Complementarity between energy and physical capital in a simple model of economic growth

Energy is one of the most important factors of growth, needed to power physical capital. This implies complementarity between these two factors, but in most theoretical papers, substitutability is assumed. In this paper, the main question is if complementarity between energy and physical capital hampers balanced growth or not. In order to answer this question, we consider the simple economic growth model with two sectors – output production and energy production – where energy is complementary to physical capital. Two forms of capital – physical and human – are distributed in this model between two sectors to maximise output. We consider the equilibrium state of this model, analyse comparative statics and derive necessary conditions for balanced growth. We also analyse some of the effects of technological progress. The analysis brings us to the conclusion that, in general, it leads to an increase in output, but that changes in technology of production have an ambiguous influence on output. We also derive explicit paths of growth for all macroeconomic variables. We find that, in general, if the obtained conditions are fulfilled then complementarity is not an obstacle to economic growth, subject to our assumptions which are quite standard in this kind of research.