Chaos in Economies
The applet's first equation x = cx(1 - x) is known as the Standard Logistics Difference Equation. It models, among other things, the way in which the population of a product grows within its potential market. In this context, the constant c is an amalgam of two factors. The first represents productivity - the number of product units which can be realised by one unit of human effort. This is amplified by production technology. The second represents the number of product units which can be sold into the market by one unit of human effort. This is amplified by communications technology. However, it is diminished by competition. The population of a product within a market is thus held in balance by a mechanism similar to that which holds life-form populations in balance with their environments.
Nature yields bounteously the needs of life in return for human labour. In the absence of war, oppression and exploitation all could therefore live in comfort and well-being. The value of c provided by nature (let us suppose it's around 1.3 or 1.4) is more than adequate for the needs of mankind. It creates an economy with a smooth productivity curve. But the human life-form then started to develop technology. First tools then the wheel, then machines, then automation, computers, communications and mass-media.
The smooth sigmoid reached to ever-greater heights. Once c passed 2.34 the curve started to 'ring' as it reached the top. That is, production over-shot and then fell back to its stable rate. The ringing became more pronounced until at c = 2.9 it gave birth to an almost steady (albeit shallow) rhythm of boom/bust which Western economies have gradually seen emerge from the end of World War II.
Nevertheless, as the applet's Time Graph shows, the ratio between boom and bust gradually fades away (proving every time of course that government economic policy is working!?). But technology keeps on advancing, driving productivity and marketing reach ever higher and further.
The result is that the ratio between boom and bust gets larger but now ceases to fade away. As c increases further, so does the boom-bust ratio until eventually its rhythm becomes more complex. We will probably leave the 20th century with many national economies booming and busting to this mesmerising 'waltz rhythm'. But of the future? What does the new millennium hold in store for national economies? In a word: chaos. Technical progress will not stop. On the contrary, its rate of progress will accelerate. The boom-bust cycle will probably soon be following the profile of c = 3.68 which is what was being traced out by the applet when you first saw it.
Chaotic economic cycles are unlikely to hurt national economies or these who control them. However, they will ruin and destroy the economic lives of ordinary people. That is, unless the rules of engagement between the individual and the body-corporate are substantially re-engineered.
The applet depicts the growth in population of a single product sold by a single supplier in a simple market. Although in reality a national economy is far more complicated, its behaviour boils down to what bears an uncanny resemblance to what the applet displays. Chaos is scaleable. I goes into this subject in far greater depth in my book The Lost Inheritance.
© November 1997 Robert John Morton