The impact of climate damage function on the social cost of carbon and economic growth rate

This paper analyzes the impact of climate damage function on the social cost of carbon (SCC) and the economic growth rate. In a two-sector economic model with endogenous growth, we construct a 7-dimensional nonlinear system and then linearize the nonlinear system to derive the expression of the SCC containing the damage function. We find that the selected damage function has significant impacts when we calculate the SCC. In our model, the long run SCC per unit of output is the discount flow of the damage function caused by temperature rise and it is also affected by temperature adjustment rate and some other parameters. The specific form of damage function directly affects the social evaluation of the externality of pollution. The concavity of the SCC in the time path depends on second derivative of the damage function in infinite time. Higher-order damage function increase the SCC. We find that when the society is in an optimal state, the long-term economic growth rate can still be guaranteed to be positive when the convex damage function is chosen. The key of mitigation and adaptation strategies is the development of effective climate policies. Thus, as global recommendations for mitigation and adaptation strategies, we recommendation policy makers to use a highly convex damage function to calculate the SCC. We suggest policy makers consider carbon tax policies based on SCC. This makes the economic view of pollution closer to the mitigation target of climate policy-makers.