Optimal control of a global model of climate change with adaptation and mitigation

The Integrated Assessment Model (IAM) has extensively treated the adverse effects of climate change and the appropriate mitigation policy. We extend such a model to include optimal policies for mitigation, adaptation and infrastructure investment studying the dynamics of the transition to a low fossil-fuel economy. We focus on the adverse effects of increase in atmospheric CO2 concentration on households. Formally, the model gives rise to an optimal control problem of finite horizon consisting of a dynamic system with five-dimensional state vector consisting of stocks of private capital, green capital, public capital, stock of brown energy in the ground, and emissions. Given the numerous challenges to climate change policies the control vector is also five-dimensional. Our solutions are characterized by turnpike property and the optimal policy that accomplishes the objective of keeping the CO2 levels within bound is characterized by a significant proportion of investment in public capital going to mitigation in the initial periods. When initial levels of CO2 are high, adaptation efforts also start immediately, but during the initial period, they account for a smaller proportion of government's public investment