The average cost to host an Olympic Winter Games is around $3 billion, and the average Summer Games is $5 billion. Rio will cost around $5 billion itself.
Rio may be spending tens of billions of dollars on subway lines, tunnels, airport enhancements, etc in addition to the cost to put on the games, but that's a long term decision for the city with its current needs in mind. Reducing commute times from two hours to thirty minutes has nothing to do with the Olympics and everything to do with improving Brazil's most important city for doing business in. They'll be thankful for these infrastructure improvements decades from now, long after all the stadiums are torn down.
If you ask me why London and Sochi were so expensive compared to the average, I have no clue. I assume Russia wasted a lot of money due to corruption and also just wanted to put on a flamboyant show that would wow the world. As for London I have no idea what the hell they were doing. London 2012 did see a lot of British success in the medal count, so maybe it was all worth it. You'd have to ask them. For that matter, the Russians performed marvelously in Sochi too, so maybe it was worth it for Russia as well.
But most Olympic host cities have kept the costs down and it's easy to do so if you just make it your focus. LA held an Olympics for a measly $1 billion.
Now here's the really amazing part. The Rio 2016 Olympics is set to earn $5 billion as well, via tv broadcasting rights, sponsorships, ticket sales/etc. Now, maybe most of that money goes to the IOC and only a little of it goes directly back to Rio or Brazil. But surely that's at least $1 billion off the price tag for the host country. So now we're only talking about $4 billion here.
$4 billion as a percentage of Rio's gdp, which has had 7 years to prepare for these Games, is 4 billion divided by ($3.2 trillion dollars x 7 years) x 100 = .02%
So we're talking 1/5,000 of the economy was devoted to putting on these Olympic games by the Brazilian people. Compare that to the cost of the cathedrals of medieval Europe, or the pyramids of Egypt, or any of the megaprojects of the past. I very much suspect more than .02% of French gdp was put into embellishing its ancient glory during the time it took to build its landmarks. The Olympics has come to South America for the first time in 120 years. I doubt they're going to be getting it back anytime soon, so it's not like they'll have to contribute another 1/5,000 of their income anytime during their lifetime. It's just a once in a lifetime experience where the whole world descends onto your soil and celebrates your existence on the world stage. Isn't that worth a penny out of every fifty dollars over the course of seven years?
This isn't going to bankrupt Brazil. The concept is laughable. It isn't going to bankrupt anyone else either. I bet even Lichtenstein could host an Olympics if it wanted to. It's a minor, almost invisible inconvenience to the host nation, while the memories will last a lifetime and the pride of being Olympic hosts and winning home gold will last forever.
The argument that even $4 billion is too much to waste on 'frivolous games' is nihilistic. If we can't afford to kick back and have fun with the Olympics, when exactly are we supposed to enjoy ourselves? If the Olympics aren't pure enough to enjoy, what is? If we couldn't afford the Olympics, then I guess we can't afford any other entertainment either, since people spend way more than .02% of their budget on entertainment other than the Olympics. If all spending must automatically be routed to health care until everyone in Brazil is in perfect health, then your people will never be allowed to enjoy anything about their newly extended lives, so why would they even want to be healthy in the first place? The same is true of education. What's the use of being educated if you can't enjoy yourself? What's the use of getting a good job and being more productive than before because of your superior knowledge based skills, if you can't turn around and buy fun things for yourself like the Olympic Games?
The true purpose of education is to gain a wide enough vocabulary to read good books. Education is also just a tool to stay entertained. In fact everything in life is just a struggle to be entertained. If what you are receiving can't ultimately be turned into entertainment, then it's utterly worthless. Knowing how to read is an entertainment capital good, because it opens up books, anime, video games, visual novels, etc for viewing pleasure. But if entertainment is banned, then there was no point getting an education in the first place, since it can't be used for anything useful.
If people still refuse to believe entertainment should ever be spent on, just go watch AKB0048 and learn for yourself why you don't have a bloody clue about this issue. People need more than just worker bee drudgery in their lives. They need something fresh, invigorating, something that inspires hopes and dreams. The once every 4 years Olympics provides just that spark to billions of people all around the globe, and for the first time ever, that eternal flame is burning on the soils of South America. Surely once every 120 years is not too much to ask as a deviation from health care and education spending.
If people still refuse to pony up the piddling expense necessary to host the Olympics, then they're just a bunch of scrooges without any humanity left in them. If the world seriously can't scrounge together a measly four billion a year to put on the Olympics, then the world deserves not just to lose the Olympics, but to simply flame out and die entirely. It's utterly ridiculous to say we can't afford them. World GDP is $114 trillion. Work something out. If you value entertainment even a smidgen, you'll find that there's more than enough money to pay for one Summer Games every four years.