Production and Carbon Emission Permits Trading Dynamic Optimization in the Duopoly Market

Within the constraints of carbon emissions, the question of how to optimize the production, the trading carbon emissions and the emissions of purification to maximize the firm's profit is investigated with the dynamic Cournot model. Besides, the corresponding solutions in the equilibrium state and in each period are obtained. The strategy of carbon reduction and the impacts of the regarding policy of government and the price of carbon emission permits on the firm's decision-making as well as the operating mechanism of the trading carbon permits in the competitive market are present. We find that there exists the equilibrium state in the dynamic Cournot market within the constraints of carbon emissions and that the maximum profit is obtained in a lower rate of carbon reduction while excessively pursuing a higher rate will result in a lower profit. The firm should purchase excess carbon emission permits at a lower price in good time and sell the surplus at a higher price to increase its profit and reduce its cost. In addition, the firm's profit increases in the allocation coefficient of carbon emissions permits.