In the recent literature on mathematical models of economic growth, attention has been devoted mainly to the existence and stability of competitive equilibria. These models are based on a rather crucial but simple savings assumption: that savings form a constant proportion of income both being evaluated in terms of numeraire. In this paper, the savings decision is treated as a derived decision, i.e., as an implication of the more basic behavior of utility maximization over time. Using a simple two-sector, two-commodity, two-factor model, optimal growth paths corresponding to the maximization of the sum of the discounted future stream of consumption per worker are worked out. Savings behavior and asymptotic properties of these optimal paths for varying positive discount rates are also discussed.