Non-smooth climate change and emergent novel equilibria in an environmental-economic system

Abstract

In this paper we study a basic model of economic growth where we integrate a zero-dimensional energy balance model of the Earth. The albedo of the Earth is the piecewise smooth function of the average surface temperature, thus, taking into account possible feedback effects of a higher temperature. The analysis of the model shows that the model with a jump in the albedo has either a unique regular steady-state or two regular steady-states. When the albedo is described by a piece-wise linear function there exists a non-degenerate pseudo-equilibrium where the temperature stabilizes at the upper switching point of albedo increase with a strictly positive level of consumption.

Keywords: Piece-wise smooth system, climate change, optimal control

JEL Classification: Q54, C61, O41