Transitional Dynamics to Optimal Sustainable Growth

This paper presents a simple model of optimal sustainable growth when the environmental stock enters the consumers' utility function and production depends on produced capital and on a flow of environmental services. Endogenous growth is obtained by making the productivity growth of the environmental services dependent on past capital accumulation. Both the effect of environmental preservation on the consumers' utility function and the effect of past capital accumulation on the productivity of environmental services are seen as externalities, which are internalized along an optimal growth path. Optimal growth is sustainable when the use of the environmental asset for production is equal to the regeneration capacity of the environment. The paper describes the features of the optimal sustainable balanced growth path: it is shown that the form of the utility function is crucial in obtaining it. The transitional dynamics to the balanced path are discussed showing that, under not unreasonable assumptions concerning the structure of preferences, the path leading to sustainable balanced growth may either be completely unstable or exhibit indeterminacy. This creates problems in defining an appropriate environmental policy, which is shown to require a combination of emission taxes and a subsidy to capital accumulation.