In this paper a highly simplifed model is considered which describes the interaction of anthropogenic climate changes represented by the influences due to the enhanced emission of Co₂ resulting in the increase of the averaged surface air temperature on one side, and the economical effects described by the abatement costs for the reduction of emissions on the other side The model is formulated as a linear-quadratic optimal control problem with a compact control region. By applying the standard necessary conditions, a multipoint-boundary-value problem is derived and its numerical solution obtained by multiple-shooting technique is presented. Special attention is paid to the computation of the reachable set of the system and to the dependence of the control structure on the final state prescribed In order to smooth a certain irregular behaviour of the solutions near the end of the arbitrarilly fixed time-interval, an additional monotonicity constraint for the CO₂-concentration is introduced. Solutions of this extended optimal control problem are presented too and they are compared with the former solutions