Pollution, Human Capital, and Growth Cycles

To investigate the growth effect of pollution, we apply an optimal growth framework in which human and physical capital accumulation are two growth engines. Pollution is emitted from the stock of physical capital and has a negative impact on the formation of human capital. In this simple growth model, sustainable endogenous growth never occurs and a unique steady state emerges because of the negative impact of pollution. The model shows that (i) if the extent of the external effect of pollution is relatively small, the steady state is stable and the economy starting in the neighborhood of the steady state converges to it, (ii) if the extent of the external effect is relatively large, the steady state is unstable and the economy diverges away from it, and (iii) a Hopf bifurcation occurs at a certain intermediate extent of the external effect. The numerical analysis illustrates the global dynamic behavior in which the economy exhibits a closed orbit as sufficient time passes if the steady state is unstable.