The Frontiers of Exact Science

Disequilibrium Economics Revisited, insights after 30 years of journalism and writing on economics and politics.
Dealing with King Chaos, part 3.



By Frank van Empel

In 1980 I finished my studies at the University of Tilburg in the Netherlands with a thesis about disequilibrium economics. I tried to visualise the process of adaptation in a nonlinear model, by distinguishing three levels in economical processes:
1. the potential- or ex-ante level of intentions and expectations;
2. the effective level, an inbetween level of adapted intentions and expectations;
3. the realised- or ex-post level.

Conventional economists usually take only level 3 into account. They postulate that markets are cleared in no time, faster than sunshine. Moreover the economic players (producers, consumers, middlemen and the like) in scientific models are supposed to have all information about what’s going on in the heads, bodies and souls of consumers, producers, investors, et cetera. They have a perfect view on what is coming. The future holds no surprises or no adventures.
All of this has little to do with reality. In the real world, people go to a market with particular intentions and expectations. Once arrived they usually confront a total different situation. They have to adapt their intentions and accept a compromise, to make a deal. The same kind of adaptation process can be noticed on the demand- as well as on the supply-side of markets in general and the labour market specifically. See box (just for mathematic freaks and whizz people).



The hyperbolic tangent (see box above) is used for modeling complex nonlinear dynamic processes. The S-curve represents a tension. It’s a weight that goes from +1 to -1. At the far end it determines if a variable is positive or negative. It’s something like laughing versus crying or construction versus destruction. If you insert such a tension in just one equation of a traditional linear equilibrium model, it immediately becomes nonlinear. By that we mean, that the outcomes are completely unpredictable.

Simply stated, something is linear if its output is proportional to its input. If, when you're reading late at night, you want twice as much illumination (output) to see the book, then you double the number of light bulbs (input) by bringing over one more similar lamp. Something is nonlinear if its output is not directly proportional to the input. Nonlinear problems are of interest to engineers, physicists and mathematicians because most physical systems are inherently nonlinear in nature.

Nonlinear equations are difficult to solve though. They give rise to interesting phenomena such as chaos. The weather is famously chaotic, where simple changes in one part of the system produce complex effects throughout. Nonlinear systems are irregular, unstable, even chaotic. That leads almost always to unexpected developments. Life is nonlinear. If you’re in your twenties, you simply don’t know where and with who you’ll be when you’re fifty-plus. The human body loves nonlinearity too. The time between two heartbeats differs continuously. Should the time between two beats be the same, better get yourself to the hospital: A heart attack is in the making.

Another nonlinear body process is caused by the army of the Emperor of anomalies - cancer – inside, a chaotic, unpredictable process too. According to the mainstream of scientists nature is actually in a continuing state of disturbance and fluctuation, like the lives of most people, and the economy, yet most economists still don’t know how to handle nonlinearity in their models, like my own professor in Tilburg 30 years ago.

In his book Power and Chaos, published in 1980, prof. dr. D.B.J. Schouten acknowledged that an ‘endogenising of the elasticity coefficients’, which mirrors the amount of wage- and price-competition, is very complex. Schouten: ‘By doing this, our models are no longer linear, which in an inconceivable way raises complexity. That brings us to the frontiers of the exact economy practice.’

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