Productivity in general is usually defined in terms of the ratio of output versus input:

"Productivity measure is expressed as the ratio of an aggregate output to a single input or an aggregate input used in a production process, i.e. output per unit of input, typically over a specific period of time." https://en.wikipedia.org/wiki/Productivity

All types of business or economic activity is usually measured in terms of such productivity (or in terms of profit after subtracting investment).

I wonder whether anyone has ever proposed the evaluation of scientific productivity using the ratio of output by input. Specifically, it is common to evaluate scientific output in terms of the number of publications, citations or patents. However, I have yet to find an index which would normalise this output using the total 'investment by the society', this being educational and research grants, salary or whatever other input can be used quantitatively. Nowadays most funding and budgetary information is disclosed and publically available, therefore it should be possible to evaluate this kind of normalisation. I wonder whether this has previously been proposed and if so, I would appreciate a reference. It is not mentioned in "Nine Criteria for a Measure of Scientific Output" by Kreiman and Maunsell, Front. Comput. Neurosci. 2011; 5: 48.