Necessary and sufficient conditions for an environmental Kuznets curve with some illustrative examples

We propose a set of necessary and sufficient conditions for the environmental Kuznets curve (EKC) phenomenon in a general model that permits non-smooth preferences and feasible sets and corner solutions for welfare maximisation. These conditions pertain to the relationship between the sets of preference and technology-based shadow prices at an outcome reached by an emission-held-fixed-effect (EHFE), where the emission policy does not adjust to an increase in the economic resource base and only consumption adjusts. In particular, an EKC arises if and only if there exists a threshold level of resource such that, at any level of resource below (respectively, above) the threshold, the outcome reached by the EHFE is one where the set of preference-based shadow prices lies completely below (respectively, above) the set of technological shadow prices. This characterisation is employed to study and construct examples of preference-technology combinations that can potentially result in an EKC, when emission is a consumption externality. In particular, the cases of homothetic economies, increasing returns to abatement, emission as a normal good, and EKC in a model with economic growth are studied.