*by* soj
*Sat Jul 23rd, 2005 at 04:24:24 AM EST*

*Editor's note: Bumped to the top by whataboutbob for more exposure.*

*We are posting this on behalf of Jerome*

In Colman's recent thread How rich are you?, I pointed out fairly abruptly that that income and wealth were two very different concepts mathematically speaking, and that mixing them up can create terrible confusion.

Of course, both have to do with money, and both are apparently counted in the same units, currencies, but in fact, they are not. The same thing happens about global wealth, GDP and growth.

Let me go into the basic math. Please rest assured that you'll be able to follow me even if you hate the sound "math".

:::::::: More (and much more) below ::::::::::

To understand economics, let's get back to basic stuff: driving, which all of you should understand. Imagine you are driving in a straight line.

- The first bit of data which can be of interest is your position, which we shall measure in kilometers (or meters) from your point of departure. This is the concept of
*distance* or *location*.

- The second bit that may be of interest is your
*speed*. This is the amount of distance that you move per unit of time: it's measured in kilometers per hour, or meters per second: distance divided by time.

- The third concept is that of
*acceleration.* You stopped, and your start again; you speed changes from 0 to say 50 kph, in ten seconds, that was an acceleration of 5 kilometers per second per second. It is speed divided by time, or distance divided by time divided by time.

The link with economy is as follows:

- the equivalent to distance/location is
*wealth*. This is measured in a unit of value, typically a currency, say euros. That's what you use to measure the value of a house, of a car or of anything else. That's what **assets** are counted in.

- the next step is to measure the change in wealth, i.e. how quickly you accumulate (or spend). Distance divided by time becomes value divided by time, typically euros per year or per month. That's where
**income** can be classified: the amount of wealth you earn for a given period of time. Euros *per year*.
Wealth and income have the same kind of relationship as your location and your speed. Telling someone how fast you are going tells them nothing about where you are - unless possibly if they know where you started from, and when.

The reason this distinction is important is because GDP, the number we use to measure "wealth", is actually a *speed* - the rate of creation of wealth per unit of time, in this case, per year. (I won't go here into the fact that it is highly flawed way to measure wealth creation, as it counts for instance using resources as a creation of wealth, but the fact remains about its intent). GDP is the measure of **change of wealth**, and it is measured in euros per year. The fact that GDP is in euros per year and not in euros is a fundamental fact that should make its nature clear but that most people, starting with journalists, don't seem to always have in mind.

The same goes with inflation - inflation is a change in value per unit of time (again, typically, per year) and it is really expressed in euros per year. The inflation for bread, for instance (the "speed of the price" of bread) is 2 cents per year.

- It logically follows that the economic equivalent of acceleration is
**growth**. What we call growth is not the change in wealth, it is the change in the rate of change of wealth. It is an acceleration of wealth, and it is measured in euros per year per year. Now, we usually express it as a percentage 2%, 3%, etc, but think about it precisely: growth of 2% means that GDP this year is two per cent larger than GDP last year. So it is a variation of GDP per year. As we have seen above that GDP is already expressed in euros per year, we do end up with euros per year per year. Similarly, a change in the inflation rate is really an acceleration of prices, also measured in euros per year per year.
If you want actual numbers, let's take the USA. Household assets, a first proxy for wealth, is around 60 trillion dollars. GDP is approximately 10 trillion dollars per year. Growth, at say 3% in economist units, is equal to about 300 billion dollars per year per year. That means that next year, total wealth will increase by 300 billion dollars *more* than the previous year, i.e. by 10.3 trillion dollars per year instead of 10 trillion dollars per year (and wealth will have increased by 20.3 trillion in two years, NOT by 300 billion dollars).

What this means, and please never forget this, is that when people - economists, punidts, talk about the change in economic growth, they are talking about the change of an acceleration, which becomes a pretty tricky concept to visualise in the real world.

In mathematical parlance, speed is a first derivative, acceleration is a second derivative. Thus growth is a second derivative of wealth, and changes in the growth rate are third derivatives. When you start mixing up different derivatives, you have what are called differential equations, which are the hardest equations to solve - in fact, many of them are strictly impossible to solve mathematically and can only be resolved by lenghty calculus to slowly get closer to the answer.

So economists - and all of us - are merrily playing with extremely complex mathematical concepts when we talk about the economy, and most of the time, they mess it up.

Describing growth as an acceleration should make it pretty clear that is is not something that can go on forever in a finite world. Our "growth", far from being something entirely positive, also means that we are going towards these limits *increasingly fast*. Of course, it should be noted that GDP is an imperfect measure of wealth change, as most of the wealth "created" in each period is consumed in that same period, and the net change in wealth for the period is much smaller. What that means is that the human race, as currently in operation on earth, cannot seemingly survive below a certain wealth-speed (i.e. the quantity of wealth that needs to be "created" each year for us to survive), and our current civilisation is such that that wealth-speed in increasing each year.

But let's back down from that gloomy talk (I'll let DeAnander expand on these ideas...) and let's get back to our initial question, where we were asked for our yearly income ans told about how "rich" we were. If "rich" is defined by how much you earn (how much wealth you "create" per year), then the test is correct, but somehow, I doubt that this is what people have in mind when they think about "rich". Rich means Bill Gates, who actually had negative "income" in recent years as the value of his Microsoft stock fell in value with the stock market (despite probably comfortable income from dividends and the like). So if he answered, truthfully, that he "earned" minus 5 billion dollars in our test, would that make him the 6,298,675,456 richest person on the planet?
(*by the way, you have to love the precision of these numbers - a sure thing that the creators undertand nothing about numbers. NEVER give more digits (other than 0s) than the precision with which you actually know the underlying value, or it becomes false information*).

Similarly, when you hear these comparisons about the top 50 richest people being "richer" than the 50 poorest countries, again, this is highly misleading, as you are comparing on one side the stock of wealth and on the other side the creation of wealth for one year. It's like comparing the acceleration of a Porsche vs. the speed of a train to determine which is "fastest".

Wealth - location - stock

GDP - speed - change of stock - first derivative

Growth - acceleration - change in the change of stock - second derivative.

Wealth is the chairs you sit on when you eat. GDP is the food you bring on the table every day (and consume), and the new chair you build. Growth is when you go from building one chair per day to building two chairs per day. Economic slowdown is when the next year, you go to two and a half chairs per day "only" (your wealth is increasing faster than ever before, but you feel that your work is making less "progress" than before).

It's quite fascinating actually that our mind seems to be more comfortable with the concept of speed (first derivative) as its basic unit to measure things up rather than that of location/underlying wealth. It's very worrying that we end up using units of location/wealth when we talk about the rate of change. Of course, everybody knows that we talk about something that happens over the course of a conventional period, but we forget it. GDP is not 10 trillion dollars, it is 10 trillion **dollars per year.**

20comments (20 topical, 0 editorial, 0 hidden)20comments (20 topical, 0 editorial, 0 hidden)