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

Paper number: 14/07

Paper date: April 2014

Year: 2014

Paper Category: Discussion Paper

Authors

Sushama Murty

Abstract

We propose a set of necessary and suffcient 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 (defined using the Clarke's normal cone), 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 could be helpful in empirical testing for an EKC based on smooth-parametric or non-smooth non-parametric specifications of preferences and technology. We illustrate the characterisation with some examples that study homothetic economies, increasing returns to abatement, and emission as a normal good.

Keywords: environmental Kuznets curve, Clarke's tangent and normal cones, shadow prices, marginal willingness to pay, marginal abatement cost, welfare maximisation, homotheticity, normal good, increasing returns to abatement.

JEL classification codes: Q56, D62, C60

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