Green economy with efficient public incentives

There is a widespread interest among institutions and economic agents for a reduction of the environmental impact of the production system. An important role seems to be played by the ability of public institutions to push the transition toward a green economy also through the application of fiscal policies that envisage a system of rewards and penalties, respectively, for those companies which adopt green strategies and those which do not. It is clear that readjusting older production systems to new pollution regulations can lead in the short term to profitability reductions for the companies implementing them, even though it is possible to assume increases in profitability over medium-long time horizons. One possible approach to this issue is the classical econometric one, which analyzes the effect of different parameters of multivariate models, that influence the level of pollution due to production systems with different propensity for environmental protection. Optimal control models have been also considered with control variables relating to the technologies of production systems and public incentive policies for the green economy: see for example (Tan et al. in J Syst Sci Inf 9(1):61–73, 2021). In recent years, many scholars have studied the relationship between environmental regulation and enterprise technological innovation using evolutionary games, involving mainly economic incentives and fiscal strategies (see see Suyong et al. in Appl Math Comput 355(15):343–355, 2019; Zhang and Li in Appl Math Model 63:577–590, 2018). In our article, we propose a dynamical model where the public administration uses pollution penalties as a control variable in order to push a production sector toward better performances concerning two targets, pollution level and profitability. To this end, we consider the effects of competitiveness among firms and technology innovation.