In fact, the opposite is true, Tainter said. "Possibilities range from little effect to a mild recession to a major depression to a collapse."

Looking at a previous society, the Roman Empire, he said as agricultural output slowly declined and population increased, per-capita energy availability dropped. The Romans "solved" this problem by conquering their neighbors to appropriate their energy surpluses (metals, grain, slaves, etc.).

However, as the empire grew, the cost of maintaining communications, garrisons and civil government grew with it. Eventually, this cost grew so great that any new challenges such as invasions and crop failures could not be solved by the acquisition of more territory. At that point, the empire fragmented into smaller units.

"When some new input to an economic system is brought on line, whether a technical innovation or an energy subsidy, it will often have the potential at least temporarily to raise marginal productivity," he said. "Eventually, barring continual conquest of your neighbors — which is always subject to diminishing returns — innovation that increases productivity is in the long run the only way out of the dismal science dilemma of declining marginal returns on added investments in complexity."

Tainter avoids conclusions and recommendations, but he believes in replacing the one thing that has allowed the United States to boom — oil — with the one thing that will forestall its collapse — renewable energy.

The complexity/collapse model also would explain the increase in the complexity of the American financial markets, their collapse, and the fragmenting of the banks and the auto industry.

E-MAIL: jthalman@desnews.com