Before us is Mishnah 3 in the ninth chapter of Tractate Bava Basra. Let us begin with the halachic background necessary to understand its teachings, which involves three rules we have already encountered in the Talmud.
Three preliminary rules:
Improving another's field without permission: If a person improved his fellow's field without permission - for example, he installed a sprinkler system - it makes no difference whether he thought it was his own courtyard, nor does it make a difference whether he did so out of a desire to profit. Since the owner of the field benefits from the system, he is obligated to pay at least the direct expenses incurred by the improver. He is not paid for his labor, but if he spent a thousand on the sprinklers and piping - this amount must be returned to him.
This rule has a ceiling: the value of the benefit that the field owner received. If the benefit he derives from the sprinklers is only five hundred while the system cost a thousand - this is a bad investment, and the landowner will pay only five hundred, since he is not obligated to pay more than the benefit he received.
Work that the owner clearly desires, without a set price: When it is clear to the worker that the field owner wants the work done - due to the relationship between them or due to a previous discussion - but no price was set, the worker receives the standard rate for workers. Just like a sharecropper who receives a third of the field's produce, one who does the work of the field in plowing and planting without a prior agreement takes the standard price.
Partners: Two partners in a field, where one part belongs to this one and the other part belongs to that one, and one of them does all the work himself. The basis of the partnership is economic interest, and therefore when one partner does the work for his fellow, he is certainly doing so out of personal economic interest. Therefore, for his own portion he takes all the profits, and for his partner's portion he takes those profits that would have gone to any other sharecropper, according to the standard worker's wage in the market.
Brothers who inherit - an involuntary partnership:
Our Mishnah deals with brothers who inherited from their father, and are therefore partners in the assets. However, this partnership was not created out of an economic motive - they did not enter a business venture together, but rather they are brothers. Therefore, the Mishnah opens with a basic assumption: since they are brothers, they care for one another and each acts for the benefit of the other.
And in the words of the Mishnah: "Hini'ach banim gedolim u'ketanim, hishbichu gedolim es hanachalah - hishbichu la'emtza" - if he left adult and minor sons, and the adult sons improved the estate, they improved it for the middle. The deceased left behind four sons, two adults and two minors, and the older brothers took money from the family fund and installed a sprinkler system in the field. Everyone benefits from this, since the system operates in the shared field. Therefore, the improvement is "for the middle" - everyone shares in it equally, as the assumption is that the older brothers acted for the benefit of the younger ones as well.
It should be noted that this is not the case when the brothers actually performed physical labor and did not merely spend money. In such a case, they receive wages for their work according to the law of a partner, at least as the standard wage for a sharecropper, and the rest is divided among everyone.
Declaration before a beis din:
All this is assuming that the brothers are acting for the benefit of all. But if they made it clear that they are acting for their own economic interest - for example, they came to a beis din and said: we have two younger brothers, and even though they inherit with us, they do nothing; we will not leave the field or orchard to stand desolate, since this damages it, and therefore we will work it ourselves and take all the produce of the season in exchange for our labor - in such a case the Mishnah states: "Im amru: re'u mah shehini'ach lanu aba, harei anu osin v'ochlin - hishbichu l'atzman" - If they said: see what our father left us, behold we are working and consuming the produce, they have improved it for themselves. The accumulated profit belongs to them, since they did all the work and made it clear that it is not being done for their brothers but for themselves.
However, the younger brothers have the right to protest, and then the halachah will not be decided this way. The reason these things are stated specifically before a beis din is that the beis din appoints a trustworthy guardian over the minors, to care for their affairs. In an orchard where the trees would be damaged if not tended and pruned, this is to the minors' benefit and they lose nothing, and therefore the older brothers are permitted to take their profits. But if they inherited a gold mine, and the older brothers are depleting the minors' resources - they will certainly protest, and this protest is effective. As long as there is no one protesting, the brothers have the right to say: we are doing all the work and we are taking all the profits.
We find from here that if all the brothers are adults and there is no minor among them, and two of them wish to work and two do not wish to work - it is sufficient for them to declare before their brothers and before two witnesses: we are doing the work and we are taking the profit. Since the other brothers do not object, there is no need for an actual beis din, but only for this declaration before witnesses.
And similarly with sisters:
The Mishnah adds that the same law applies when the heirs are sisters. If one of them improved the property, we assume she did so for her own benefit and the benefit of her sisters. If she declared that she did this for herself alone, the law is just like that of the brothers - the profit is hers. The reason the Mishnah needed to teach us this is that one might have thought a woman's motives in her work are different, and perhaps she is doing so in order to attract a new husband and show herself to be a hard worker. The Mishnah therefore comes to teach that there is no difference between inheriting brothers and inheriting sisters.
However, the case the Mishnah chose is an unusual one: the heir is a woman inheriting from her husband. This specific case is not absolutely necessary, but this is the example the Mishnah used. Generally, a woman does not inherit from her husband at all. However, a situation is possible where the widow inherits from him because she is not only his widow but also his relative - his niece. How so? Reuven and Shimon are brothers, and Shimon has three daughters. Reuven marries one of them, who is his niece, and he has no children. When Reuven passes away, his inheritance goes to his brother Shimon; and if Shimon is no longer alive, it passes to his descendants - his daughters, who are the widow and her sisters. This is the case in our Mishnah.
In the words of the Mishnah: "Vechen ha'ishah shehishbichah et hanachalah - hishbichah la'emtza" - the profits she produced from the inherited property belong to all of them, as we assume she acted not only for her own benefit but also for the benefit of her sisters. However, she is allowed to appear before the court and say that she is doing so only for her personal profit, and this is binding, since she is acting within her rights.
"Im amrah: reu mah shehiniach li baali, harei ani osah ve'ochelet - hishbichah le'atzmah" - I will do all the work to improve the fields, and I will take all the profits that result from it. In this case, she is the one who takes the profit, because she did the work and declared her intentions before the court, and her sisters did not object, nor did their guardians or the court object. Her declaration is binding, and she will enjoy all the profits for herself.
In summary: Our Mishnah establishes that when brothers and sisters inherit, their partnership does not stem from a financial motive. Therefore, the presumption is that they acted for the benefit of everyone - and the improvement is shared. However, one who declares before the court that he is working and consuming the profits for himself, and no one objects - he improved the property for himself, and this includes even a woman who inherited from her husband.