Capital accumulation subject to pollution control: A differential game with a feedback Nash equilibrium

Abstract

This paper studies a differential game of capital accumulation subject to pollution control. In the industrial sector, capital is used to produce output, which also creates pollution. Investment is chosen to maximise the present value of net profit. The policy maker (government) values output positively but pollution negatively. Its objective is to tax industrial output and spend the proceeds on pollution abatement, to maximise a social welfare function containing consumption and pollution as arguments. We solve the game for its feedback Nash equilibrium, and the resulting paths of capital and pollution accumulation are obtained explicitly. Finally, the feedback Nash and open-loop Nash solutions of the game are compared.