Power Law Inequalities & Geniuses

In response to my recent Blog post on inequality, a friend brought up power laws and asked about their relationship with inequality. This is very apt at a time when we've just been subjected to a sub-standard piece of propaganda from the BBC called The Super Rich & Us - a recent programme presented by someone who doesn't understand much about economics, interviewing other people (some of whom were economists) who also don't understand much about economics. With a better understanding of the subject, they wouldn't have spent the best part of two hours utterly confused about most of the matters regarding inequality, power laws, living standards, supply and demand and consumption.

The relationship between power laws and inequality is largely built on society's revealed preferences, but there's a little more to it than that. Power laws do lead to concentrations of wealth falling in a small proportion of the population's hands. But they are nothing much to worry about: they are to be expected because in a free market where goods and services are freely exchanged for money, the rate of consumption always exceeds the rate of service for an individual.

In other words, there are more ways for Jack to procure goods and services from other providers than there are ways for Jack to provide goods and services to others. Whether you're a lawyer, a taxi driver or a circus clown, you earn money providing a particular skill to your customers.

But the money you spend (at Tesco, on Amazon, at the hairdresser’s, at the garage, etc) goes in multiple directions. Lots of people want food, books, a haircut, fuel, etc, so concentrations of wealth fall in the hands of large-scale providers, who are a small proportion of society, relative to the number of consumers.

(By the way, point of technicality, even consumers are providers in that their consumption provides producer surplus for other providers, but that’s not central to the point being made).

So you can hopefully see why power laws exist, and also how wealth can be concentrated in a few hands very quickly. To give you a much simpler illustration than something as complex as UK society; suppose 20 people are put on an otherwise uninhabited island with treacherous weather conditions. They have to stay on the island for one year, and each inhabitant is given 15 tokens a day with which to buy food from a delivery helicopter that lands every day at noon. What they don’t spend on food, they keep, and at the end of the year whatever tokens they have saved can be exchanged for £3 per token.

During their stay it emerges that there is an expert in building safe, warm tent sheltering from the natural plants. For a fee of 350 tokens per person, payable over the next 50 weeks, all 19 of the other inhabitants can have a tent built for them, thereby enjoying warm, dry and safe nights of sleep for their island duration. At the end of the year our tent building expert will have seen a significant concentration of wealth in his hands, at the expense of the other 19 islanders, but they will have enjoyed a year’s worth of tent-related benefits.

That’s a very simple illustration of a much wider phenomenon that is going on across society, where innovators, writers, musicians and hugely successful business owners are the beneficiaries of these power law transfers. Nobody would have any difficulty seeing a just power law inequality in my island scenario - but yet when the situations apply to real business goings on in society, preferences, they don't seem to get it. To the extent that most inequality is the result of an aggregation of society's revealed preferences - inequality is one of the most democratic of all human phenomena.  

But if you take society as a collection of individuals, you’ll find another important trend that plays out in power laws: there should be a continual natural trend towards progression and improvement. Here's what I mean.

Humans are generally working (either together cooperatively or independently) to make their own lives better, and despite exceptions, this engenders an inclination towards making the world a better place, whether it’s through all the benefits of trade, innovations with which we are continually seeking to improve products, technology and new designs, or lest we forget, the numerous formal institutions that (with mixed results, but generally more pros than cons) make laws and implement regulations that are thought to make society a better place to live.

Because the nature of trade and work constantly involves tweaks, improvements and innovations here and there, and further multiplied both across society and in a fairly linear fashion across time, we have a situation where (despite obvious peaks and troughs and chaotic anomalies and degrees of randomness in the system – world wars, financial crashes, tsunamis, etc) there is a fairly inevitable (or at least high probability) and stable trend of human progression built into the system.

And it's this trend that's another catalyst for generating inequality - the fact that nature is not very democratic (looks, size, shape, talents, intelligence, sensory apparatus, opportunity and background), and therefore it is expected that there won't be equal outcomes. There is a notable difference in all of these human qualities in each of us, as their attainment depends on undemocratic things like fortune and pursuit, as well as hard work, skill and application.

Consequently, then, inequality has a lot do with the fact that humans are tenaciously trying to improve themselves, and the fact that progression is in our blood - it is not just an inevitable part of our journey, it is an exhibition of how influential and advancing our species can be - particularly when you factor that into this observation about human beings.