Solow growth model: capital convergence
A quick visual walkthrough of how capital per worker converges toward steady state under the Solow model, with adjustable savings and depreciation.
- economics
- macro
Setup
The Solow model describes how an economy's capital stock evolves over time
under a fixed savings rate s and depreciation rate δ. Capital per worker
k follows:
Δk = s · f(k) − δ · k
When s · f(k) > δ · k, capital accumulates; when the inequality flips, it
depreciates faster than it's replaced. The economy settles at the steady-state
k* where the two terms cancel.
Convergence under different savings rates
The chart below traces k(t) over 50 periods for three savings rates, holding
δ = 0.05 and a Cobb–Douglas production function f(k) = k^0.3.
Takeaway
Higher savings rates push the steady state higher, but the rate of
convergence is governed by δ and the curvature of f. Two economies with
identical fundamentals but different starting capital both converge to the
same k* — the textbook conditional convergence result.
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