If you have worked to be wealthy or lucky to be one, you should see it as a social responsibility to help the less privileged people in the society. If I may ask, do you feel comfortable driving past several beggars on the street when you have billions of money in your account that you or your entire family may not be able to exhaust in the next 100 years?
Think about this seriously. With the so much money in the world, poverty can greatly be reduced if not totally eradicated.
All that is necessary is the distribution of this wealth.
There is enough to go round.
Note:
You must not necessarily give physical cash or money directly in order to help the poor or the less privileged. You can set up an empowerment scheme where they could be empowered or work to earn a living for themselves. It is like teaching them how to fish instead of offering them the fish directly to eat. I guess it is best that way.
Eradicating poverty completely is very much possible with the efforts you mentioned but I also do feel some beggars do it on intention as they don't want to work hard for their living and they find it easy to beg(Not in all cases of course). Governments and people are doing it as much as possible to help eradicate it by making NGO's and self-awareness centers and many other things.
Lastly, a person has to be determined to push himself out of poverty the help which he needs to do that will definitely be supplied from some sources.