Consider the following two non-linear coupled differential equations(*)

that describes the spread of malaria.

Rate of increase of infected humans = Rate of new infections of humans

which depends on the number of infected mosquitoes – Rate of recoveries or deaths of humans

Rate of increase of infected mosquitoes = Rate of new infections

of mosquitoes which depends on the number infected humans – Rate of recoveries or deaths of mosquitoes

You will note that the two equations are entirely symmetric. If these two equations describe the entire world of possibilities (e.g. other animals can not carry malaria), we can make the following interesting statements: Humans infect mosquitoes and mosquitoes infect humans; malaria does not exist independently of two hosts; the way to eradicate malaria in mosquitoes is to kill all humans (or vice versa) — both sides are working hard on this.

(*) In terms of general useful mathematics in order of importance, it is addition, subtraction, multiplication, division, followed by coupled differential equations …

A market economy divided into producers and consumers is also a coupled linear system. Producers can not exist without consumers and vice versa. Hence, this is a symbiotic relationship unlike the malaria relationship where one party would be happy to get rid of the other.

Symbiosis is why capitalism works so exceedingly well(*). It is the most efficient way of matching demand with supply. However, demand does not always match supply. When this happens, it is called a recession. Keynesians believe that this is due to lack of demand, whereas Austrians believe is it due to over supply. They are both right or wrong as it may be, because they are missing the point.

Once again, in terms of general useful mathematics in order of importance, it is addition, subtraction, multiplication, division, followed by coupled differential equations!

(*) Of course the problem with this model is that there is a third factor called nature. Economists generally feel free to ignore this component which acts as a limiting factor using the hypothesis of substitution (e.g. if fish become too expensive, people will eat soylent green) and innovation (based on the hypothesis that scientists can make miracles happen if you give them enough incentives). These hypotheses are false which is why you see increasing environmental resistance, that is, growth decreases and competition increases.

Originally posted 2009-04-24 04:53:22.