Regulation in a Mean-Field Investment Game with Climate Damage

We study the problem of optimal investment in brown (carbon-intensive) production amid climate change and the impact of rising global temperatures. Our approach is based on a mean-field model of firms that produce goods whose productivity is adversely affected by temperature-related damages, which are in turn linked to the global stock of greenhouse gas (GHG) emissions. Each firm controls its investment rate in view of increasing its capital stock, which evolves stochastically due to idiosyncratic Gaussian shocks and is subject to exponential depreciation in the absence of investment. Firms aim to maximize their expected discounted profits, net of investment costs, by choosing investment strategies that respond to the level of aggregate GHG emissions and their adverse impact. We constructively establish the existence and uniqueness of a mean-field equilibrium, by characterising it as the unique solution to a bespoke three-dimensional system of forward-backward ordinary differential equations. This characterisation enables the implementation of the model to support numerical analyses for exploring the implications of climate damage on equilibrium outcomes and policy design in terms of taxes and phase-out dates for brown production. We also conduct a sensitivity analysis showing that the functional form of climate damage has relatively little influence on the optimal tax on brown production, whereas the temperature decay rate in the absence of emissions plays a far more significant role.