>For every act of production, there must be an equal and opposite act of consumption.
The key thing is, the production and consumption need not occur simultaneously. Say I dig up a really spiky plant. I could immediately consume it. Or, I could use it to bludgeon an ox to death that I couldn't otherwise kill. The latter use is a form of investment: the plant is turned into a tool that increases my productivity, allowing me to obtain more food (the ox) than without it.
A similar decision applies in some way to everything that's produced. It can be consumed sooner, or it can be invested and consumed later, in a manner than increases overall ability to produce/consume.
Take a look at http://faculty.lebow.drexel.edu/lainczc/cal38/Growth/Levine_..., a metastudy that identifies "a positive, robust correlation between growth and the share of investment in GDP"; more investment leads to more growth.
>Trying to classify people into "productive" and "nonproductive" is very nearly impossible even within small groups who perform that same basic work in the same building.
By unproductive I was speaking of the stereotypical welfare-dependent individual to which the conversation I was replying to seemed to be referring. If somebody does not work or study, just sits around receiving money for doing nothing, most people would not consider that productive.