AK Endogenous Growth Model

The AK model removes diminishing returns to broad capital. Output is Y = AK, so the average and marginal product of capital do not fall as capital accumulates.

Rebelo's work made the constant-returns-to-accumulable-factors case central to endogenous growth. Policy can affect the long-run growth rate because saving and productivity change the slope of accumulation and the income level.

The model is intentionally stark. It treats broad capital as physical capital, human capital, and knowledge-like assets bundled together.

Capital evolves with investment minus depreciation. With output linear in capital, the growth rate is g = sA - delta.

There is no finite steady-state level of capital when g is positive. The economy follows an exponential path rather than converging to a fixed capital-output ratio.

The knife edge is clear: if sA exceeds depreciation, the economy grows; if it falls short, capital shrinks.

Growth-policy debates use the AK model to show why education, infrastructure, and knowledge accumulation may change growth rates rather than only income levels.

The model gives a clean reason to care about investment efficiency. Raising saving has little value if A is low because capital is misallocated or institutions are weak.

It should not be used as proof that any subsidy raises growth. The capital concept is broad, and the constant-return assumption needs evidence.