GDP per Installed Computing Facilities I would like to quantify the importance of computing power for economic aggregate output in an economy in a "simple" GDP-to-installed-CPU ratio.

The idea is to calculate a measure similar to GDP-to-capital.

The challenge lies in quantifying installed CPU power in an economy. That is, to define an adequate (and feasible) measure of installed computational facilities and have an idea how to measure this.

There have been objections to a previous version of this question on the basis that this is difficult. It might, in fact, be.

Any suggestions on parts of this problem are highly welcome.
I have electrical engineering training, and the focus on CPUs creates a technical issue. Before the early 1990s (when I did my degree), CPUs would have largely been only embedded in what are recognisably digital computers. Electronics would otherwise be implemented with simpler digital/analog circuits. Currently, the path of least resistance is to just use a CPU for practically everything. For example, cars have plenty of embedded CPUs, whereas back in the 1970s, many might have been almost entirely analog circuits (the radio being the only possible exception).

So any measure of CPUs per unit of GDP should be exploding higher. This is just a reflection of electrical engineers’ design preferences.

If we just try to confine ourselves to CPUs in digital computers, we could try to compute some normalised computing capacity. (This raises problems: do we include phones? Game consoles? Tablets?) 

The next problem is: so what? My computer CPUs have been getting faster over the decades, but at the same time, the bloated operating system chews up more of the resources. I end up doing roughly the same tasks in the same amount of time. Even without having any data, knowing what we know about computing power, my experiences are obviously be widely replicated. That is, real GDP is growing at around 2% per year in the developed countries, but installed CPU capacity has to be growing way faster than that, even if we take a narrow definition of “computer”.

Realistically, you might need to identify some industries that might show a correlation between their growth and CPU usage. It’s hard to see how adding server farms can increase the production of restaurants and barber shops.