Endogenous Growth Theory - The AK Model

The AK Model

The model works on the property of absence of diminishing returns to capital. The simplest form of production function with diminishing return is:

where

, is a positive constant that reflects the level of the technology.

capital (broad sense to include human capital)

, output per capita and the average and marginal product are constant at the level

If we substitute in equation of transitional Dynamics of Solow-Swan model (Exogenous growth model) which shows how an economy’s per capita incomes converges toward its own steady-state value and to the per capita incomes of other nations.

Transitional Dynamics equation, where Growth rate on is given by,

on substituting, we get,

We return here to the case of zero technological progress, because we want to show that per capita growth can now occur in the long-run even without exogenous technological change. The figure 1.1 explains the perpetual growth, with exogenous technical progress. The vertical distance between the two line, and n+δ gives the

As, n+δ, so that. Since the two line are parallel, is constant; in particular, it is independent of . In other words, always grows at steady states rate,.

Since

, equals

at every point of time. In addition, since

,

the growth rate of

equals .

Hence, the entire per capita variable in the model grows at same rate, given by

However, we can observe that technology displays a positive long-run per capita growth without any exogenous technological development. The per capita growth depends on behavioural factors of the model as the saving rate and population. It is unlike neoclassical model, which is higher saving, s, promotes higher long-run per capita growth .