You're assuming the GM gets ten students a month...
The fact of the matter is that in tournaments, the prize money usually isn't that great unless you win, and only 1 person gets to win (or more in joint-first, but then the prize money is split). So, unless you're winning all the tournaments, your income from playing chess isn't that great (okay, unless you're in the top 10 players in the world).
That's why so many chess players have to supplement their income by teaching, or creating YouTube videos and training DVDs. Even then, you're living off sales in a niche market with a lot of competition.
I constantly see ppl whining about how hard it is to make a living playing chess and then if you look for a teacher you will some crazy rates, which you never see in other professions, like mathematics.
Players who are just around 2000, ask more money that an English or Mathematics teacher. GM rates are astronomical and on top of that they can sell books, tutorials and general chess aiding material over the internet. I honestly don't want to offend anyone, but it just puzzles me, the whine and also, how much money can someone make by seriously playing a game. Just saw a GM from a country with an average monthly salary of 200$ for 2016, ask around 60$ per hour. With only 10 hours of work per month he could make 600$, triple the average and if he worked almost full time, lets say 35 hours per week, then he could make 35*4*60=8400, 42 times his national average and be extremely rich and live a life that most of his fellow citizens could only dream of.
It seems to me like chess is a very lucrative option for a living, especially if you don't live in US or other very wealthy countries.
Which I applaud, since I really like chess, but I don't get the whine and why I see in threads posts suggesting that you will live in poverty, if you choose the chess path.