Growth from ideas and human capital, models where the growth rate itself is a choice.
Warming up the engine…
Models where long-run growth is chosen inside the model, via ideas (Romer), constant-returns capital (AK), or human capital (Lucas), rather than gifted by exogenous technology.
AK model: Y = AK ⇒ g = sA − δ (no diminishing returns, saving buys growth forever)
Ideas are non-rival: my use of calculus doesn't deplete yours, so knowledge escapes diminishing returns. That's the loophole through which R&D, education, and scale sustain permanent growth, and why policy can move growth RATES, not just levels.
The exam contrast: in Solow, higher s raises the LEVEL of income; in AK/Romer it raises the GROWTH RATE.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Current equations
What if growth never had to stop? In the Solow model, saving eventually just covers depreciationdepreciationThe wearing out of capital over time, or, for currencies, a fall in value against others.. Here output is proportional to capital (think ideas and know-how, not just machines), so the saving line and the break-even line never meet. The gap between them is permanent growth.