Abbe Boulah’s Weblog

The Black Swan Neck of the Exponential Growth Curve

One of the conundrums behind the current financial crisis is the puzzle concerning the exponential growth curve. Everybody looking at such a curve will concede that its application to many economic phenomena is unrealistic and unsustainable in the long run. For example, let’s assume a bank is offering an investor a 5% interest rate on a large deposit, say $1M. So in a year, the account will have $1.05M, the year after that $1. 1M, in three years $1.016M, and so on. Understanding this principle of compound interest is widely held to be one of the necessary aspects of basic financial intelligence.

Now the bank, in order to live up to its promise of paying back the deposit with interest, will have to earn that interest, plus, of course its own profit on doing so, from other people, who are borrowing money from the bank. So it must lend money at an interest rate that necessarily must be higher than the original 5%. If is only 1% more, the interest rate at which the ‘economy’ of the combined other borrowers must ‘grow’ per period, has to be at least 6%, just to be able to pay back the loans. But of course these people are doing that to make profit of their own as well, so that profit rate will have to be added to the necessary growth of the economy as a whole. This applies to every segment of that economy. But we also know that there are certain entities and resources in the economy that are inherently limited: the amount of land, or water, for example. Even to expect the production of food to grow at the same exponential rate year after year is patently impossible and unrealistic. This measn that in order to remain a responsibly viable participant in the economy, ( that is, for larger entities, to be acceptable investment vehicles on Wall Street) these sectors of the economy must raise their prices so as to ‘produce’ the expected growth rate, at least as much as is needed to cover the difference between the overall expected growth rate and the actual growth rate of their porduction. In other words, inflation. The expected , predicted inflation rate now becomes a factor in the interest rate expectation of our original $1M investor: the interest rate must rise to also cover inflation, otherwise such an investment would be less preferable that to spend the money on goods etc. at today’s prices. This means, that for an economy functioning according to these principles, a steady rise of inflation is a necessity. It is held in check only by the fact that there will be a number of ‘losers’ in the process, whose losses reduce the required rate of inflation. The regrettable fact of there having to be such losers is glossed over by the mantra that they ‘deserve’ this fate by being less industrious, or inventive, or sufficiently smart in marketing their services — all aspects that detract from the question of the true value of whatever they contribute. It is also demonstrably advantageous for the ‘winners’ or would-be-winners in this process to ever so subtly misprepresent the value of their ‘new, improved’ contributions and to persuade people that they realy really do need these things, and even to arrange legal and regulatory conditions inn favor of their products and services, by appropriately massaging the egos and pocketbooks of legislators.

The question — apart from those regarding fairness and justice and ethics, that may be dismissed with the old nugget of ‘buyer beware’ — is: why do serious economists and government officials incurring public debt in the expectation that future growth will pay for its expenditures, still continue to rely on the exponential growth expectation as a guide to policy? Why is it that even the highest experts profess to surprise as to that and how fast the collapse was happening — the prime example of a ‘black swan’ event that nobody expected?

Could it be that the answer may be found in the human tendency to consider only short term implications of policies and tactics? This is institutionalized in form of the common habit in the financial world, of evaluating economic performance (and stock market attractiveness, etc.) according to quarterly profit growth. What this does to the analyst (who ought to know better) is this:

Instead of the dizzying steep grade of an extended exponential growth curve after a number of time periods, it allows the analyst to ‘start from zero’ again each period: the value of the end of the previous period is moved to the point of origin in the new tracking chart, and the steepness of the curve looks perfectly benign: 5%, 6%, etc.: all close enough to the ‘normal’ horizontal steady state to allay any acrophobic fears. It hides the fact that one is already high up on the curve, leaning over precipitously from the vertical so as to perceive the current point as the horizontal starting point. This delusion can go on only for so long, of course: sooner or later, the perspective so gained will have to reveal itself as unsustainable, because leaning over so far from the safe true horizontal as to cause the viewer to lose all sense of what’s up or down, and lose balance. Followed by a sobering fall.

It would be satisfactory to be able to identify some culprits or villains in these machinations, to be appropriately pilloried in the public devastated marketplace. This would be missing the point, however. All indications are that just about everybody honestly believed in the appropriateness, validity and fairness of adopting this perspective of continued growth, of interest and profit, — from the lowliest holder of a measly savings account to the top managers on global banks, and government officials at all levels. An indication of this universally shared misconception is the current rash of government bailouts of the largest investment and insurance entities, which must be realistically seen as just moving the economy back to some previous point on the curve, one that wasn’t as close to the tipping point as to scare people from more and more lending and borrowing. It is a strategy that, given the mechanics of exponential growth, must inevitably, soone or later result in the same catastrophic collapse. Mitigating the progress toward such collapse by reining in certain accelerating follies — such as the selling and reselling of loans many times over (each time expecting more interest and profit, to the point where the combined earning expectation vastly exceeded even modest predictions of the actual growth of the real economy that ultimmately would have to pay for all those profits) will only slow down the inevitable repetition of the crisis.

Does the only realistic hope, as this little thought experiment suggests, for salvaging the economy lie in a fundamental reorientation of the basic expectations relative to growth in the economic system? The mantra of growth at any cost must give way to a more meaningful measure of the viability of economic policies. And the real basis for the widespread pessimism with respect to such a reorientation is that as far as can be seen in the public discourse, nobody — in the financing system or in government, nor in the media — is even raising this crucial question.