There are many sources within Judaism that discuss the obligation to give charity, both in the individual and communal level. The principle Torah source on this issue is Devarim 15:
(ז) כִּי יִהְיֶה בְךָ אֶבְיוֹן מֵאַחַד אַחֶיךָ בְּאַחַד שְׁעָרֶיךָ בְּאַרְצְךָ אֲשֶׁר יְקֹוָק אֱלֹהֶיךָ נֹתֵן לָךְ לֹא תְאַמֵּץ אֶת לְבָבְךָ וְלֹא תִקְפֹּץ אֶת יָדְךָ מֵאָחִיךָ הָאֶבְיוֹן:
(ח) כִּי פָתֹחַ תִּפְתַּח אֶת יָדְךָ לוֹ וְהַעֲבֵט תַּעֲבִיטֶנּוּ דֵּי מַחְסֹרוֹ אֲשֶׁר יֶחְסַר לוֹ:
The issue is also discussed in Mishnayos Peah (ch.8), Kesubos (67b), in Mishnah Torah Matnos Aniyim (ch. 7) and elsewhere. There are also many sources that discuss the agricultural requirements for charity, but one would need to figure out how to apply their principles nowadays. Few people are farmers nowadays, and there is also much greater wealth and standard costs than before.
Everything a person earns he owns, wealth cannot just be re-distributed by some government to create equality. Each person then as an obligation to give charity. Every year, he must give a small amount to charity to fulfill the most basic obligation. However, he is expected to give at least 10% of his income to charity, (but not more than 20%), either m'drabanan or by minhag (or even md'oraysa, according to one view). If he does not give enough charity, the courts can forcably take large amounts from him:
כי הא דרבא כפייה לרב נתן בר אמי, ואפיק מיניה ד' מאה זוזי לצדקה. (Kesubos 49b)
It seems that the individual in general can choose to some extent how he wants to give away his money, just that if he doesn't give, it will be collected forcibly. It seems that he must give a flat-rate of 10% to charity, but it may be that this might they vary based on social need. The issue is to define what is considered a need that will require the rich to give charity to the poor. The gemara discusses the different charity organizations that existed and who was eligble to receive from them. For example, one who had less than 200 zuz, could take from maaser ani (the argicultural tithe). If one was even poorer, he was eligible to take from the weekly money collection (kupah), and the truly poor would take from the daily food collection (tamchui). The issue is applying these amounts to modern times when expenses have changed so much.
R. A. Levine Discusses these issues at length in "Economics & Jewish law". He demonstrates that poverty should be defined as "bare subsistence". The Talmud learns from " דֵּי מַחְסֹרוֹ" that we are not obligated to make the poor wealthy. He argues that one should take the "budgetary approach" to defining poverty, which evaluates the basic costs of food and what percentage they take up of a poor family's expenses to define certain poverty lines. Such definitions would establish when a person is able to receive public assistance. However, someone slightly poor may still be eligible for private assistance.
In summary, there is no Jewish idea of wealth redistribution to create equality, but society must provide for the basic needs of the poor. The individual has certain leeway in choosing where to give, but if he fails, the government should collect it by force. The basic rate of giving seems to be a flat-rate, but if there's great need perhaps that may change.