Thermodynamic constraints and the use of energy-dependent CES-production functions A cautionary comment

Particularly in the context of energy and climate policy models, CES production functions are used as a basis for deriving sustainable development paths. Of crucial importance here is the reduction of the energy intensity of production processes with the help of substitution processes away from energy to other inputs. The modeling of these substitution processes must, of course, comply with the laws of physics. Therefore, the CES function is often used because it is supposed to satisfy thermodynamic laws. This is assumed to be met if the elasticity of substitution between energy inputs and other non-energy inputs is less than 1. The following commentary is meant to show that this specification is only a necessary pre-condition for fulfilling the thermodynamic laws. The permissible values of the other parameters of the CES- production function are subject to additional restrictions. Using an empirical example, the thermodynamic parameter restriction space for an aggregated production function of the English economy are presented. The consideration of thermodynamic limits can also be included directly into the design of production functions. An analysis of the linear-exponential production function derives various characteristics relevant to policy analysis. It is a priori not possible to decide which approach is preferable. Future empirical studies can help to clarify this question.