I want to teach an economic model to my students (Solow, 1956), using a simple "device", or physical system that I can take to my lectures. The system must have these three properties:
- There is one equilibrium, which is stable (e.g. the bottom inside an empty sphere).
- Variable (say, $x$) converges over time to it (e.g. a ball inside the sphere with friction on its inner surface will end up at the equilibrium).
- The speed of convergence is directly related to the distance between $x$ to that equilibrium. In other words, the speed decreases the closer $x$ is to the equilibrium. Unfortunately, the example of a ball inside a sphere does not fulfill this condition, because the ball oscilates around the equilibrium before reaching it.
No particular speed of convergence is needed (in fact, in the Solow model it takes infinite time to reach the equilibrium). The key is point 3, that the movement towards it depends directly on its distance.
I'm looking for a system as simple as the ball inside a sphere (which I could easily replicate with basic tools) but where the three conditions hold. I just can't think of anything like this.