The natural sciences have established a general scaling law that relates metabolism and body size of animals. Recently this association - known as Kleiber's law - has received deep theoretical foundation by network theory and has been fruitfully applied to explain various biological phenomena, in particular ontogenetic growth. Here we derive a similar power law for economic metabolism (energy consumption per capita) and economic size (capital per capita). Invoking the power law we provide a metabolic-energetic founded law of motion for capital per capita. Using data for the U.S. states we test the resulting structural model and find evidence in favor of a scaling parameter, between energy and capital per capita, of about 2/3.