If efficiency is calculated by output divided by input, and the difference, input minus output, is distributed to the public good rather than to cronies would it be OK?

A currency-issuing government should be investing in the things that make us more competitive and productive, such as education, healthcare, infrastructure, etc. Its ability to make such investments is infinite, not the result of a formula that serves only to artificially constrain.

The real constraints are the availability of needed resources and labor to achieve the goals the spending is deployed to accomplish. We can always build schools and hospitals, but can we fill them with qualified teachers, Drs., and their support staffing? If not, then we need to take a step back and invest in producing those first, and then move ahead to the primary goals.