Optimal timing of technology adoption under the changeable abatement coefficient through R&D

Abstract

Advanced abatement technology adoption has been attached a great importance upon the economic profit especially in the traditional energy intensive industries. In making the adoption decision, a firm has to evaluate the economic profit between the adoption of the advanced technologies and the traditional ones. Moreover, due to the learning-by-searching (LBS) effect, it is preferable to invest upon the installed abatement technology to further increasing the economic profit. Thus, to describe a comprehensive decision strategy, we proposed a hybrid model including output, R&D investment as well as the adoption time to be optimized at the same time. Regarding these as the decision variables, our formulation gives rise to an optimal switching problem for a hybrid system, however, which can hardly be solved analytically. To implement the numerical simulation, we make a transformation in the parameter filed in order to use the control vector parameterization method to solve the original problem. Thus, the proposed optimal control problem can be converted into a non-linear programming problem (NLP), which can be solved conveniently and effectively using the current technique. Based on these facts, we shows that some key economic parameters that inherently define the revenue relationships outside the firm can significantly influence the time of adoption. Furthermore, considering the problem in the multi-technology adoption case, the process can perform in such an unusual way that the firm can leap over some transition technologies to adopt a higher advanced one directly, from which corresponding results are discussed as well.