I have good news for the reader: I have solved the problem of financing pensions in ageing societies. The plan requires a minimum of one-time precautionary saving. Let’s save a single dollar for pensioners of the future! Even today’s stressed Hungarian budget will accommodate this. Let’s keep the money in a risk-free, interest bearing investment until the interest earned on the collected amount is sufficient for the continuous payment of pensions.

The flaw of this idea is obviously that it will solve the problem only in the long term – let’s ignore this for the moment, and calculate how many years we should struggle to live until it starts to work.

To answer the question, we must know the amount we want to pay in pensions. As I personally wish to secure a splendid retirement for the elderly, I suggest that each Hungarian pensioner should receive an annual income equivalent to the world’s current real GDP. At today’s rates, this is approximately $70,000 billion. To obtain the total amount paid on an annual basis, the figure obviously needs to be multiplied by the number of beneficiaries. Let’s assume the latter to be 3 million. At this point, this comes to $210 quintillion (210×1018). And as this should be paid from the interests of the accumulated amount, an assumption should also be made about the average real interest rate. Let’s assume the rate to be 1 percent. Based on historical data, this appears to be a rather conservative and easily viable estimate. That is, an amount corresponding to a total of $21 sextillion (21×1021) should be made out of the initial single dollar.

How long?
Guess how long that will take. A million years? A billion? Would the 13 billion years in the life of the universe be enough for a stunt like this? Surprisingly, a few thousand years will do the trick, 5,165 years to be precise. And at this point to me the affair becomes very suspicious. Indeed, this is a reasonable time horizon given the extreme assumptions I’ve been making. Pensioners might also be satisfied with less than today’s world GDP; surely much less will be sufficient to make ends meet. Or the initial savings may be more than $1. We may also save each year, not only once. All these options radically reduce the amount of time required. Why worry about pensions?
On the other hand, five thousand years ago there were already well functioning societies; Mesopotamia flourished and Egypt erected pyramids. Around that time, money also came to be used. Could it be true that it would have been enough for someone to save one present dollar’s worth of shekels or drachmas to make today’s world the land of milk and honey? I wonder why no-one thought of it.

Increased savings
Let’s take a look at what the amount saved would look like over time. As interest is reinvested each year, the process is described by an exponential function, more precisely: 1.01t, where t is the number of years elapsed. One feature of exponential functions is that when a logarithmic scale is applied to the vertical axis, they will appear to be straight lines. In our case, the function of the 1 percent growth rate looks like this:


Savings and time
This may better explain how the initial single dollar becomes a sextillion so soon. The value of an exponential function will leap to the next magnitude with each time unit, i.e. within a reasonable time, extremely large numbers will be produced. This is why it appears very likely that the real process described by the function will be unsustainable in the long term even if the rate of growth is low. The whole thing is illusory; indeed, why couldn’t something grow by 1 percent each year? This seems absolutely plausible. At the same time, I don’t believe that in five thousand years the same thing will be a sextillion times its current value, be it energy consumption, real GDP or real savings (we’re talking real quantities – obviously, in nominal terms the situation looks different, e.g. any number of zeros could be printed on a bank note). Yet, the two propositions are the same. And if this is really not possible, the year will indeed come when the 1 percent growth is apparently no harder than in the previous year, but for some reason it just can’t go on any longer. And if, on top of it all, our system is built on continuous growth, at this point serious problems will arise in its operation. Our monetary system, based on continuous growth, hit such a ceiling in 2008, and nearly fell apart. How exactly this happened will be discussed in the next part.

Original date of Hungarian publication: 03 november 2014