Economies can definitely grow with decreasing energy usage, but appropriate measures need to be taken. The United States will be concentrated on in this entry; however, the principles apply to the rest of the world.
For one, in the commercial and residential sector, which make up 39 percent of total United States energy consumption, HVAC and lighting are the majority energy functions. Therefore, common sense would say that if the efficiency of HVAC systems and lighting is drastically improved, the total energy usage would decline substantially while economies increase. Making these systems very efficient is possible, but as of now requires a financial compromise. Currently, HVAC systems are more or less designed strictly to function, not worrying about the efficiency because not many businesses are willing to pay extra for higher efficiency systems. It is this financial barrier which will be hard to overcome. In terms of lighting, the switch from incandescent bulbs to florescent could make a substantial difference.
Also, the transportation sector guzzles up 29 percent of America's total energy consumption, predominantly driven by gasoline. As cars that run on batteries gain popularity and get integrated more and more in the general public, the gasoline numbers will drop severely. This would decrease energy usage and grow the renewable energy economy.