A Note on Pollution Inertia and Endogenous Cycles in Ramsey Economies

The literature has pointed out that a limit cycle (Hopf bifurcation) can emerge near the steady state of a competitive Ramsey economy when a pollution externality sufficiently increases the marginal utility of consumption (the compensation effect). The literature has also emphasized that, when pollution originates from production, a necessary condition for a limit cycle to occur is that pollution behaves as a stock variable with strong inertia (i.e., low natural absorption). Interestingly, this condition is not highlighted in the literature when pollution arises from consumption. The objective of the present paper is to clarify this point: Is strong pollution inertia also necessary for a Hopf bifurcation to occur when pollution stems from consumption? To answer this question, we develop a competitive Ramsey economy in which a pollution externality arises from both production and consumption. By comparing the conditions under which a Hopf bifurcation occurs at the steady state when pollution comes solely from consumption and when it comes solely from production, we demonstrate that no restriction on pollution inertia is required when pollution arises exclusively from consumption. To explain this result, we emphasize the role of decreasing marginal productivity.