Theoretical relationship between energy consumption and economic output

In this study, the theoretical relations among the growth rate of energy intensity, energy consumption, and economic output are inferred and named as the "3GR" model. In some economic entities, the growth rate of energy consumption is equal to the corresponding growth rate of energy intensity and economic output, and their product. Based on the "3GR" model, some conclusions could be obtained: (1) for the expected goal of growth rate of economic output and energy intensity of some economic entities, there is a linear relationship among the growth rate of energy intensity or economic output; (2) for the expected goal of growth rate of energy consumption of some economic entities, there is an inverse relationship between the growth rate of economic output and energy intensity; (3) energy consumption of an economy is equal to the product of the initial level of energy consumption, product of "one plus growth rate of economic output", and product of "one plus growth rate of energy intensity".