Interactive modelAdvanced Macro & Growthadvanced

Endogenous Growth (AK Model)

Growth from ideas and human capital, models where the growth rate itself is a choice.

Current equations

Saving s·A·k: y = 0.12·kBreak-even (n+δ)k: y = 0.09·k

What if growth never had to stop? In the Solow model, saving eventually just covers depreciation. 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.

Shift the curves

Saving rate0

Unlike Solow, the saving line never bends down to meet break-even: the gap is permanent growth.

Productivity of ideas (A)0

No diminishing returns to knowledge: better A raises growth forever, not just the level.

The Endogenous Growth (AK Model) model, in writing

Definition

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)

The intuition

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.

Exam tip

The exam contrast: in Solow, higher s raises the LEVEL of income; in AK/Romer it raises the GROWTH RATE.

Related models in Advanced Macro & Growth

IS-LM →Mundell-Fleming (Open-Economy IS-LM) →Fisher Equation →Government Budget Constraint & Seigniorage →