The optimal decision rule of environmental regulation:an analysis of the cement industry

Abstract

The cement industry, despite its strong profitability, will face numerous challenges that are posed by the environmental and the sustainable development issues. The efficiency of environmental regulation tools is critical to the balance between ecological protection and economic development. This study builds a decision-making model to discuss the optimal intervention time scheme of environmental regulation by assuming that the variation of the basic assets of cement industry P(t) complies with the geometric Brownian motion with a jump, and that the incremental investment of compliance technology correlated with the respective unit of cement I(t) complies with the general geometric Brownian motion. Based on the Ito's lemma and the Bellman equation, the threshold of optimal decision-making is set, and the solution of threshold is clarified by using the Genetic algorithms. Besides, the sensitivity of the environmental regulation value yielded from the optimal decision-making scheme is presented numerically, as well as the threshold to the average incidence of shock events (λ). It is found that regions with higher average drift rates of basic assets (ap) normally have higher option values (equated with the environmental regulation value) at the threshold and show higher sensitivity to the shift of I(t). However, as λ increases to 0.8 continuously, the option value at the threshold and the sensitivity to the change of I(t) for the region with the lower ap can give a mutation and surpass some regions with higher ap. Furthermore, the cement price threshold P∗ turns out to be more sensitive to the change of λ for the region with low expected growth of the basic assets.