Is one qurbani sufficient for the whole family?

Is it enough for a man to sacrifice one qurbani/ udhiyyah on behalf of his family? Or  is it necessary for him to sacrifice one for each  member of his family?

Imam Malik (ra), Al-Lays (ra), Shafi (ra), Al-Avzai (ra), Imam Ahmad (ra) and Iskhak (ra) stated that it is enough for a man to sacrifice one qurbani for himself and his family according to the following hadith:

Yahya related to me from Malik from Umara ibn Yasar that Ata ibn Yasar told him that Abu Ayyub al-Ansari had told him, "We used to sacrifice one sheep, and a man sacrificed for himself and his family. Then later on people began to compete with each other and it became boasting." (Ibn Majah)

The hadith reported by Abdullah bin Hisham is one of the prooves of this opinion as well.

“Prophet (pbuh) used to sacrifice one sheep for himself and for his family.”

According to Hanafi Scholars and Imam Savri (ra), to sacrifice one sheep suffices for only one member of the family. So each member of the family whose wealth exceeds the amount of nisab should sacrifice one qurban. (Musnad)