Economic Growth and Capital Accumulation

Trevor Swan’s 1956 paper illustrates, with two diagrams, the connexion between capital accumulation and the growth of the productive labour force in a one-sector economy, then devotes a long appendix to defending the neoclassical treatment of capital as a factor of production against Joan Robinson’s contemporaneous critique. In the main text, output is produced from capital K and labour N under a constant-returns production function Y = K^a * N^b (a+b=1), giving the growth-accounting identity y = as(Y/K) + bn, where s is the saving ratio and n the (initially constant) rate of growth of the labour force. Plotting growth rates against the output-capital ratio, the growth line of capital (a ray of slope s through the origin), the horizontal growth line of labour (at n), and the growth line of output (their weighted average) must intersect at a single point, where the output-capital ratio settles and the whole economy grows at rate n regardless of the saving ratio – a higher saving ratio permanently raises the level of output per head reached along the way, and briefly accelerates growth during the transition, but does not raise the long-run equilibrium growth rate itself. Adding a constant rate of “neutral” technical progress shifts the growth line of output upward and establishes a new equilibrium at which output per head is not merely permanently higher but perpetually rising, at a rate that exceeds the rate of technical progress itself because capital’s own growth is sustained at a higher level too. Introducing land as a third, fixed factor (Section 3) converts the model into an explicitly classical one: the growth line of capital now lies everywhere above the “Ricardian line” (the locus of population-growth/output-capital-ratio combinations consistent with a constant standard of living), so that, absent technical progress, the output-capital ratio falls indefinitely toward a stationary state at the origin – a mechanism Swan reads as the formal counterpart of the classical doctrine that accumulation ultimately leads to stagnation, checked only if technical progress raises the Ricardian line fast enough. Section 4 shows the model is formally equivalent to Harrod’s warranted/natural-rate apparatus, with the growth line of capital as Harrod’s warranted rate and the growth line of output as the natural rate. The paper’s substantial Appendix, “Notes on Capital,” then takes up Joan Robinson’s contemporaneous claim that Capital cannot be given an operative meaning as a factor of production even in a stationary state: using a “scarecrow” model of durable, freely-reshapable “meccano set” capital, Swan argues that at the margin of a single stationary equilibrium capital can validly be measured as “an equilibrium dollar’s worth” without needing a natural technical unit, reworks Wicksell’s point-input/point-output and Akerman durable-equipment models to show the same marginal-productivity apparatus applies there too, and shows that the “Wicksell effect” – part of an increase in social capital being absorbed by rising wages and falling interest rather than appearing as extra physical capital – can run in either direction (the “Wicksell effect in reverse”), which he takes as evidence against Robinson’s claim that the effect is “the key to the whole theory of accumulation and of the determination of wages and profits.”

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Economic Growth and Capital Accumulation