14 AK-Models and Others

The treated hereafter called AK-model is a model of endogenous growth theory, dating back to the economist Sergio Rebelo, and has the simplest possible approach:

    (14.1)

AK-models, however, are generally singular with respect to the unknown functions Y and K, as they use to derive the relationship between production and capital stock functions from only one basic equation. So the approach can impossible lead to a self-consistent solution of the problem. The production functioncan be arbitrary and thus be choosen to adapt to any presumption or series of measurements. Therefore such models can only interpolate any presumption or measurement to the future. It contains no reliable statement about cause and effect (or sources and sinks). The IMFs 2005 model turns out to be but also an AK-model, because it can, as in (1.5) is shown, by example with or a similar function been rephrased to an AK-model. This is an effect as can be shown, that applies to every mathematically singular model. The same applies to the classic post-Keynesian growth model of Harrod and Domar (Harrod, 1939, Domar 1946), because it is based on the approach

    (14.2),

with the definition ofas capital productivity. This results trivially inand thus is likewise a typical AK-model with and has of course the same problem.

Amazingly also the other known mathematical models of growth are AK-models. This results in many cases from using the so-called Cobb-Douglas production function (CDPF). Therefore in the next chapter we will deal with this very often involved function to estimate growth questions in classical macroeconomics.