In the 1980s it became progressively clearer that the standard neoclassical exogenous growth models were theoretically unsatisfactory as tools to explore long run growth, as these models predicted economies without technological change and thus they would eventually converge to a steady state, with zero per capita growth.
A fundamental reason for this is the diminishing return of capital; the key property of AK endogenous-growth model is the absence of diminishing returns to capital.
In lieu of the diminishing returns of capital implied by the usual parameterizations of a Cobb–Douglas production function, the AK model uses a linear model where output is a linear function of capital.
Its appearance in most textbooks is to introduce endogenous growth theory.
[1] The AK model production function is a special case of a Cobb–Douglas function with constant returns to scale.
This equation shows a Cobb–Douglas function where Y represents the total production in an economy.
A represents total factor productivity, K is capital, L is labor, and the parameter
= saving rate In an alternative form
In the above equation A is the level of technology which is positive constant and K represents volume of capital.
Hence, output per capita is: The model implicitly assumes that the average product of capital is equal to marginal product of capital which is equivalent to:
The model again assumes that labor force is growing at a constant rate ‘n’ and there is no depreciation of capital.
(δ = 0 ) In this case, the basic differential equation of neo-classical growth model would be:
To avoid the contradictions, Russian economist Vladimir Pokrovskii proposed to write the production function in the united form where
correspond to output, labour and substitutive work in the base year.
This form of the theory explains growth as a consequence of the dynamics of the production factors, without any arbitrary parameters, which makes it possible to reproduce historical rates of economic growth with considerable precision.