3.1. Model Overview: Eliminating Diminishing Returns

The AK model represents the first and simplest version of endogenous growth theory. Its goal is to explain sustained, long-run economic growth without relying on the deus ex machina of exogenous technological progress.

To do this, the model makes a single, radical departure from neoclassical theory: it assumes away diminishing returns to capital at the aggregate level. This is captured in its strikingly simple aggregate production function:

Y = AK

Here, A is a constant representing the economy’s total factor productivity. The economic rationale for this assumption is that K should be interpreted not just as physical capital (machines, buildings) but as a broad composite of capital that includes physical capital, human capital (skills and education), and the stock of knowledge or intellectual capital that embodies technology. As this broad capital stock accumulates, the technological progress embedded within it naturally counteracts the diminishing returns that would apply to physical capital alone.

3.2. The Main Insight: Endogenous Growth

The central result of the AK model flows directly from its core assumption. We begin with the standard capital accumulation equation: K̇ = sY – δK. By substituting the Y = AK production function into this equation, we can solve for the economy’s growth rate (g):

g = K̇/K = sA – δ

This equation has a profound implication: the economy’s long-run growth rate g is now determined endogenously (within the model) by economic parameters. Specifically, growth is an increasing function of the saving rate s.

This stands in stark contrast to the CKR model. In the neoclassical world, a policy that raises the saving rate leads to a temporary period of faster growth as the economy moves to a higher level of income, but the long-run growth rate remains unchanged. In the AK world, a policy that permanently raises the saving rate can permanently increase the economy’s long-run growth rate.

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The mathematical assumption about technology is therefore not a mere technical detail; it is the core determinant of the model’s predictions. This fundamental divergence in assumptions and outcomes between the neoclassical and endogenous growth paradigms warrants a direct comparison.