Public debt, pollution and environmental taxes: Nash and Stackelberg equilibria

Public debt accumulation and pollution result to disutility while time path must be sustainable. Policy weapons available to the government with regard to public debt is the generation of primary surpluses to sustain public debt while concerning pollution environmental taxation is expected to reduce emissions. In this paper, we address these factors in a simple dynamic game in order to find ways at which the notions of public debt, pollution, and taxation are interrelated. The starting point of the model is the identity of current account as the equation of motion of public debt, while public debt is considering as a stock and the stress of the regulator is to raise the nation’s primary surplus. Nash and Stackelberg differential game solutions are used to explore the strategic interactions. In the Nash equilibrium establishment of cyclical strategies, during the game between the polluters in one hand and the government on the other, requires that the discount rate of the polluters must be greater than government’s discount rate. That is the polluters must be more impatient than the government. In the case of hierarchical setting, the analytical expressions of the strategic variables and the steady state value of public debt stock are provided. Furthermore, we found the analytical expressions of the value functions, making, therefore, the policy implications an easy task. Finally, we found the conditions under which the conflict is more intensive, in the two cases of equilibrium, according to the shadow price of the environmental damages.