When considering emissions control problems associated with carbon dioxide (CO2), social planning over quite a long-term horizon is usually considered to be necessary because it takes much time for the full absorption of CO2 by oceans and forests. Sometimes the required time horizon even becomes infinite. Such a fact seems to impose patience beyond the limits of human cognition. However, this study proves that the first-best emissions scenario can be achieved only by local altruism, which is dubbed parentage. Parentage is defined as the action of applying zero social discount rate to its subsequent generation, and discounting the utility of generations thereafter infinitely. In this sense, the nearly first-best emissions scenario is feasible within the ordinal cognition and benevolence of human beings. This paper also examines the definition of egalitarian sustainability, in which the utility of every generation must be kept constant, and reveals that such a definition of sustainability possibly provokes the inefficient intergenerational allocation of CO2. This is because the vested interest of the predecessors is put much importance in the process of the planning. It is required more rigid sustainability concept, in which the utility of each generation is no less decreasing through time and at least strictly increasing locally, to achieve the efficient allocation of CO2. One will find that the intergenerational allocation by the local altruism satisfies this property.