Pollution, Human Capital, and Growth Cycles

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