Three pitfalls in the construction of family-based models of population growth

This paper describes 3 pitfalls in the construction of family-based models of population growth which must be avoided if internal consistency and empirical relevance are to be maintained. Models of the family in which the number as well as the quality of children are subject to choice were pioneered by Becker in 1960 and more recently have served as a base for the theoretical analysis of population size. In these economic models of population, family size and bequests are the outcomes of utility-maximizing family decisions, with the utility of each family viewed as depending on family consumption, family size, and prospective welfare of children, while the age structure of the population is an endogenous variable. All the models are static and focus on the properties of steady states. The 1st pitfall concerns the internal logical consistency of the models and consists in the possibility that the typical family's maximization problem may have no solution, even with a well-behaved concave utility function. The other 2 pitfalls concern the consistency of the model with some "gross facts of life", 1 deriving from the possibility that, even when the family's maximization problem has a solution, the phase diagram for the stock of capital may contain no steady state other than the origin, and the other that even when there exists a non-trivial steady state for the stock of capital, the community may nevertheless face extinction. The 3 pitfalls can be avoided if utility and production functions are subjected to more stringent restrictions than are usually found in economic theory.