Dynamic modeling of environmental subsidies

In this research, the intertemporal optimal management of subsidies offered by the environmental regulator and the dynamic conflict between two groups of economic agents involved in environmental quality are discussed. First the environmental model is examined in its optimal control management form with two state variables. The analysis of the improved model, inspecting the social planner's decision (policy) variable, the variable which influences not only environmental quality but the national budget stock, reveals that is dependent on the growth of the national budget stock. A negative growth rate leads to the long run saddle point equilibrium, while an incremental growth rate, but less than the model's discount rate, leads to an interesting complicated limit cycle equilibrium, for which under certain parameter values the orbit's phase portrait can be drawn. For the dynamic game model between the social planner and natural resource exploiters, the equilibrium conditions are examined. It is rather a richer than the point equilibrium for which the cyclical strategies have great importance. Therefore, the conditions for that rich equilibrium are found. As a continuation, the paper concludes that the equilibrium condition is that the players' discount rates are both greater than the national budget interest rate. Finally, the certain values of the equilibrium strategies and national budget stock are provided.