What does the Torah mean when it writes about a firstborn animal "Lo Yakdish"?
Rashi: It means that one is not permitted to take a Bechor and declare it another Korban (an Olah or a Shelamim), since it is not his
(to declare Hekdesh).
Ramban, Moshav Zekenim: The Torah means (not that one may not, but) that one need not declare it Hekdesh.
Since it is already Hekdesh.
Since, if it is a calf or a Seh, it automatically belongs to Hashem.
Here it says "Lo Yakdish", but in Devarim (15:19) it says "Kol ha'Bechor ... Takdish la'Hashem Elokecha"!
Rashi #1 (Devarim 15:19): Although a Bechor is automatically Kadosh, it is nevertheless a Mitzvah for the owner to declare it Hekdesh
Rashi #2 (Devarim 15:19): Although one cannot sanctify the actual Bechor as another Korban, one can however, declare Hekdesh his Tovas Hana'ah
, and he must give this amount to Hekdesh.
Ramban: What the Pasuk in Devarim means is that one should treat it as Hekdesh, not to work with it or to shear it, and to eat it in Yerushalayim.
This can perhaps be compared to the Mitzvah to add fire to the Mizbe'ach, even though fire comes down from Heaven.
Rashi (Bechoros 53b):
This is the amount that another Yisrael would pay him on condition that he give it to [a Kohen that the latter chooses, e.g] his grandson.