Do the kohanim, priests, contribute to the half-Shekel or are they exempt? TB Shavuot 14

Everybody agrees that the bull (פָּר) the High Priest sacrifices on Yom Kippur atones the priests for their defiling of the Temple or its sacrificial foods. Everybody agrees that the scapegoat (שָׂעִיר הַמִּשְׁתַּלֵּחַ) sent into the desert on Yom Kippur atones for the other transgressions of the Jewish people. And finally, everybody agrees Israel gains atonement on Yom Kippur through the goat whose blood presentation is performed inside the Sanctuary (שָׂעִיר הַנַּעֲשֶׂה בִּפְנִים).

Today’s daf TB Shavuot 14 wants to know how do the priests gain atonement for their other transgressions. Rabbi Shimon holds that they gain this atonement from the bull the High Priest sacrifices on Yom Kippur. Rabbi Yehuda holds that they gain atonement from the scapegoat. The Gemara explains why Rabbi Shimon doesn’t believe that the scapegoat atones for the priests’ other transgressions.

“What is different about the goat of the people that explains why it does not atone for the priests? The difference is that the priests did not forfeit any money over the purchase of it. Therefore, it does not atone for the priests, but only for the Israelites, as it is written with regard to the internal goat: “Of the people.” With regard to the bull of Aaron as well, the priests do not forfeit any money over the purchase of it, so it follows that they should not achieve atonement through it. And therefore, to explain why they do achieve atonement, the baraita states that all of the priests are collectively referred to as: His household.” (Sefaria.org translation)

This position necessitates that the priests do not contribute the half-Shekel like the rest of Israel for all public sacrifices. However there is an opinion in daf TY Shekalim 2 and daf TB Menakhot 21b that the priests do contribute that half-Shekel. According to this opinion they should gain atonement for other transgressions through the scapegoat. Tosefot ד"ה דְּלָא קָא חָסְרִי בֵּיהּ מָמוֹנָא answers that the priests participation is not absolute. For example, if there’s not enough ready money to purchase the scapegoat and they have to solicit funds for its purchase, the priests do not have to participate in this fundraiser. The Tosefot also ask if the priests are not partners in the half-Shekel donation, how can they gain atonement through the sin offering which is a goat of Rosh Hodesh (the new month) and the Pilgrimage holidays? The answer is that Yom Kippur is unique because the atonement is not uniform amongst the entire people of Israel. On the other hand all public sacrifices atone for the entire public and certainly priests are also part and parcel of the public.