Is the sacrifice sufficient for the one offering it and his household, or for the one offering it alone?

The sacrificial animal suffices for its owner and his household. This is based on what Muslim narrated from Aisha, that the Prophet, peace and blessings be upon him, sacrificed a ram and said: "O Allah, accept it from Muhammad and the family of Muhammad, and from the Ummah of Muhammad." And what Malik narrated from Ata' ibn Yasar from Abu Ayyub al-Ansari, who said: "During the time of the Prophet, peace and blessings be upon him, a man would sacrifice a sheep on behalf of himself and his household."

The implication of these hadiths is that the sacrifice suffices for the household if the sacrificer slaughters it on his own behalf and theirs. However, the sharing of the cost of the sacrificial animal among members of the same household was not part of the Prophet's guidance.