Carbon Neutrality and Net-Zero Regulation

We analyze the impact of carbon dioxide regulation on a system of polluting, heterogeneous companies. We consider two compliance frameworks: one based on an emission trading system (ETS) mechanism and the other relying only on abatement efforts. The shocks in the economy are spanned by a multivariate Brownian motion, and the companies' emissions are modeled as general diffusions. Firms must match their projected emission imbalance with their reduction effort at the compliance date in both frameworks. Under the ETS program, to do so firms can both abate and trade carbon permits in the ETS permits exchange. Existence and uniqueness of the optimal abatement and trade, together with the equilibrium carbon price, are proven under mild necessary and sufficient conditions. The optimizers and the carbon price are explicit, and their analytic expressions provide an instance of classic economic principles. Numerical examples illustrate the flexibility of the model in the study of the effect of significant allocation policies. Under the net-zero framework, firms can only rely on abatement, which is also provided in closed-form.