A large number of small amounts

koenfucius

February 2

(featured image: Het Luilekkerland, Pieter Bruegel the elder, Wikimedia Commons/PD)

Our intuition struggles to correctly interpret the combination of very large and very small numbers

The medieval mythical land of Cockaigne, graphically represented by Pieter Bruegel the Elder in his 1567 painting, Het Luilekkerland (literally, the "lazy-tasty land"), is a nice example of humanity's yearning for an existence in which we can get something for nothing. Such a land of plenty, where we can obtain all we need without any effort is, sadly, an unattainable ideal. That doesn't stop us looking for ways, though, and sometimes believing we found one.

The tax that costs (almost) nothing

One example I came across the other week was a tweet from entrepreneur Carl Gough, proposing a small charge for each email that is sent. Every single day of 2023, an estimated average of 347.3 billion emails were sent and received. A one-cent levy on each email would thus raise nearly 3.5 billion dollars every day, or more than 1.2 trillion dollars in a year. It reminded me of a fantasy I used to have as a seven-year-old. I had learned at school that the population of Belgium (my native country) was about 9 million (it is a little while ago). I imagined that, if every one of them gave me 1 franc (a negligible amount back then – it would buy just two pieces of bubble gum), I'd be a multi-millionaire. Most people would not even notice if their wealth reduced by 1 franc, but all together it would make me filthy rich. Wow! (My imagination stopped short of working out exactly how I would go about getting my compatriots to each give me that franc, though. But it made for a pleasant daydream.)

3.5 billion a day, that is a lot of pennies (image: foreverseptember/Flickr CC BY ND 2.0)

The similarity between my scheme and Mr Gough's is that both rely on the fact that the individual sacrifices are insignificantly small, but they are multiplied by a very large number. That is as close as we can hope to get to the pipe dream of getting something for absolutely nothing. Leaving my own wild boyhood imagination to one side for the moment, might the idea of a minuscule tax on emails raising a lot of money actually work? The concept of a transaction tax is not new, and perhaps we can learn something from how it has fared. (The fact that there are no large-scale implementations might already tell us something. But let's not jump ahead.)

Perhaps the best known (yet still somewhat obscure) example of the concept is the Tobin Tax, named after economist James Tobin who first formulated a version of it in 1972. Initially, its intention was not even to raise money, but to ensure the stability of the foreign exchange markets. Charging a levy on currency transactions would discourage rapid conversions in both directions seeking to take advantage of arbitrage opportunities (and thus reduce the risk of runaway speculation). The idea of a transaction tax to curb speculation in very liquid markets itself had been suggested several decades earlier by none other than John Maynard Keynes.

A working paper by Thornton Matheson, an economist at the International Monetary Fund, looked at the pros and cons of such Financial Transaction Taxes (FTTs). Of course, financial transactions are different from sending and receiving emails. They serve a specific purpose: maximizing the long-term return of an investment. A measure that interferes with the ability to transact freely will necessarily affect that long-term goal. With email traffic, there is no equivalent. However, the effects on both the investment and on the revenue that is raised is ultimately driven by two factors that are common in the two settings: the cost of the tax itself, and the way that cost affects the behaviour of the players (investors or emailers), notably what they might do to avoid the tax.

Not so insignificant

Most realistic proposals for an FTT are based on a level of 0.5 to 1 basis point (0.005-0.01%) of the transaction value. Anything higher is deemed to be detrimental to asset prices and liquidity, which percolates into the cost of capital to businesses and returns to savings. This directly or indirectly impacts everyone. The reason is that even a modest return may require numerous transactions, the costs of which – small as they may be – accumulate over time, and inevitably depress the return.

What would be the effect of a 1-cent levy on each email sent? Say a typical citizen might send between 500 and 1000 private emails per year, which would cost 5-10 dollars, or 10-20 cents per week. This small amount is unlikely to significantly affect most email users' behaviour. But this is not the whole story. Let us assume, as an upper limit, that about 4 billion people on our planet send on average 1000 private emails per year. They thus account for some 4 trillion emails per year, or about 11 billion per day. To save you returning to the start of this article, the daily total is around 350 billion. Just over 3% of that would be private email. So, 97% of the tax, $3.4 billion per day or around $1.2 trillion per year, is paid for by companies and organizations. To position that figure, it is equivalent to $150 for every human on the planet, or 1.2% of the world's GDP. It may be made up out of a huge number of tiny levies, but it is, by any benchmark, a Very Large Amount – an amount that will, without any doubt, ultimately be recharged to the end consumer, and that is all of us. Since we will eventually end up paying for the tax on every email, it is as if every mail we send will cost us about 30 cents. That is no longer so insignificant.

Now, while we might not be too bothered about our own share of ten bucks per year, large emailers might look for non-email communication. This already happens, for reasons of convenience, but if a bill of the magnitude of 1.2% of turnover is heading for a company's bottom line, it will happen a lot more for financial reasons. Companies will communicate via direct messaging on their own website or via their own app, or via social media platforms and the likes of WhatsApp. That will cut everyone's cost, but it will also drastically reduce the revenue this levy was supposed to deliver.

So, it looks like, unfortunately, Mr Gough's idea of raising vast amounts of money without anyone really noticing any significant cost, is not a practical possibility.

Something for nothing? Forget it

Keep on cutting for free chocolate forever (image via Science ABC)

That said, there are some unsubstantiated urban legends of individuals trying to put into practice my childhood idea, acquiring great riches through large numbers of very small amounts of money. This even has a name, salami slicing, referring to the fact that it typically involves the diversion of undetectably small 'slices' (often fractions of pennies or cents) from customer accounts into a dummy account created by a computer programmer. A related, genuine, scam was that of a programmer who set up 58,000 brokerage accounts with fake identities to steal the "micro-deposits" that financial institutions make to validate a newly opened account. The perpetrator (ironically named Michael Largent – "l'argent" is French for "the money") was sentenced to 15 months in jail and restitution of $200,000.

So, much like a perpetual motion machine, a mechanism to produce income without any form of effort or sacrifice appears to be impossible. Any argument to the contrary should be treated with scepticism. Intriguingly, there is a physical equivalent to the kind of salami slicing that produces the apparent financial gain out of nothing: the infinite chocolate trick. It looks like you can, by cutting it in a peculiar way, keep on removing one little piece of chocolate, without diminishing the large slab. But, just like with taxes that appear to raise vast amounts without seeming to cost anyone anything, it is an illusion.