Influence of carbon emission reduction of enterprises on economic growth under climate warming

Global warming, as the main feature of the climate problem, is gradually coming into our field of vision. Under this background, Poisson jump is applied to describe the arrival of natural disasters caused by global warming. Households and firms can dynamically update their beliefs about the arrival rate of disasters. In order to mitigate global warming, firms pay a share of the cost to reduce the carbon emissions in the process of production. In this paper, we discuss the social planner equilibrium and the competitive equilibrium, respectively, and obtain the Hamilton-Jacobi-Bellman (HJB) equations of value function in both contexts. Then, the equations are numerically simulated, leading to the following conclusions: under the same level of pessimism, investments and values of firms, as well as household consumption, all decrease as the emission abatement rate increases, and the social welfare is almost unchanged compared to the situation without the cost of emission reduction. Furthermore, in order to deal with the short-term adverse effects on the economy caused by emission reductions, the government subsidy is introduced into the model. The results show that, under the same level of pessimism, the government subsidy drives the growth of investment and consumption. The value of the firms that pay the emission abatement has been boosted, and economic growth rate has risen to a certain degree, while social welfare remains almost the same.