pensions and natality

Francois-Rene Rideau
Mon, 12 Apr 1999 01:12:38 +0200

Dear Cybernethics readers,
   french people are very concerned about the "pension problem":
as people die older and older, yet work less and less, and have growing
needs and expenses, state-managed pensions look tinier and tinier,
and people complain about their being insufficient to lead a decent life.

I once heard a cousin of mine, allegedly an economist, spread
the all too common thesis (at least among french media) according to which
"pensions are a problem in France because french people do not have enough
children". I was appalled by this, and tried to convince her that having
more children was a particularly stupid way of putting the problem back
instead of solving it, but apparently, she didn't even understand that the
sum of riches produced by all people during their whole lives didn't change
whether you sum over people then over lives or over lives then over people.
So I'm writing here to expose my simple economical views on the problem.

Consider the sum of available riches (specifically NOT any kind money,
unless it be considered by its sole intrinsic value; rather, consider
food, clothes, tools, furniture, buildings, factories, infrastructure, etc)
in a country, and its evolution over time.

First proposition: there can only be life and civilization if the sum of
available riches is positive. Take it as an axiom, if needed.

Now consider each person's contribution to these riches: production
and consumption of wealth. Second proposition: we assume that, to simplify,
that there exists a way to measure riches and individual contributions,
even though this way is not directly accessible to us humans.

Third proposition: the sum of riches is the same as the accumulated
contribution of everyone since the beginning of times. What is available
is everything that was ever produced, minus everything that was ever
consumed. Actually, we may have to consider "gratuitous" production and
destruction of riches by natural means. But to simplify, we will share
and distribute this natural contribution among individuals in some way.

Fourth proposition: we can split the sum of riches between
the part that was contributed by now dead people, and the part
contributed by people still living during their past lives.

Fifth proposition: the part contributed by dead people is positive
if and only if people in the average produce more riches than they consume
during their lifetime. This follows the very definition of average.

Sixth proposition: unless the production of living people can outweight
the sum of all riches contributed by their ancestors from aeons past,
there can only be civilization if people in the average
produce more than they consume. The fact that people of a given generation
will in the average produce more than they will consume, I will call
a _stable_ evolution of civilization.

Seventh proposition: if the production of riches by active living people
grows very fast (at least exponentially) thanks to gains in productivity
and possibly thanks to increase in number of people, it becomes possible
that people on the average produce less than they consume, if during the
active period of their lives, they can outweight the accumulated deficit
of past people as well as of inactive people. I will call that a
_metastable_ evolution of civilization.

A model of exponential growth in production (population*productivity)
can account for the possibility of a metastable evolution of civilization
[mathematically speaking, it can be that sum(i,c_i exp(-ki))>0 while
sum(i,c_i)<0]. Note again that such an evolution requires that new
generations have a combined weight and productivity during their active
period such that progresses faster than the _accumulated_ deficit of
living and dead people; it works by a bet on continuous progress, and is
very instable in presence of accidental drops in production.

The thesis according to which the only solution to the pension problem
is to have more children is flawed. Having more children only helps when
in a metastable evolution, and even then, it only makes the instability
greater with respect to fluctuations in the evolution of production;
anyway it isn't a parameter that can be increased without the good will
of individuals, and the best way to encourage people is to provide them
with a feeling of security incompatible with the metastability of the
economical equilibrium.

Even when in a metastable evolution, the essential parameter that counts,
the one that politicians and economists are meant to help increase,
is _productivity_. And since we are considering increasing it, the best
and the safest is to strive toward reaching a stable evolution of the

All in all, the only stable solution to the pension problem, in France
and elsewhere, is to have people be more productive than consumptive;
to have them produce more than they consume, create more than they destroy,
be it by working longer and/or by otherwise working more efficiently,
so they can finish their old days on the (individual or amortized) surplus
that they helped create when they were younger.

This is all so simple that it ought to be common wisdom!
Yet it looks horribly heretical to my cousin economist.
Shame on french schools of economics!

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