In the previous Mishnah we learned that the obligation of the kolbon arises when a person gives a whole sela on behalf of two people. Our Mishnah comes to draw a distinction: one who joins together with his fellow as partners and they give a single sela for the two of them - they are obligated in the kolbon; but one who pays on behalf of another person who is not obligated in his own shekel, and does so as a favor and as a gift - we do not require him to add a kolbon.
Who is exempt from the kolbon:
One who gives on behalf of another as a gift - a person who pays a half shekel for himself and for a poor man, or for his neighbor or for another resident of his city, when he does so as a gift for them - is exempt from the kolbon. This obligation was stated specifically where the joining of the two people constitutes a partnership and both of them are obligated in their shekel; but one who takes care of the matter on behalf of someone else does not fall into this category.
One who lends to his fellow - if this is not a gift but a loan, that he is paying in their name temporarily and expects them to repay him - then they are partners in every respect, and they are obligated in the kolbon.
Partners and the tithe of animals:
From here the Mishnah moves on to discuss the definition of partnership, not only regarding the kolbon but also regarding an entirely different area of law - the tithe of animals. The obligation of the tithe of animals is to separate one out of every ten of the animals born in the herd and to bring it as an offering. But this law does not apply to partners: partners in a herd of animals are exempt from the tithe of animals, and certainly so by Torah law.
Brothers who inherited their father's property:
Here the Mishnah distinguishes between two situations, before the inheritance has been divided and afterward:
Before they divided the inheritance: we do not view the property as a partnership between them, but almost as though it is still the father's money and in his possession. And just as a father is not obligated to pay a half shekel on behalf of his son, and if he did so he is like one who pays on behalf of a poor man - so too here we do not require a kolbon.
After they divided the inheritance: once each one took his portion, and afterward they joined together again and combined their funds and conduct their affairs in partnership - they are like ordinary partners in every respect. And just as ordinary partners who join together and give a single sela for the two of them are obligated in the kolbon, so too are they.
In light of this, the words of the Mishnah are understood, in the language of the text: "Achim shehem shutafin - chayavin bakolbon" - brothers who are partners are obligated in the kolbon. Why are they obligated? Because they are brothers who function as partners, having already divided the estate and afterward combined their funds together in the way that partners do. We do not view the matter as though the father is paying on behalf of his sons, and therefore they are obligated in the kolbon. And for that very same reason they are considered partners with regard to the tithe of animals as well, and partners are exempt from the tithe of animals.
By contrast, "kesheheim chayavin b'ma'aser behemah" - when they are obligated in the tithe of animals - that is, in a situation where they have not yet divided the father's property, which is not considered a partnership but rather the father's money, almost as though the father is the owner even though he is no longer alive, and this is nothing more than an estate - then they are exempt from the kolbon, for we view the matter as though the father's estate is paying on behalf of his sons, and a father who pays a half shekel on behalf of his sons is like one who pays on behalf of a poor man, and is exempt from the kolbon.
The amount of the kolbon:
After the Mishnah concluded the subject of the kolbon, it asks: and how much is the kolbon?
Rabbi Meir: one twenty-fourth of a sela - and since a half shekel is half a sela, it turns out that it is one twelfth of a half shekel.
And the Sages say: half of that amount - one forty-eighth of a sela, which is one twenty-fourth of a half shekel.
In summary: in this Mishnah we learned that the obligation of the kolbon depends on the definition of partnership: one who gives on behalf of a poor man, a neighbor or another person by way of a gift is exempt, whereas one who lends to them on condition that they repay him - they are partners and are obligated. We also learned the distinction regarding brothers who inherited: before the inheritance is divided, the money is considered their father's, and therefore they are exempt from the kolbon and obligated in the tithe of animals; and after they divided it and then entered into partnership again, they are partners, and they are obligated in the kolbon and exempt from the tithe of animals. And finally we clarified the amount of the kolbon - one twenty-fourth of a sela according to Rabbi Meir, and half that amount according to the Sages.