See why saving and capital build a richer steady state — but only productivity sustains long-run growth.
Understand why capital accumulation alone yields a steady state rather than perpetual growth, and that only productivity shifts long-run living standards.
Raise the savings rate (s) from 25% toward 50% and watch the transition chart.
Before you act, predict what will happen. Did long-run growth speed up and stay fast, or did output settle at a new, higher level and then flatten again? Then do it — did your prediction match what happened?
The Solow diagram
Saving (s·y) has diminishing returns; break-even investment (n+δ)·k is a straight line. Where they cross is the steady-state capital per worker, k*.
Transition to the steady state
Output per worker over time, starting from a low capital stock. Growth is fast at first, then peters out as the economy approaches k* — capital accumulation alone cannot sustain it.
The Solow model explains why economies grow, and why capital accumulation alone eventually stops driving growth. Output per worker depends on capital per worker, but capital has diminishing returns — each extra machine adds less than the last. Saving turns output into new capital, while depreciation and a growing population eat capital away; the amount of investment just needed to keep capital per worker constant is break-even investment. An economy settles at its steady state, where saving exactly offsets depreciation plus population growth, and there capital per worker stops rising. A higher saving rate lifts the steady state to a richer level, but it does not produce permanent growth — because of diminishing returns, growth slows to a halt at the new, higher plateau. That is the model's central surprise: you cannot save your way to endless growth. The one thing that shifts living standards permanently is total factor productivity (A) — how much output you get from given inputs, driven by technology and know-how. The model also predicts convergence: poorer economies, starting with less capital, grow faster and tend to catch up toward richer ones with similar fundamentals.
You adjust the saving rate, depreciation, population growth, and productivity, and watch capital per worker climb to the steady state where the saving and break-even lines cross. Raising saving yourself lifts the plateau but doesn't make growth permanent; only raising productivity shifts the whole curve — the model's core lesson made visible.