#### Optimal Savings and the Value of Population

**Abstract: **We study a model of economic growth in
which an exogenously changing population enters in the objective function under
total utilitarianism and into the state dynamics as the labor input to the
production function. We consider an arbitrary population growth until it
reaches a critical level (resp. it stops growing altogether). This
requires population as well as capital as state variables. By letting the
population variable serve as the surrogate of time, we are still able to depict
the optimal path and its convergence to the long-run equilibrium on a
two-dimensional phase diagram. The phase diagram consists of a *
transient curve* that reaches the *classical curve*
associated with a positive exponential growth at the time the population reaches
the critical level. In the case of an asymptotic population saturation, we
expect the transient curve to approach the equilibrium as the population
approaches its saturation level. finally, we characterize the approaches
to the classical curve and to the equilibrium.