Differential game of pollution control with overlapping generations

Stefan Wrzaczek, Vienna University of Technology
Gustav Feichtinger, Wittgenstein Centre (IIASA, VID/ÖAW, WU), Vienna Institute of Demography/Austrian Academy of Science

We formulate an overlapping generations model on optimal emissions with continuous age-structure. We compare the non-cooperative solution to the cooperative one and obtain fundamental differences in the optimal strategies. Also including an altruistic motive does not avoid the problem of the \textit{myopic} non-cooperative solution. Finally we define a time-consistent tax scheme to obtain the cooperative solution in the non-cooperative case. The model can be extended in a couple of directions. First, the damage of the stock of pollution should be allowed to be a general (non-linear) function. Convex, concave as well as other forms are possible. Second, the cooperative solution should be extended to the infinite time horizon. In this case it is interesting to derive the condition and the level of a steady state. Further the difference to the above case with the finite time horizon is interesting and will propose important conclusions from a political point of view (politicians act usually up to a finite time horizon, e.g.\ the average temperature should not increase by more the $2$ degree in the next century).