Section 2

Model Comparison

The two models diverge at the level of the production function; everything else follows from that choice.

Harrod-Domar

Fixed capital-output ratio $v$ . Output requires capital in exact proportion to input — no substitution. If warranted and natural growth rates diverge, the economy cannot self-correct.

G_w = \frac{s}{v}

Solow-Swan

Variable capital-output ratio. When capital accumulates faster than labour, diminishing returns lower the marginal product of capital, raise $K/Y$ , and slow capital accumulation — automatically. The economy converges to $k^*$ .

\dot{k} = sf(k) - (n + g + \delta)\,k

Dimension-by-dimension

Dimension	Harrod-Domar	Solow-Swan
Production function	Leontief (fixed $K/Y$ ; no substitution)	Neoclassical Cobb-Douglas ( $Y = K^\alpha (AL)^{1-\alpha}$ ; $K/Y$ varies)
Capital-output ratio	Fixed ICOR $v = K/Y$	Variable; rises with capital accumulation
Stability	Knife-edge: deviations from warranted rate compound	Globally stable: economy converges to steady state $k^*$ from any starting point
Technology	Absent from core model	Central: TFP growth $g$ drives long-run per-capita income growth
Long-run per-capita growth	Zero unless $s > v \cdot n$ ; savings rate determines it	$g$ (TFP growth), regardless of savings rate
Policy implication	Active state intervention required to hold $G = G_w = G_n$	Market self-corrects to steady state; policy shifts the level of $k^*$ , not the long-run growth rate
Primary use	Development planning, aid-gap analysis	Academic growth theory, convergence empirics, TFP accounting

The table's deepest entry is stability. In Harrod-Domar, if actual growth briefly exceeds warranted growth, firms see rising demand and invest more, pushing growth further above warranted — a self-amplifying spiral. Solow breaks this by letting the capital-output ratio rise when capital accumulates faster than labour: the marginal product of capital falls, slowing investment, until the economy settles at $k^*$ .