The components for capital per employee okay is due to this fact a constant-elasticity-of-substitution (CES) combination between the preliminary degree of capital per employee and the steady-state degree of capital per employee okay* given above, with elasticity of substitution equal to 1/α > 1 and a weight on the preliminary degree of capital per employee that begins at 1 and exponentially decays on the fee (1-α)δ with the steady-state degree of capital per employee okay* having a complementary weight such that the 2 weights add to 1.
The components for capital per employee, which drives all the opposite evolving variables within the mannequin, implies that the convergence fee is the same as (1-α)δ. (That convergence fee generalize to circumstances with different manufacturing features, so long as α is interpreted as capital’s share on the steady-state degree of capital per employee.) It is a fairly gradual fee of convergence. For instance, even when δ is comparatively excessive, at a continuous-time fee of 10.5% per yr, convergence could be a continuous-time fee of seven% per yr if capital’s share is the same as 1/3. Meaning by the rule of 70 that the half-life of exits from the steady-state could be ten years, because the economic system nears the regular state. (The rule of 70 is solely a consequence of the the pure logarithm of two equaling roughly .7.)
On the regular state, capital per employee is unchanging over time. That additionally implies that unchanging on the regular state. Intuitively, funding is sufficient to compensate for depreciation. If there’s inhabitants development, or development within the efficient variety of staff past inhabitants development due to technological progress, the differential equation and its answer above proceed to carry so long as okay is interpreted as capital per efficient employee and δ is interpreted as
δ = depreciation fee + inhabitants development fee + fee of labor augmenting technological progress.