thanks for your thoughts.
I assume a strong longterm relationship between growth and interest, since at a certain rate "r" of interest, only firms with higher growth expactation than "r" would borrow money to expand. Furthermore I assume, with more and more investments, the return of investments lessens. So despite other factors affecting interest, growth is the one, which determines an equilibrium around which the interest rates should theoretically fluctuate (fluctuation is probably mostly because of bernanke and his colleagues).
The next step I take is to assume, that human capital investment like other investments must follow the same trace along the growth path. Aquiring human capital must be profitable, else one would do 3 years of work instead of a bachelor degree and leave some of the money in stocks and bonds or something. In fact there are studies which claim the return of human capital investment to be around 6-7.5% per year of schooling. This is pretty much the average interest rates of the past decades plus some compensation for the years where no income could be obtained.
I will try to break down the invention thing to the micro level:
- some new invention is made (steam engine, railroad, car, electronics, pc, internet)
- from now on, the economy might grow by exploiting the new invention
- there are some entrepreneurs (e.g. a railroad company, ibm, volkswagen, google) who are able to generate tremendous profits (far more than rate "r")
- those will pay above average wages to people willing to enter this sector and if neccessary adopt new skills
- on the other hand some workers of the "old sector" might even get unemployed (the only potentially negative part)
- other sectors will also grow (but at a lower rate) and pay higher wages because the new high-paid workforce of ibm, volkswagen, google has more purchasing power
You wrote: "When unqualified workers have access to new machinery they produce more and can bargain for better wages."
This is exactly how I think inequality of wages arises. Workers of IBM, Google etc. can bargain for way higher wages. But I guess you are right if some invention can easily be exploited by untrained or former low-income workforce (railroad might be an example or three-field (crop) rotation) and not only by trained people (like in electronics or it). Actually, measured with the Gini-coefficient, inequality almost always drops when some random wages rise! not sure if the gini is a proper measurement then

But to come back to the original question for a moment: The relationship between growth and interest seems so trivial, that it must be mentioned by some austrian economist. Any idea in which book to look that up? Reason is I need some sources of quotes from where to start with my ideas. Furthermore it would be neat to have some austrian texts about human capital.