Can someone explain the economics of the tour? What are the prizes? What do you get for winning a stage? For coming in second or third? What do you get for winning the Tour? What does the team get? More generally, how are the professional racers paid/supported? Does each team derive most of its revenue from sponsorship and endorsements, plus prize money?

I can't find the prize list for this year, but I do have numbers for last year. The prizes should not be radically different.

Basically, you win money for winning a stage, or placing in the top 25:
For the 2003 Prologue, 1st = 3810 Euros, 2nd = 1525E. ..., 25th = 67E.
For 2003 Road stages and ITTs, 1st = 7620 E, 2nd = 4000E. ..., 25th = 127E.
For 2003 TTT, 1st = 15000E, 2nd = 7500E, ..., 22nd = 750E

You win money for intermediate sprints: 1st = 800E, 2nd = 450E, 3rd = 300E.

You win money for KOM points:
For HC climbs, 1st = 800E, 2nd = 450E, 3rd = 300E
For Cat 1 climbs, 1st = 650E, 2nd = 400E, 3rd = 150E
For Cat 2 climbs, 1st = 500E, 2nd = 250E
For Cat 3 climbs, 1st = 300E
For Cat 4 climbs, 1st = 200E

You win 350E for each day you win the yellow jersey and 300E for each day you win the green, polka dot, or white jersey.

The top young rider each day wins 500E, except on the TTT stage.

The top team each day wins 2800E, except the TTT stage (strange!)

The most combative rider each day wins 2000E, except time trial stages

There are special primes depending on the course, such as the Souvenir Henri Desgrange for being first over the Tourmalet, and Souvenir Jacques Goddet for being first over the Galibier.

In 2003 there was a 50000E special 100th anniversary prize for the highest placed rider in the five original cities that made up the first TDF.

Then there are the overall classifications.

The top 150 riders on GC are paid. 1st = 400000E, 2nd = 167495E, 3rd = 91470, ... 150th = 381E

The top 10 riders in the points classification (green jersey) are paid: 1st = 22867E, 2nd = 15245, ... 10th = 915E. The pay scale is identical for the top 10 riders in the mountains classification (polka dot jersey).

The top 4 young riders are paid: 1st = 18294E, 2nd = 13720E, 3rd = 9147E, 4th = 4573E

The top 5 teams in the teams classification are paid: 1st = 30490E, 2nd = 28392E, 6th = 6098E

The overall most combative rider wins 20000E.

Finally, if your team finishes in Paris with at least 7 riders, you win 150E per rider.

Lastly, it's not a prize, but each team gets 30000E for travelling expenses.