On environmental Kuznets curves arising from stock externalities

We develop a stock externality model in an optimal growth framework and examine the relationship between economic growth and the environment. We find that as incomes rise over the growth path, both the marginal benefits of pollution control and the marginal costs of pollution control rise. If at a given income level the marginal benefits rise more than the marginal costs, the emissions-income relationship has a negative slope at that income level and vice versa. We are thus able to generate examples of emissions-income relationships of varying shapes by varying pollution specific parameters which determine marginal costs and benefits, such as the convexity of the cost function, the rate of decay of the stock of pollution, and the share of consumption in the composite good. An inverted U-shape relationship (an "environmental Kuznets curve") requires only minimal assumptions. A convex cost function and that environmental quality a normal good imply an inverted U-shape relationship for an open set of parameters. We also examine how environment-income relationship varies according to what measure is used for the environment (emissions, stock of pollution, or emissions control).