total amount of money (X+Y) against the total supply of apples. The maximum can only be whatever one purchaser is able to pay for it. Later I’ll highlight some scenarios where that will not be the case.

Inflationary concerns
Naturally Bob may accept a lower price for the apple despite the fact that Carol has more money than Alice. There are many reasons why this might be the case but I’ll overlook that here. In such a scenario we could say the price of apples is deflationary because the nominal value of the apple has dropped. As above I would prefer to offer greater clarity by saying price-deflationary.

If Bob is being particularly stubborn and Carol doesn’t have enough then she may appeal to Alice for credit in order to increase her own supply of money and hence pay a higher price to Bob. The amount of credit can only be at most X, which is everything that Alice has to offer. In such a simple scenario we can see that there is essentially no way for Carol to pay Alice back other than to give her the apple (which she used to own). In this scenario the price of the apple is X+Y but it isn’t the most realistic. We could re-work this example by assuming that Carol is able to cajole the money out of Alice for free (no debt obligation), or that the apple exchanges hands a few times among the three of them until a ‘final’ transaction where the price paid is equal to the total amount of money in the system (X+Y). This is an over-simplified scenario but the aim is to highlight possibilities of a larger, and more complicated, system. The goal here is to show that prices cannot rise forever but are instead capped by the total amount of money in the system, which in giant economy with many participants and many objects we will never see a single item being sold for the entire amount of global money supply. The likely maximum price is the total of amount of disposable income held by the ‘richest’ possible purchaser which includes any available credit.

Relation to the stock market
As an example let’s take a single share of Warren Buffett's Berkshire Hathaway and ask for the maximum possible price. We could take the total disposable income/savings from Mighty Bank, including credit, and use that to find the maximum price of a single share. This will of course yield some huge value but we must note that it is finite. An obvious remark but the number of people I’ve met who assume that prices can rise indefinitely (essentially to infinity) has prompted me to highlight this. Once this single share has been sold the maximum possible amount then we will also realise that it is possible to sell it again for a higher price, as we defined this situation to be the one where a single purchaser has the greatest amount of ‘money’. There might be another purchaser with equal amount of money but not greater, by definition.

These scenarios is also akin to the greater fool theory: assuming that there is going to be a purchaser with more money out there who is willing to pay a higher price. The other problem here is that once a single share sells at a higher price then ALL the shares are now worth that higher price. In this way stock market prices increase faster than the total supply of money (not sustainable), and seemingly create wealth. One problem is that while in theory all shares are priced at the higher price that does not necessitate that there are more buyers who are able to purchase at that price. The global, universal, price of an item can only rise and stay up if there is a sustainable supply of purchasers for that higher price. This is demonstrated most clearly in the scenarios with Alice, Bob and Carol.

Open versus closed system
Let’s reiterate with an example. Alice sells an apple to Bob for 5 dollars (or whatever currency you want), so the price of all apples is now 5. In previous examples there was only one apple. Now let’s assume that Carol also has an apple then its value would be automatically set to 5 in the modern global financial market. All items of the same type have the same price globally, that is to say that shares in IBM sold in Hong Kong will sell for the same price as they do in London (accounting for currency differences). There are some caveats there such as arbitrage etc but I can safely ignore that here. The question now is whether Bob has enough money to also pay 5 dollars for Carol’s apple, let’s assume he wants it, or whether he is able to get it for a lower price. Whatever price he pays, both apples will be set to that new price. In this way we can see that value can essentially be added into a system. Although I do not see this as sustainable. Once Bob has both apples and the two girls have all of his money then we have to wonder how can the price increase further? Someone would need to be able to obtain more money and hence buy a single apple at a greater price. It should be clear that such a system has a way of preventing prices increase indefinitely. This system is closed; confer with closed systems in physics where the total amount of energy is conserved.

Now let’s give Carol a printing press where she can freely print as much money as she wants. That is to say that the total supply of money in the system can increase without bound (to infinity). In such a scenario Carol could offer as much money as was necessary to purchase an item. Bob demands 100 dollars for the apple and let’s assume Carol is happy to oblige. The maximum price of the apple is in theory whatever amount Carol decides is the maximum price that she will pay. In a mock scenario where such as this she can add as many zeros as she wants, and this scenario becomes rather abstruse. If Carol buys an apple from Bob at 100 dollars, then she gives that money to Bob and she takes the apple. Now if we assume that Alice also has an apple then the price of that apple is also 100 dollars. Bob could easily buy her apple for that price with the money he now has. Then he decides to sell it to Carol who is happy to buy again but this time Bob demands 500 dollars and Carol is also happy to oblige. Carol now owns all the apples, which are priced at 500 dollars a piece. Bob has 500 dollars and Alice has 100 dollars. Neither of whom can pay a higher price beyond the current price of 500.

Bob could use his 500 to buy fish which was only 10 dollars piece, although in theory he could pay up to 500 for a single fish. In doing so he will make it impossible for Alice to buy any fish (she already can’t buy any apples). Carol decides she will buy Bob’s fish and they settle on a new price of 1000 dollars each. The printing press warms up and prints off enough money to make the purchase. We can iterate this process indefinitely and at each turn we can a greater amount of money into the system. This is an open system where prices can increase indefinitely. This is a truly inflationary scenario where the total supply of money increases. It is only in such a system where prices can increase indefinitely and without bound, although it could take an infinite amount of time to do so. Again confer this to an open system in physics where the total energy of the system is not fixed.

In such an inflationary system we can see where it is possible for certain people to lose out and essentially never be able to afford certain items. In this way it is basically whoever gets there first can make the purchase but if you are too let then the price will be too high. This is of course an unfair system that rewards timing which is essentially luck. If Carol had a printing press but never used it then there would be no problem. There would also be a lessened problem if Bob decided to destroy all the money Carol gave him and so closing the system again. The last possibility is that Bob uses that money to buy items from Carol and so the printed money never leaves that part of the system. Essentially one part of the system would be closed while the other open, the problem would be when the two systems are no longer independent by cross-over each other and essentially resulting an open system on the whole.

The last point refers to the possibility of a central bank printing without limit but then only buying items from commercial banks who in turn only transact with the central bank again. The reality is that there will be some cross-over and that money, or value, will seep from the open system into the (assumed) closed system.

Summation of system types
1) When the total amount of money in the system is fixed then we have a closed system.

2) When the total amount of money increase then we have an open system which is inflationary (our current real-life system).

3) When the total amount of money is destroyed at the same rate it is created then we have a system in ‘open balance’. The system is open without a fixed total amount of money but the rate of increase matches the decrease and essentially we should see something that is the same as a closed system.

4)When the total amount of money decreases then we have an open system which is deflationary. We should note that there is a finite amount of money to destroy. A highly obvious remark but consider what happens when all the money is destroyed. An apple would appear to be zero dollars but then again such a system is meaningless as dollars would not exist. Trade would have to be based in another unit of currency.

Conclusion

An additional insight to this is to reverse our mode of thought and to price money in terms of apples. Such that an apple priced at 500 dollars is another way of saying that a single dollar can only purchase a five-hundredth of an apple. We could therefore say that the value of the dollar as priced in apples (or gold ;-) ) is now less than it was. The inflationary scenario will always see a decrease in the value of money.

A further illustration from these scenarios is that the rate of credit can’t be higher than the rate of disposable income. Marc Faber said that the nominal rate of credit can’t increase faster than the nominal rate of gdp. This is almost the same as what I’m saying. Both are statement that the rate of credit cannot increase faster than the amount of money earned  (me) or spent (Faber). Where this money comes from is the difference between the two statements: disposable money (including savings) is not the same as GDP (which includes purchases made with credit).

NB: This is an unfinished work that is likely to be revised in the near future.