Thursday, 2 May 2013

"Wealth health"

Rosamund Urwin in today's Evening Standard:

Headlines this week claimed that — contrary to the cliché and a certain ubiquitous F Scott Fitzgerald novel — money may make you happy after all. According to a study by economists Betsey Stevenson and Justin Wolfers, there is positive correlation between wealth and wellbeing across the world.

But what they also showed is that extra moolah has the greatest effect for those who have the least: each additional pound will increase happiness by a lesser amount than the pound before it. So while some saw this as a victory for GDP-obsessed capitalism, really it was making a case for redistribution.


The fancy term for this is the law of diminishing returns, which is blindingly obvious. I'm not even sure if the extra happiness is even geometric. If your wage doubles from £10,000 to £20,000, it makes a huge difference; if it doubles again to £40,000, then it makes a big difference; if it doubles to £80,000 you are a lot happier; beyond that, it's just numbers on bits of paper and conspicuous consumption.

UPDATE: according to TW in the comments, happiness is proportional to the logarithm (presumably to base ten) of your income, which means that if your income goes up by a factor of ten, your happiness level only doubles.

For a more detailed look at the numbers, I refer you to our Homey-in-Chief:

Around 35 per cent of members of households earning under $10,000 a year claim to be very happy... At $10-20k, 42 per cent are very happy and 47 per cent very satisfied [and so on up the income scale] those on $500k and above are all very happy and very satisfied.

If that $500k is truly earned income, good luck to them. But the chances are that most people in this category are rent seekers (landowners, bankers, quangocrats, politicians, lawyers and accountants etc). If you prevent that $500k being diverted into their pockets in the first place so that fifty people can keep more of their earned income and move from $10k to $20k, for every "very happy" person you lose at the top, you get an extra three or four "very happy" people at the bottom. That's basic maths.

12 comments:

Richard Allan said...

"if it doubles to £80,000 you are a lot happier; beyond that, it's just numbers on bits of paper and conspicuous consumption."

Ah yes, the infamous "My income plus 20k is as much as anyone could ever need" argument. Closely related to "Popular culture peaked when I was twelve" and "The voting age should be my age minus a few years".

Ah, only joking Mark.

Mark Wadsworth said...

RA,

a) what makes you think my household income is less than £80k?

b) Popular culture peaked when you were 15 - 20 years old, not 12.

c) I'm happy with voting age 18, aren't most people?

Kj said...

I was in my prime in the mid-90s, and in retrospect I can actually admit that wasn't the peak of popular culture.
MW: do you think owner-occupied imputed rents have the same happiness effect as earned income? ;)

Tim Worstall said...

"The fancy term for this is the law of diminishing returns, which is blindingly obvious. I'm not even sure if the extra happiness is even geometric."

Log of income apparently.

Mark Wadsworth said...

Kj: "do you think owner-occupied imputed rents have the same happiness effect as earned income?"

No, because most people don't realise that they are getting benefits worth thousands or tens of thousand pounds a year, unearned and nearly tax-free*.

On the other hand, it's very nice to live rent and mortgage free, but that's a yes/no thing and doesn't relate to the rental value of your home.

* But they will HOWL WITH OUTRAGE if they have to pay £1,000 or £2,000 council tax.

Mark Wadsworth said...

TW, I messed up there.

Having thought about this later on, I think I should have written "a logarithmic progression" or something a bit more mathematical sounding.

The "log of income" would suggest that your happiness doubles if your income goes up by ten. I'm not sure if the effect is as little as that, but it is easily observable that if you spend ten times as much on something it probably only gives you double the happiness, i.e.

second hand car £2,000
new family car £20,000
new Lambourghini with all bells and whistles £200,000
vintage Ferrari £2 million

etc.

Bayard said...

"do you think owner-occupied imputed rents have the same happiness effect as earned income?"

Well, the value is proportional to the imputed rents, and value of your house tends to reflect your income, so I'd say "yes, but you don't neccessarily realise why".

Sarton Bander said...

Pure rent seeking looks like an PERSONAL increase in productivity.

You get more money without putting more of your time in.

Of course in the wider economy it is a negative.

Rational Anarchist said...

Sorry, as a maths geek I have to jump in here and make a slight correction:

UPDATE: according to TW in the comments, happiness is proportional to the logarithm (presumably to base ten) of your income, which means that if your income goes up by a factor of ten, your happiness level only doubles.

Actually, a log in this case means that a multiple of income gives a fixed increase in happiness. Which base you choose makes no difference.

For example, using the numbers given here, if we set the level of very-happiness at income 10k to 35%, and at 20k to 42% then we see that a doubling adds 7%. Turning this into a formula gives:

happiness = log(income)*0.232534963292695-0.58014
using base 10. This maps fairly well, with 500k income giving 98% happiness.

If we instead use base 2, then we get:
happiness = log(income)*0.07-0.58014

In both cases the results are identical, and a doubling gives an increase of 7%.

Coming a little more on topic, it seems clear that reducing the income of those on over 500k to 500k and giving the money to those on less should increase overall happiness. But there are a number of unstated assumptions in that statement.

Around 35 per cent of members of households earning under $10,000 a year claim to be very happy This would not be earned income, so may have little effect on happiness. Also, is the greatest happiness for the greatest number actually something that we want? Perhaps unhappiness promotes striving and increases total productivity?

Robin Smith said...

The intellect does a couple of uni papers on this one every year. Nothing new is ever discovered, the blindingly obvious is missed each time. Very amusing psychology.

1) Wealth is great, everyone is better off with more of it regardless of the relative differences. More of it means less work all else being equal all the way to infinity. Unless you are insane you will never want to do more work when there is an opportunity to do less for the same reward. Even charity (though most charity thinks its saving the world for free they still want the rewards more than the charity, fuckin hypocrites)

2) BUT... there are things in life more valuable to everyone than mere wealth. What these great thinkers keep toiling over with enormous intellect and little wisdom, is that people are unhappy, in all cases because they value wealth MORE than these things which have more value to them. Is it any surprise they are unhappy holding such an insane view of life, no matter how wealthy they are. They're forgoing the more valuable for the less, knowingly. Of course its a matter of personal affirmation what you think of the higher things in life

Living in The Matrix network. The #1 pyramid sale. MELT

Mark Wadsworth said...

RA: "Actually, a log in this case means that a multiple of income gives a fixed increase in happiness. Which base you choose makes no difference."

Yes, but your equation now has one unknown which is "a fixed increase" so it is not much use to us.

Using log to base ten gives you the amount of the increase, i.e. ten times the income = twice as happy.

To the extent that you can measure "happiness" that scientifically or accurately, which you can't anyway.

RS, you've missed the point a bit.

Mark Wadsworth said...

RA: "reducing the income of those on over 500k to 500k and giving the money to those on less should increase overall happiness."

You are now wildly misquoting me, can you please go back and read it properly?