Sustainability and the Greenhouse Effect: Robustness Analysis of the Assimilation Function

Optimal control models with an environmental stock highlight the intertemporal trade-off between consumption and environmental quality. In these models it is generally assumed that the assimilation function of nature is linear (Nordhaus, 1982). At the same time there is quite some uncertainty on the general form of this function outside a specific range of values. In this paper, we look at different (non-linear) specifications of the assimilation function in the case of the Greenhouse Effect. The optimal trajectories and the steady states are analysed for the various functional forms. Slight variations in the assimilation function can result in a dramatic change in the steady state values. Besides, neither multiple equilibria nor the absence of non-zero production steady states can be excluded. This will be shown with the use of simulations in a simple model of the Greenhouse Effect.