The present paper studies the equilibria of a simple overlapping gener
ations model of pure exchange in which money is traded. There is a con
tinuum of agents in each generation and population growth is endogenou
s via voluntary decisions on children. Any monetary steady state has t
o satisfy the ''golden rule'' that the interest rate equals the growth
rate. Still such a monetary steady state may be inefficient. If raisi
ng children is not excessively profitable, then there exists a transfe
r scheme, in favor of those who raise children, which improves upon th
e steady state.