The elasticity of substitution and the way of nesting CES production function with emphasis on energy input

This article proposes the way to choose the optimal bundle among inputs by combing the translog cost function and Constant-Elasticity-of-Substitution (CES) function. The translog cost function is applied to select the most appropriate nested structure by estimating elasticities of substitution between inputs. And then the CES function is used to get the elasiticities among inputs. It introduces the empirical simulation model for the Chinese industrial sectors focusing on how energy combines with non-energy inputs. Derived from the estimated elasticities of substitution, the results present that (capital-labor)-energy is the most appropriate way. And the two-level elasticity of (capital-labor) and energy is 0.9432.