  Integrated Assessment Models (IAMs) are mainstay tools for assessing the
long-term interactions between climate and the economy and for deriving optimal
policy responses in the form of carbon prices. IAMs have been criticized for
controversial discount rate assumptions, arbitrary climate damage functions,
and the inadequate handling of potentially catastrophic climate outcomes. We
review these external shortcomings for prominent IAMs before turning our focus
on an internal modeling fallacy: the widespread misapplication of the Constant
Elasticity of Substitution (CES) function for the technology transitions
modeled by IAMs. Applying CES, an economic modeling approach, on technical
factor inputs over long periods where an entire factor (the greenhouse gas
emitting fossil fuel inputs) must be substituted creates artifacts that fail to
match the S-curve patterns observed historically. A policy critical result, the
monotonically increasing cost of carbon, a universal feature of IAMs, is called
into question by showing that it is unrealistic as it is an artifact of the
modeling approach and not representative of the technical substitutability
potential nor of the expected cost of the technologies. We demonstrate this
first through a simple but representative example of CES application on the
energy system and with a sectoral discussion of the actual fossil substitution
costs. We propose a methodological modification using dynamically varying
elasticity of substitution as a plausible alternative to model the energy
transition in line with the historical observations and technical realities
within the existing modeling systems. Nevertheless, a fundamentally different
approach based on physical energy principles would be more appropriate.
