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

The economy-climate interaction and an appropriate mitigation policy for climate protection have been treated in various types of scientific modeling. Here, we specifically focus on the seminal work by Nordhaus [14, 15] on the economy-climate link. We extend the Nordhaus type model to include optimal policies for mitigation, adaptation and infrastructure investment studying the dynamics of the transition to a low fossil-fuel economy. Formally, the model gives rise to an optimal control problem consisting of a dynamic system with five-dimensional state vector representing stocks of private capital, green capital, public capital, stock of brown energy in the ground, and carbon emissions. The objective function captures preferences over consumption but is also impacted by atmospheric $ \mathrm{CO}_2 $ and by mitigation and adaptation policies. Given the numerous challenges to climate change policies the control vector is eight-dimensional comprising mitigation, adaptation and infrastructure investment. Our solutions are characterized by turnpike property and the optimal policies that accomplish the objective of keeping the $ \mathrm{CO}_2 $ levels within bound are characterized by a significant proportion of investment in public capital going to mitigation in the initial periods. When initial levels of $ \mathrm{CO}_{2} $ are high, adaptation efforts also start immediately, but during the initial period, they account for a smaller proportion of government's public investment.