The Theory of By-Production of Emissions and Capital-Constrained Non-Cooperative Nash Outcomes of a Global Economy

The reduced form approaches that are commonly adopted in the literature to model emission-generating technologies (EGTs) do not distinguish between emission-causing and non-emission causing goods in production. We provide a new set of axioms to describe EGTs. Technologies that satisfy these axioms are called by-production technologies (BPTs). A distance function representation of BPTs is derived and it is shown that a BPT can be decomposed into a standard neo-classical intended-production technology and nature's emission-generation set (the relationship in nature between emissions and emission-causing goods). As an illustrative application of the BP approach, we study cross-country differences in emission levels due to cross-country di erences in capital endowments at a noncooperative Nash equilibrium, where emissions impose both local and global externalities. The change in emission levels as we move from capital-poor to capital-rich countries is decomposed into income and substitution e ects. The latter are a result of changes in the trade-off between intended-production and emission-generation, which is attributed to diminishing returns to emission-causing inputs or cleaning-up activities, while the nature of the former is governed by the assumption that emission is an inferior good. The implications of increasing returns to capital, substitutability or complementarity between capital and emission-causing inputs such as fuels, extraction costs of fuels, and inter-fuel substitution in production are studied and a set of conditions that result in an environmental Kuznets curve is derived.