Baba Basra 137b - Is an Esrog Owned by Partners Called "lachem"?

The gemara says that when brothers inherit an esrog from their father, they cannot use it for a mitzvah unless they are not makpid on one another so that it can belong to the one who is taking it for the mitzvah entirely. But, if they would remain partners in the esrog, it would not qualify as "lachem" and they cannot fulfill their mitzvah with it. The Rashbam explains that "lachem" requires that the person using it for the mitzvah have complete and total ownership over it, to the exclusion of an esrog which two people are partners in, that is only partially owned by the person using it. Based on this the Rashbam says that when the community purchases an esrog together and each member of the community is going to use the esrog on the first day of succos for his mitzvah, it is understood to be using the mechanics of a מתנה על מנת להחזיר so that at the time each of them uses it for the mitzvah, it is theirs entirely.

There is an interesting opinion of Rabbeinu Avigdor quoted in the teshuvos HaRosh, cited by the kapos temarim in succah 41a. He understands that the term "lachem" rather than "li'cha" would include even an esrog that their are multiple partners in, provided that the esrog was purchased jointly for the purpose of them fulfilling the mitzvah. The reason our gemara understands that the brothers couldn't use the esrog of tefusas habayis is because it wasn't purchased for the purpose of being used for the mitzvah. The kapos temarim struggles with trying to understand the distinction between an esrog purchased by partners for the mitzvah which can be used vs. an esrog purchased by partners for business which cannot be used. Rabbeinu Avigdor is not assuming that when purchased for the purpose of the mitzvah, there is an automatic מתנה על מנת להחזיר, rather he is holding that even though the person using it doesn't own it entirely, it would qualify as "la'chem".

In truth, this issue whether an esrog that is shared by two owner is considered "la'chem" seems to be a machlokes Rashi and Tosafos in succah 27b. Tosafos holds like the rashbam, but rashi implies that it would be "la'chem". The shulchan aruch (658:7-9) paskens like Tosafos. Although the Rama seems to make the distinction of Rabbeinu Avigdor, that if it was bought together for the purpose of mitzvah it qualifies as "la'chem", it is really just based on the assumption that they will then have in mind to give it to each other as a matana when it is time to be yotzei with it.

The minhag for many generations was to collect money from the entire tzibur to purchase one esrog for everyone. Although the intent of the ka'hal is that everyone should be able to be yotzei with this esrog, the m.b. (38) quotes from the Chayei Adam that anyone who can afford to contribute and refuses to contribute cannot be yotzei with it because the tzibur would not give over their portion to him.