**16 Uzawa-Lucas and Solow-Swan-Models**

The Uzawa-Lucas model (1988) grew out of criticism of the AK model, in which capital is considered independently of its expression. Lucas leaned it on a model by Uzawa (1965) :

(16.1).

Here one tries to compute the importance of
human capital *H*. Now human capital is always a part of the production *Y*,
which can be represented byas a share of
GDP. The functionmay of course be
any arbitrarily complicated function that represents this proportion as
correctly as possible. By simple algebraic conversion, we now get:

(16.2)

which the Uzawa-Lucas model also identifies as a specific AK-model. The same goes for the older Solow-Swan model (1956), which is based on the approach

(16.3).

here means the labor,
which of course can also been represented as a partof GDP, and thus also is an AK-model with

(16.4).

These facts led historically to the fact that
the mathematical theory of economic growth, pushed by an emphatic post-war
phase, to the end of the last century got into the background. The fundamental
impossibility^{35} of forming a self-consistent theory
had not been detected directly, but one rejected the virtually no useful results
mostly. The IMF 2005 model is in principle after all still the best of the
current classical models, as it, if one chooses different and realistic, at least points
to some extent in the right direction. However, the growth of the capital
coefficient is significantly underestimated, and the capital productivity
greatly overestimated.

The IMF, therefore, summarized in his 2005 report:

„*The investment equation is less
successful than the saving equation in tracking recent developments. This
result is similar to other recent studies, which have found that traditional
econometric models of investment have difficulty explaining recent trends. The
equation overpredicts investment in both the
industrial and emerging market regions, in some cases by large margins. For
instance, while the equation predicts that investment should have increased in
industrial countries - largely as a result of the decline in the cost of
capital - investment in several key industrial countries, including Japan and the
Large Euro countries fell. Similarly, the equation fails to explain the drop in
investment in emerging markets, particularly in the east
Asian countries. The equation suggests that the investment accelerator -
whereby investment rates and output growth move in the same direction - has not
worked as strongly as expected in recent years in these countries, most likely
because corporates have focused on reducing debt and
strengthening balance sheets, rather than on investing in capital.“. *

In an actual working paper [Arcand, Berkes, Panizza, 2012] of the IMF titled *“Too Much
Finance?”* the International Monetary Fund agrees by statistical means
with the conception, that to much assets will stall
the economy.