Energy, complexity and sustainable long-term growth

We introduce the concept of product complexity in an endogenous growth model with renewable energy and expanding product variety à la Grossman-Helpman (1991). We describe the complexity of a product as an increasing function of the variety of inputs it consists of. Considering that energy is necessary to all human activities (including research), we highlight what type of long run growth path is possible according to a) the potential of energy e ciency gains in the various human activities and b) the e↵ect of the product complexity on the energy intensiveness of its production process. In a finite world, a neoclassical growth path where economic growth can be both quantitative and non-quantitative (i.e. takes the form of an increase in the quantity of produced goods and in the product variety) is only possible if the potential of energy e ciency gains is unbounded in all human activities. If the energy intensiveness of the final production is bounded from below by a strictly positive constant, quantitative growth is not possible in the long run but non-quantitative growth may persist if (i) the impact of product complexity on the energy intensiveness of production is null or weak enough and (ii) the energy intensiveness of research activities tends to zero. If these conditions are not met, no form of long run growth is possible.