# How can a positive relationship between capital per effective worker and technological change be explained?

I'll get to the point: so, in the context of theories of long-run economic growth, I understand at a basic level that, in the Solow model, there is a negative relationship between capital per effective worker (K/AL) and technological change () - higher amounts of technological change means it is harder for firms to keep with up new innovations in capital terms.

In contrast, there is, supposedly (speaking in very simplified terms) a Schumpeterian-type ('market for inventions') model, where there is a positive relationship between K/AL and technological change, because technological change is determined, in part, by K/AL, as this increases the supply of 'innovations'.

I do not understand how an increase in K/AL would increase the supply of innovations within this model - would someone please explain for me why this relationship might hold true?

## 1 Answer

Your question is not that clear. So let me elaborate an answer on what I have understood from your question.

Note that for the Solow model, when technological change increases, it is the "per capita" capital which decreases. This one is normal because you should give much more capital to your workers, as they are more productive (here the technical progress increases the productivity of workers.)

I don't understand in which context $\frac{K}{AL}$ increases supply of innovations. What spurs innovation in Schumpeterian type growth models is the labor allocation in R&D (or spendings in R&D). This increases the creative destruction rate in the economy. For example, in this case, a decrease in labor $L$ can be consiidered as an increase in labor allocation in R&D.

Or another possible interpretation that I can make is the following one. There exists a stock effect in Schumpeterian models. This means that if your knowledge stock $A$ is high enough, it would be difficult to make new innovations. (See Acemoglu 2009, chapter 14)

So, in this case a higher $\frac{K}{AL}$ implies more innovation.

• Firstly, I apologise for the lack of clarity - no doubt it reflect(ed) my confusion on what I had read/been taught. And my tardiness in answering (I didn't think I'd get a response). Both your explanations make good sense to me. Supposedly the 'direct' answer, according to Crafts (2014:35), on the question of the relationship between K/AL and innovation, is that a higher capital to labour ratio suggests a larger market for innovations--making it more profitable to innovate. Supposedly commentary on this relationship is also in Carlin and Soskice (2006). The answer seems almost too intuitive! Jan 6 '17 at 8:09