This is the 740th most frequent Icelandic word.
eigið
The Icelandic word "eigið" means "own" in English, as in possession or ownership.
Here, 'eigið' modifies the noun 'hús' to denote possession by the subject.
Hver ætti að eiga eigið hús.
Everyone should own their own house.
In this sentence, 'eigið' is used in a reflexive manner to emphasize the possessiveness of the noun 'lífi'.
Þú berð ábyrgð á þínu eigin lífi.
You are responsible for your own life.
The word 'eigið' is being used to denote that 'framlag' belongs to or is provided by the subject, 'Við'.