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Wealth, Income, Growth (by Jerome a Paris)

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.

You left off the third derivative of distance with respect to time, which represents Jerk. Seriously, that's the rate of change of acceleration, which is noticed as a jerk, for example, when you suddenly apply the brakes on your car. (Constant pressure on brake pedal gives constant acceleration; changing pressure on brake pedal gives jerk.)

I would suggest that perhaps the economic third derivative relates to how suddenly the economy changes.

For example, if we run out of oil over 50 years and do something about it early on, we may be able to control the change in growth that (may) go along with it. If we don't do something, then there will be a sudden economic disruption. So what we need to control is the rate of change of growth...

by asdf on Fri Jul 22nd, 2005 at 01:13:50 AM EST
Note to self: never post semi-serious things with numbers in them. It makes the local investment bankers tense.
by Colman (colman at eurotrib.com) on Fri Jul 22nd, 2005 at 02:11:44 AM EST
Colman, please continue posting semi-serious things, I enjoyed it. Besides tense local investment bankers write great interesting and educative comments.

I think the problem with measuring being rich or wealthy is that most of the time it only considers the material aspect. Probably most people have experience the phenomenon that when they are happy they feel rich and wealthy and while unhappy they do not, even if there was no actual change in material possession. So to me being wealthy or rich also has a psychological dimension, which is to often not accounted for, especially in a capitalist system where wealth is counted by share-holder values instead of 'happy' and productive employees. I do believe that Europe is living more up to that standard and hopefully will not change to much its social system.  

by Fran on Fri Jul 22nd, 2005 at 02:25:30 AM EST
[ Parent ]
I do not think it is the investment banker in me that reacts. Bankers are no better with these concepts than lesser humans not supposed to deal with numbers all the time...

Actually, the lack of understanding of basic math concepts (such as a model being only as good as its hypotheses - cf calculating a return on investment with 2 digits when one of the variables is the oil price) in bankers is sometimes scary...

In the long run, we're all dead. John Maynard Keynes

by Jerome a Paris (etg@eurotrib.com) on Fri Jul 22nd, 2005 at 04:39:20 AM EST
[ Parent ]
Well I'm impressed.  This diary is really good Jerome.  It is clear, easily understandable, and conveys an subtle, important, point viz differential equations.  Good job.  

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre
by ATinNM on Fri Jul 22nd, 2005 at 12:28:49 PM EST
[ Parent ]
"A ceux qui blâment les mathématiques"

Tant plus je vois que vous blâmez
Sa noble discipline,
Plus à l'aimer vous enflammez
Ma volonté encline.

Car ce qui a moins de suivants,
D'autant plus il est rare,
Et est la chose entre vivants
Dont on est plus avare.

Il n'est pas en votre puissance
Qu'y soyez adonnés ;
Car le ciel dès votre naissance
Vous en a détournés ;

Ou ayant persuasion
Que tant la peine en coûte,
Est la meilleure occasion
Qui tant vous en dégoûte.

Le ciel orné de tels flambeaux
N'est-il point admirable ?
La notice de corps si beaux
N'est-elle désirable ?

Du céleste ouvrage l'objet,
Si vrai et régulier,
N'est-il sur tout autre sujet
Beau, noble et singulier ?

N'est-ce rien d'avoir pu prévoir
Par les cours ordinaires,
L'éclipse que doit recevoir
L'un des deux Luminaires 7

D'avoir su, par vraies pratiques,
Les aspects calculer ?
Et connaître les Erratiques
Marcher ou reculer ?

Toutefois il n'est jà besoin
Que tant fort je la loue,
Vu que je n'ai vouloir ni soin
Que de ce l'on m'avoue ;

Car que chaut-il à qui l'honore
Qu'elle soit contemnée ?
Science, de cil qui l'ignore,
Est toujours condamnée.

Assez regarde l'indocte homme
Du ciel rond la ceinture,
Mais il s'y connaît ainsi comme
L'aveugle en la peinture.

Celui qui a l'âme ravie
Par les cieux va et passe,
Et soudain voit durant sa vie
D'en haut la terre basse.

Cette science l'homme cueille
Alors qu'il imagine
La facture et grande merveille
De la ronde machine.


Jacques Peletier du Mans (1517 - 1582)

"Dieu se rit des hommes qui se plaignent des conséquences alors qu'ils en chérissent les causes" Jacques-Bénigne Bossuet

by Melanchthon on Fri Jul 22nd, 2005 at 04:56:47 PM EST
[ Parent ]
"L'excès de précision, dans le règne de la quantité, correspond très exactement à l'excès du pittoresque, dans le règne de la qualité. La précision numérique est souvent une émeute de chiffres, comme le pittoresque est, pour parler comme Baudelaire, « une émeute de détails ».

On peut y voir une des marques les plus nettes d'un esprit non scientifique, dans le temps même où cet esprit a des prétentions à l'objectivité scientifique. En effet, une des exigences primordiales de l'esprit scientifique, c'est que la précision d'une mesure doit se référer constamment à la sensibilité de la méthode de mesure et qu'elle doit naturellement tenir compte des conditions de permanence de l'objet mesuré. Mesurer exactement un objet fuyant ou indéterminé, mesurer exactement un objet fixe et bien déterminé avec un instrument grossier, voilà deux types d'occupations vaines que rejette de prime abord la discipline scientifique".

Gaston Bachelard in "La Formation de l'Esprit Scientifique"

"Dieu se rit des hommes qui se plaignent des conséquences alors qu'ils en chérissent les causes" Jacques-Bénigne Bossuet

by Melanchthon on Fri Jul 22nd, 2005 at 05:13:38 PM EST
[ Parent ]
I swear I will translate the second text, but not the 16th century French poem...


"Dieu se rit des hommes qui se plaignent des conséquences alors qu'ils en chérissent les causes" Jacques-Bénigne Bossuet

by Melanchthon on Fri Jul 22nd, 2005 at 05:18:25 PM EST
[ Parent ]
Translation from the Google Language Tools:

"The excess of precision, in the reign of the quantity, corresponds very exactly to the excess of picturesque, in the reign of quality.  The numerical precision is often a riot of figures, as the picturesque one is, to speak like Baudelaire, "a riot of details"

One can see there one of the clearest marks of a nonscientific spirit, in the time even where this spirit has claims with scientific objectivity.  Indeed, one of the paramount requirements of the scientific spirit, it is that the precision of a measurement must refer constantly to the sensitivity of the method of measurement and that it must naturally take account of the conditions of permanence of the measured object.  To measure a reducing or unspecified object exactly, to measure exactly a fixed and well defined object with a coarse instrument, here are two types of vain occupations which rejects first of all the scientific discipline ".

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Sat Jul 23rd, 2005 at 11:37:01 AM EST
[ Parent ]
After 10 yrs on the bench, very little makes me tense.

I did enjoy someone showing a clear example of the use of derivatives though.  Just don't ask me to solve any diffy -Q's though -- been about 3 decades too long ....

The diary does point out the root problem of the original survey.  Our current income is moderate but it keeps the large net worth intact as our lifestyle is pretty simple.

by HiD on Sun Jul 24th, 2005 at 06:14:41 AM EST
[ Parent ]
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.

And most of the time the basic assumptions they make are silly.
by Colman (colman at eurotrib.com) on Fri Jul 22nd, 2005 at 02:15:44 AM EST
Damn!! Our family income is (according to the "How Rich Are You?" list) somewhere in the top .080-.075% of the wealthy in the world...with about 5 billion 900 million people poorer than us...and we are STILL just paying the bills!!! If 54 million people are "wealthier" than us, I wonder how many of them are just getting by? Yes, we are wealthy in comparison to others...but its all about perspectives, isn't it?

But this little lesson on GDP does help me understand this statistic a bit better...hmm, the speed of growth...

"Once in awhile we get shown the light, in the strangest of places, if we look at it right" - Hunter/Garcia

by whataboutbob on Fri Jul 22nd, 2005 at 04:58:08 AM EST
this reminds of a story re J. Paul Getty.  He always claimed he felt poor(less powerful?) because Exxon and Shell were so much bigger than his company.  Pretty laughable given his net worth and the lifestyle he led.
by HiD on Sun Jul 24th, 2005 at 06:16:31 AM EST
[ Parent ]
(Editor's note) I just bumped this back to the top, because we want to give this some more exposure, so...here it is!

"Once in awhile we get shown the light, in the strangest of places, if we look at it right" - Hunter/Garcia
by whataboutbob on Sat Jul 23rd, 2005 at 04:33:29 AM EST
Here's a question for all you socialists. (There aren't many in the USA to ask.) How do you reconcile the socialist motto "workers of the world, unite" with protectionist trade measures supported by the left? One might think that socialists would be the strongest free-traders, since the best way to improve the wages of third-world workers would be to integrate them fully into the world economic system. It seems like the current western socialist motto is more like "workers of the west, unite against the workers of the third world."

The income comparison site uses a flawed method for comparing individual wealth, but it's hard to avoid noticing that practically everybody in the West is wealthy compared to practically everybody in the Third World.

"The European peoples, and especially the British, have long owed their high standard of life to direct or indirect exploitation of the coloured peoples. This relationship has never been made clear by official Socialist propaganda, and the British worker, instead of being told that, by world standards, he is living above his income, has been taught to think of himself as an overworked, down-trodden slave." -- Orwell

"Unlike liberals, socialists must necessarily attempt to understand the world as a totality, or find themselves slipping backwards into privileging the interests of one or other state over those of one or more others." -- Marx

What is the distinction between the anti-free-trade movement, including the protestors at various global economic forums, and international socialists? Why do the socialists associate with such strong nationalists?

by asdf on Sat Jul 23rd, 2005 at 08:55:02 AM EST
Not sure how to answer your question, but I think some of it is people trying to deal with the problems in front of them.  You say:

The income comparison site uses a flawed method for comparing individual wealth, but it's hard to avoid noticing that practically everybody in the West is wealthy compared to practically everybody in the Third World.

and that's little solace to the poor.  Starving to death in the U.S. is not a different experience from starving to death anywhere else in the world.

Yesterday in Phoenix, 19 people died from the heat, 14 of them homeless.  I doubt they would have found consolation in the fact that they were technically wealthy, globally speaking.

Limited resources, or the impression of limited resources, doesn't make for friendly neighbors.

Maybe we can eventually make language a complete impediment to understanding. -Hobbes

by Izzy (izzy at eurotrib dot com) on Sat Jul 23rd, 2005 at 06:48:06 PM EST
[ Parent ]
I agree.  Forget globally speaking. You can't compare poor people from different countries strictly by income...just because 9 thousand may be ridiculously wealthy to some person in a third world country does not mean that 9 thousand here in the US is even close to a decent life.

"People never do evil so throughly and happily as when they do it from moral conviction."-Blaise Pascal
by chocolate ink on Mon Jul 25th, 2005 at 04:08:08 AM EST
[ Parent ]
The anti-globalization movement includes both labor activists, who are advocates first and socialists second (if at all!); and anti-capitalist groups and NGOs who point out that the benefits of free trade accrue primarily to the shareholders of the developed world while the developing world shoulders a disproportionate share of the burdens.

Your observation: It seems like the current western socialist motto is more like "workers of the west, unite against the workers of the third world." is apt; in Germany, this is why some commentators question whether the WASG is really "left".

The fact is that what we're experiencing right now is a top-down disaster. -Paul Krugman

by dvx (dvx.clt ät gmail dotcom) on Sun Jul 24th, 2005 at 08:38:44 AM EST
[ Parent ]
I think there's a problem here. National income or GDP is not the annual change in national wealth, because most of it is consumed. Only the part of income that is saved and invested increases the stock of wealth.
by TGeraghty on Sat Jul 23rd, 2005 at 07:34:08 PM EST
Oh, sorry, I see you said that already.
by TGeraghty on Mon Jul 25th, 2005 at 05:39:44 AM EST
[ Parent ]

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