Introduction to Modern Economic Growth x(t) h(t)=0 x’’(0) x(t)=0 x* x’(0) h(0) h* h(t) Figure 10.1 Steady state and equilibrium dynamics in the simplified Ben Porath model solution (h∗ , x∗ ) is globally saddle-path stable, with the stable arm coinciding with the horizontal line for x˙ (t) = Starting with h (0) ∈ (0, h∗ ), s (0) jumps to the level necessary to ensure s (0) h (0) = x∗ From then on, h (t) increases and s (t) decreases so as to keep s (t) h (t) = x∗ Therefore, the pattern of human capital investments implied by the Ben Porath model is one of high investment at the beginning of an individual’s life followed by lower investments later on In our simplified version of the Ben Porath model this all happens smoothly In the original Ben Porath model, which involves the use of other inputs in the production of human capital and finite horizons, the constraint for s (t) ≤ typically binds early on in the life of the individual, and the interval during which s (t) = can be interpreted as full-time schooling After full-time schooling, the individual starts working (i.e., s (t) < 1) But even on-the-job, the individual continues to accumulate human capital (i.e., s (t) > 0), which can be interpreted as spending 472