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The Solow growth model explains long-run differences in income per capita through capital accumulation, population growth, and technological progress. Capital accumulates when investment exceeds depreciation; the economy converges to a steady state where capital per worker is constant. At the steady state, output per worker grows only through total factor productivity (TFP) growth — technology. The model predicts conditional convergence: poor countries with the same fundamentals as rich countries should grow faster. It implies that sustained growth requires continuous technological progress, not just more capital.
Work through the steady-state derivation: set investment per worker equal to break-even investment (depreciation + population growth). Use phase diagrams to show convergence. Then discuss why Africa has lower steady states than East Asia using Solow parameters.
The Solow model's central insight is that capital accumulation alone cannot sustain long-run growth. Here is why: each additional unit of capital adds less to output than the previous one — diminishing returns to capital. Meanwhile, depreciation and population growth continuously erode capital per worker. The economy reaches a "steady state" where new investment exactly replaces what is lost, capital per worker k* stabilizes, and output per worker stops growing.
The phase diagram makes this concrete. Investment per worker sf(k) is an upward-curving line that flattens due to diminishing returns. Break-even investment (δ+n)k is a straight line through the origin, where δ is depreciation and n is population growth. Their intersection is k*. If you are below k*, investment exceeds break-even and k rises toward k*. If you are above, k falls back. The economy always converges to the steady state.
What happens when the savings rate s increases? The investment curve shifts up, raising k* to a higher level. Output per worker rises — but only to a new, higher plateau. Once the new steady state is reached, growth again ceases. This is the crucial difference between a level effect and a growth effect. The only mechanism that keeps output per worker growing indefinitely is continuous improvement in total factor productivity (TFP), which shifts the entire production function upward over time. TFP growth is where sustained economic growth ultimately comes from — not capital.
This logic generates the model's famous convergence prediction. Two countries with identical savings rates, depreciation, and population growth have the same steady state k*. The poorer country is further below k*, so capital has higher marginal returns there and it grows faster. Eventually both reach the same k* and income per worker — conditional convergence. The word "conditional" is critical: if the fundamentals differ, the steady states differ and there is no reason to expect income levels to equalize. This explains why some poor countries have grown rapidly (they had strong fundamentals and were below a high k*) while others have stagnated (low savings, fast population growth, weak institutions push their k* down).
The Solow model's great contribution was separating what capital can do (raise the *level* of income per worker) from what technology must do (sustain *growth* in income per worker). Its acknowledged limitation is treating technological progress as exogenous — simply assumed to happen at some rate — which is why subsequent endogenous growth models (Romer's model) tried to explain where innovation actually comes from, turning TFP from a black box into something economic actors can invest in.