A stochastic dynamic programming model for the optimal policy mix of the carbon tax and decarbonization subsidy

Carbon tax and decarbonization subsidy are an effective policy mix in reducing carbon emissions. However, there is a research gap between the deterministic and static analysis related to carbon reduction policy instruments and the dynamic green transition influenced by stochastic factors. This research investigates the optimal dynamic carbon reduction strategies that develop green technologies, increase abatement inputs, and reduce carbon emissions by applying the stochastic optimal control theory. Firms that are incentivized by decarbonization subsidies and regulated by carbon tax choose optimal closed-loop control strategies of abatement inputs to achieve profit-maximizing objectives with carbon reduction constraints. The explicit solutions of the optimal carbon tax and decarbonization subsidy are provided. The simulation results illustrate that the optimal policy mix is feasible in the effective period when the carbon emission decreases significantly, which indicates that the abatement policy mix can effectively promote carbon reduction. Our results reveal that the dynamic optimal policy mix is conducive to achieving carbon abatement goals with capital uncertainty. The government should implement a dynamic carbon tax and decarbonization subsidy policy mix simultaneously associated with optimal closed-loop carbon reduction strategies. Firms with asymmetric decarbonization efficiency can transfer progressively into a cleaner productive pattern.