Dynamic Optimal Control of a Monopolist's Investment in Pollution Abatement and Optimal Design of the Environmental Taxation under Knowledge Accumulation
Due to the dual externalities of pollution control technology innovation,external environmental regulation is essential.Environmental regulations influence the attitude of enterprises towards the natural environment through coercion and inducement.By incentivizing enterprises to improve their innovation capabilities,offsetting the costs brought about by environmental protection,and enhancing their profitability in the market,domestic enterprises can gain a competitive advantage in the international market,thereby improving industrial productivity.Numerous studies have shown that under the influence of environmental regulations,enterprises will choose different invest-ment decisions for pollution control,confirming the importance of the selection and design of environmental regula-tions.However,existing research has overlooked the issue of knowledge accumulation in the investment process of pollution control technology.Knowledge accumulation is caused by"learning by doing"in the investment process of pollution control technology.Knowledge accumulation is a by-product of the investment process,and"learning by doing"is an important way to improve production efficiency and achieve endogenous economic growth.This article applies the theory and methods of optimal dynamic control,based on the research problem of optimal investment in enterprise pollution control technology and optimal pollution tax rate design by social planners,to establish an optimal control model for monopolistic enterprises that consider knowledge accumulation in producing a single product.Compared with existing research,the problem of knowledge accumulation is considered in the investment process of enterprise pollution control technology.Based on the practical back-ground,enterprises will transfer pollution taxes to consumers,and the consumer demand function is modified with pollution taxes.Then,the optimal investment and output level of enterprise pollution control technology under the conditions of maximizing enterprise profits and social welfare are analyzed,and the optimal pollution tax rate is calculated.Finally,the evolution path of the optimal solution is numerically simulated and analyzed.Research has shown that:(1)Under the conditions of maximizing enterprise profits and social welfare,there exists a unique saddle point equilibrium in the control system.(2)Under the conditions of decision-making by oligopolistic enterprises and social planners,there exists a unique optimal pollution tax rate when the two control systems are balanced.(3)Under the condition of maximizing social welfare,the pollution control investment and production level of enterprises are higher than those under the condition of maximizing profits.(4)The cumula-tive pollution under the condition of maximizing social welfare and the pollution emissions per unit product of enterprises(the pollution control technology of enterprises)are lower than the cumulative pollution emissions per unit product of enterprises under the condition of maximizing profits.The main characteristics of this article are:(1)Assuming that the government levies a pollution discharge tax on the pollution control technology of enterprises.(2)Considering the knowledge accumulation problem in the investment process of pollution control technology.(3)Considering the issue of transferring pollution taxes and fees from enterprises to consumers,the consumer demand function is modified using pollution taxes.This study enriches the research theory on the innovative behavior of pollution control technology in enterprises consid-ering knowledge accumulation,and has practical guidance significance for the innovation management of enter-prises with knowledge accumulation characteristics.The steady-state equilibrium analysis of the optimal invest-ment in pollution control technology and the optimal pollution tax rate designed by social planners can help enter-prises formulate more scientific market competition strategies.Based on the existence of a unique optimal pollu-tion tax rate when the control system is balanced,effective enterprise investment decisions and optimal pollution tax rates can be formulated,thereby improving social welfare levels.This article mainly studies the investment problem of pollution control technology.In this article,we assume that the marginal production cost of enterprises is constant.Possible future research directions include:(1)Considering the dynamic optimal control problem of pollution control investment for monopolistic enterprises under the condi-tion of process innovation(reducing marginal production costs).(2)Considering the dynamic optimal control problem of pollution control investment for monopolistic enterprises under the condition of cross period emission trading(emission rights bank).
knowledge accumulationpollution control technologyoptimal investmentpollution tax
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