Ronaldino signs for AC Milan

Ronaldinho has signed for AC Milan from Barcelona and in the process snubbed offers from Manchester City who were paying a very much higher value than what AC Milan had offered.
Ronaldinho had completed medical and has signed a three year deal and will receive wages of 6.5million Euros.
AC Milan paid a fee of 20million euros to Barcelona and there are further bonuses depending upon Champions League performances by AC Milan.
Ronaldinho also agreed to a drop a 15% earning from the transfer which facilitated AC Milan being the front runner.
Deal was concluded today by Laporta and Adriano Galliani in Spain.





My question is,wouldn't Barcelona want more money than give out a player to fellow Champions League team?