Environmental and population externalities

In this paper, we investigate the external effects of the parent's decisions on the number of newly born children and the firm's decisions on the amount of polluting emissions that occur in industrial production. We employ an optimal control model which comprises three stock variables representing population, the economic capital stock and the pollutant immissions in the natural environment. We distinguish two different types of households, in which the decision on the number of births takes place. These two types may be regarded as two extremes: dynastic households, in which the family sticks together forever and micro-households, in which children leave their parent's household immediately after birth. We conclude that in both cases the decentralized outcome is not optimal due to two externalities: one occurs in the individual decision on polluting emissions, the other one in the individual decision on the number of births. It turns out that whereas the environmental externality is of the same form in both cases, the type of external effect from the household's decision on fertility is qualitatively different. The different types of population externalities require different policy instruments in order to internalize them. We discuss a Pigouvian tax on emissions as well as taxes on population: if an appropriate tax on the household size is applied in the case of dynastic households and an appropriate tax on children is applied in the case of small households a first best development of the economy is obtained.