On the optimum timing of the global carbon-transition under conditions of: Heterogeneous parameters and heterogeneous donors

An optimal growth model is constructed in a context of irreversible investment in different concurrent production technologies in order to study the optimum timing of the various stages that can be identified in the transition from a carbon-based economy to a carbon-free economy. Such a transition is necessary to avoid runaway global warming. The model is based on the AK-model by Rebelo (1991) and uses multi-stage optimal control methods to illustrate the importance of the notion of capital goods as a produced means of production and as the physical carriers/manifestations of different technologies for the timing and intensity of the use of carbon-based and carbon-free technologies during a just-in-time transition. The transition needs to happen within a given cumulative emissions constraint in order to avoid runaway global warming and corresponding runaway welfare losses. It is shown that the expectation of extreme weather-related damages in such a setting may induce a welfare maximizing central planner to step-up carbon-based production rather than reducing such activity, for similar reasons as the green paradox arises. A further paradoxical result is that increases in the productivity of carbon-free technologies relative to carbon-based technologies do not necessarily imply an earlier phasing in of those carbon-free technologies, but rather allow for a more gradual (and more prolonged) transition towards a carbon-free future. Finally, it is shown that having a productive carbon-based production system facilitates the transition towards a carbon-free system, i.e. investment in carbon intensive technologies may be an effective instrument in securing a carbon-free future.