Running into a brick wall
I go past the current text, Sterman's Business Dynamics: Systems Thinking and Modeling for a Complex World with CD-ROM
, to include techniques from Richardson's and Pugh's Introduction to System Dynamics Modeling with Dynamo. They teach how to initialize a model in a state of constant growth, too. That's handy for certain types of models, and it teaches a useful principle.
To sketch out their example, imagine a population of anything that can be modeled with a simple birth and death process. Births per year is proportional to current population, and deaths per year are modeled as the population divided by the average lifespan. You can work out the equations or read chapter 4 of Richardson and Pugh to figure out how to initialize a model in a state of constant growth.
Imagine you've done that for an arbitrary growth rate. If there is a limit to growth, then, at some time, births per year will exactly equal deaths per year. At that point, the net growth is zero. If you think of world population and birth rates of 4% to 5% per year (the figures quoted in the book), and if you assume that the limit to growth occurs because of an increase in deaths per year, a bit of algebra lets you compute the average lifespan at that moment of equilibrium as 20-25 years. When students discover this, the classroom usually gets very quiet as the lesson sinks in.
As the lesson comes from the equations and their behavior, it would apply to any system that has birth and death processes, whether it's a population of living things or an economic system such as our economy of businesses.
That lesson is important and the idea, while from a simplified model, is solid. Still, it's nice to see whether a similar situation occurs in the real world. Miller-McCune just published "Foreclosure Forcefield" in their January/February 2012 issue, ponting to research by Garrett Glasgow at the University of California, Santa Barbara, indicating that cities with "slow-growth policies in place to prevent rampant residential construction" fared better in the foreclosure crisis than did those that were "aggressively pro-growth." That sounds a lot like the lesson from Richardson's and Pugh's example. You can see more in "Local Development Policies and the Foreclosure Crisis in California: Can Local Policies Hold Back National Tides?" by Glasgow, Lewis, and Neiman in Urban Affairs Review, 48(1), pp. 62-83.
Or, in simple English, if you think you might hit a brick wall, it's much better to be walking slowly than running as fast as you can.