Abstract (EN)

To raise children, to guarantee a certain way of life, and to retire with a certain amount of capital can be accomplished in many different ways, particularly when couples are faced with the possibility of unemployment or poor returns to savings while trying to balance current and future consumption both personally and for their children. Not any trajectory is successful, but those which are successful are myriad. Agents’ heterogeneity is modelled both by the whole state space where each state corresponds to a different situation, and by the set of attainable states, which reflects uncertainty inherent both in decision-making and in external shocks. The delineation of all manageable states of consumption, reproduction, and saving identifies the timing of when to have children, and when and how much to consume and save. Discontinuities of consumption when a child is born are fully taken into account through continuous-discrete differential inclusions. The theory is illustrated with an empirical example; international comparison shows that lower fertility is associated with smaller sets of timely decisions.