Optimal Growth with Polluting Waste and Recycling

Abstract

We study an optimal AK-like model of capital accumulation and growth in the presence of a negative environmental externality in the tradition of Stokey (Int Econ Rev 39(1):1–31, 1998). Both production and consumption activities generate polluting waste. The economy exerts a recycling effort to reduce the stock of waste. Recycling also generates income, which is fully devoted to capital accumulation. The whole problem amounts to choosing the optimal control paths for consumption and recycling to maximize a social welfare function that notably includes the waste stock and disutility from the recycling effort. We provide a mathematical analysis of both the asymptotic behavior of the optimal trajectories and the shape of transition dynamics. Numerical exercises are performed to illustrate the analysis and to highlight some of the economic implications of the model. The results suggest that when recycling acts as an income generator, (1) a contraction of both the consumption and capital stock is observed in the long run after an expansion phase; (2) whether polluting waste is predominantly due to production or consumption, greater consumption and lower capital stock are obtained in the long run compared with the situation when recycling does not create additional income; (3) greater recycling effort and lower stock of waste are resulted in the long run.