i assume you mean employment must trend towards 0

but yes, this is going to be a problem in the next few decades

well, no, frankly i’ve seen it argued as being a problem now; i recall an article a couple years back saying the jobs lost in the recession aren’t really coming back even though the economy is otherwise doing okay now.  and iirc there’s research right now into basically automating fast food

i mean, consider: http://www.bls.gov/news.release/pdf/ocwage.pdf

among the 10 most common jobs in the US are retail clerk (4.5m), cashiers (3.3m), fast food (3.0m), waiting (2.4m), CS reps (2.4m), stock work (2.3m), and secretarial work (2.2m).

that’s 19 million people doing jobs that are either moving objects around or acting as sort of a proxy between humans and other humans.  those are tasks we’re already not too shabby at automating — and we’re getting better all the time.  how much of your shopping do you now do via amazon?  when was the last time you dialed your operator to get someone’s number?

there are 144 million workers in the US.  those people are 13% of the workforce.  one in eight employed americans.

there have been revolutions in the past, of course.  agricultural, industrial, various smaller ones in between.  but those always produced new different work to be done, saved us from working 24/7, and let us explore other pursuits.

this seems a unique case to me.  we’re already fairly comfortable (as a society as a whole).  we’re no longer primarily working just to make food and clothes for ourselves.  there are entire industries built around selling the middle class a multi-hundred-dollar cell phone that’s slightly better than the one everyone bought last year.  and we continue to aggressively optimize.

so we are barrelling towards the very awkward point where we just have more people than we have work that needs doing.

i see a handful of options, which will probably all happen in some form.  (but only after many years of high unemployment, because having the government serve its population would be socialism!!)

1. basic income, where everyone just gets a regular paycheck from the government, zero strings attached.  enough to keep everyone above the poverty line.  if you can’t find work or just don’t want to work, cool.  if you want more money, you can go earn more.  it’s been tried before on small scales and seems to have worked out.
2. far, far more government investment into R&D.  the classical way for the government to make jobs is to just go build stuff, because building stuff requires having people build it.  upgrade our networking infrastructure, give us cross-country transportation that’s not from the 19th century, send stuff into space again, destroy the credit card industry and give us easy instant money transfers.
3. heavier appreciation of creative pursuits.  above i said we would run out of “work that needs doing”, i.e., work that is immediately profitable.  we may be set on food and clothing, but there’s always room for more art.  the entertainment sector is skewed to all fuck right now: movie stars and pop bands and football players are all part of a huge established well-oiled machine that gives them millions of dollars, whereas people working on their own often have to practically beg for money.  open source software has a similar problem.  we’d need a significant cultural shift (and financial shift, see #2) to put more value on indie efforts, but if we can manage it, we could build an economy where people can support themselves without a huge struggle just by making stuff.

disclaimer: IANAE