Abstract
Classical stable population theory, the standard model of population age structure and growth, is ill suited to addressing many issues that concern economists and demographers because it is a "one-sex" theory. This paper investigates the existence, uniqueness, and dynamic stability of equilibrium in the birth matrix-mating rule (BMMR) model, a new model of age structure and growth for two-sex, monogamously mating, populations. The paper shows, by means of examples, that the BMMR model can have multiple nontrivial equilibria and establishes sufficient conditions for uniqueness. It generalizes a theorem of W. Brian Arthur to nonlinear systems and uses it to establish sufficient conditions for local dynamic stability.
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