Solow Growth Model (Neoclassical Growth)

1) What Solow adds beyond Harrod–Domar

Solow model improves on Harrod–Domar by allowing:

• diminishing returns to capital,
• factor substitution (capital and labour),
• a stable long-run steady state,
• a separate role for technological progress.

2) Basic setup (concept)

Aggregate production function:

Common example (Cobb–Douglas):

Key assumptions:

• constant returns to scale,
• diminishing marginal product of capital,
• saving rate $s$ is constant,
• population grows at rate $n$,
• depreciation rate $\delta$.

3) Per worker form (core idea)

Define per worker variables:

Then:

Saving (investment) per worker:

4) Capital accumulation equation (per worker)

Change in capital per worker:

Where:

• $s f(k)$ = investment per worker,
• $(\delta + n)k$ = break-even investment needed to:
  • replace depreciated capital ($\delta k$),
  • equip new workers ($nk$).