Converting primary resources into useful energy: The pollution ceiling efficiency paradox

We study an economy producing energy services from a polluting fossil fuel and a carbon free renewable resource under a constraint on the admissible atmospheric carbon concentration, equivalently under a constraint on the admissible temperature. The transformation rates of natural primary resources energy into useful energy are costly endogenous variables. Choosing higher efficiency rates requires to bring into operation more sophisticated energy transformation devices, that is more costly ones. We show that, independently of technical progress, along a perfect foresight equilibrium path which is Pareto optimal, the transformation rate of any exploited resource should increase throughout time, excepted within the period during which the carbon constraint is binding, a phenomenon we call the ’ceiling paradox’