Neither kanji's individual meaning seems to be related to the economy. What's the etymology? (I haven't been able to find it on my own.)

It's an abbreviation of 経国済民.

If Wikipedia is to be believed, 経済 is an abbreviation for 経世済民 which seems to be a Chinese idiom that translates to "Govern/administer the world/land and aid the people" (世を經（おさ）め、民を濟（すく）う). Apparently, the term 経済 was coined by Fukuzawa Yukichi, along with many other words that refer to concepts which were new to Japan back in the days.