This feature is exclusively available to Starter, Research, and Pro. Upgrade when you need this workflow, review pricing, or send a question before changing plans.
What you keep on Free
The OLG law of motion k_{t+1} = g(k_t) is a first-order difference equation in capital per worker. Plotting g(k_t) against the 45-degree line reveals steady states as crossings and convergence dynamics as staircase paths -- the canonical visualization for one-dimensional dynamic systems.
Steady-state capital
0.0050
Capital per worker at the steady-state crossing of g(k) and the 45-degree line.
Steady-state wage
5.49
Competitive wage at the steady-state capital stock.
Steady-state return
1.76
Net return on capital at steady state. Compare to n to assess dynamic efficiency.
Dynamic efficiency gap
12.98
Positive means dynamically efficient (r > n). Negative means over-accumulation -- the economy saves too much.
Share of wage income saved by the young. Under log utility, s = beta / (1 + beta).
Higher saving shifts the g(k) curve upward, raising the steady-state crossing point and increasing k*.
Rate at which each new cohort is larger than the last. Higher n dilutes capital per worker.
Higher n rotates the g(k) curve downward by increasing the denominator, lowering k* and shifting the crossing left.
Output elasticity of capital. Governs the curvature of the law-of-motion curve and the wage-capital relationship.
Higher alpha makes the g(k) curve more concave and changes the steady-state k* non-monotonically through opposing wage and return effects.
Fraction of capital that depreciates each period. Full depreciation (delta = 1) is the textbook baseline for the two-period model.
Lower depreciation raises the effective return on saving, which under log utility does not change saving but shifts the law of motion through the capital accumulation identity.
Kernel: time-series | Viz: Phase diagram with 45-degree line