The relationship I’ve identified between consumption and population is analogous to the relationship between power and current in a direct current electrical circuit. In the analogy, per-capita consumption corresponds to electrical potential (voltage) and the multiplier of population to get per-capita consumption corresponds to resistance (as in Ohm’s Law).
My mathematical modeling suggests that the overall “resistance” is unchanging in the world “circuit” and that “voltage” is the primary variable that affects “current.” The voltage varies exponentially with changes in the amount of available “energy” (resources), a variation that is primarily offset by control of the “voltage source” (resource extraction and distribution technology).
Because in a closed system “energy” (non-renewable resources) cannot increase, “voltage” must inevitably decrease – and with it, “current.” The world, in a sense, is like a light bulb and a fixed number of batteries; first one battery is attached to the light bulb, then another (in “series” with the first), and then another, until all the batteries are connected. Just as a battery has internal resistance that increases over time, causing the voltage across the battery to drop, the resources consumed by humanity become waste which inhibits further consumption, causing per-capita consumption (and population) to decrease.
Just as the interesting aspects of an electronic circuit are the variations in energy over time (“signals”) rather than the net amount of energy used, the world’s economy is primarily concerned with more than just the extraction of resources. Using the example of batteries and a light bulb, the point of the circuit is to create light, not to drain the battery.
Economic theory assumes that natural resources are inexhaustible. When one type of resource is running low, people will find and substitute another kind of resource for it. This same logic applies to the configurations of those resources -- products and services. The mechanism for substitution is the law of supply and demand, which in the electrical model corresponds to the truism that the amount of energy consumed by a load (such as a light bulb) can not exceed the amount of energy available in a source (such as a battery). To maintain constant power to the load (demand), the depleted energy in the battery must be replaced (the supply must remain constant, typically by switching to another battery).
The electrical term “load” can refer to any combination of devices, just as its economic analog can be a combination of factories, homes, and cars (among many mechanisms that people use to convert resources into artifacts and waste). Any electronic device can be modeled as a group of “impedances” -- resistances (which use up energy) and reactances (which modify how energy changes over time). The time variations in per-capita consumption (voltage) may therefore be explained as the result of a complex interaction between economic “reactances” within our “economic circuit,” as well as a set of impedances in the environment that permit resources of different types to pass into and out of the circuit.
© Copyright 2008 Bradley Jarvis. All rights reserved.