One opinion maintains 6-7. Another opinion is 7-8. The third opinion is 9-10.

The Gemara states that in fact there is no dispute between these opinions. It all depends on the intelligence and maturity of the child. If he is a very mature child, the age of 6 is sufficient if he already understands buying and selling. If he is slower, he might have to wait until the age of 10. It all depends at what age he has a responsible attitude towards money.

Kol Tuv,

Dovid Bloom

We find that Hefker Beis Din Hefker does actually make the transaction of a Katan into a d'Oraisa transaction. See Shekalim 1:5 where the Mishnah states that if a minor gives a Shekel to the Beis ha'Mikdash, it is accepted. The Bartenura writes that one must ensure that it is handed over entirely to the community. The Tiferes Yisrael #25 asks what does it help that it is given over properly? Since mid'Oraisa the minor is not capable of giving a present, the Korban offered will not belong to the Beis ha'Mikdash mid'Oraisa! The Tiferes Yisrael answers that since the transactions of the Pe'utos are effective mid'Rabanan, Hefker Beis Din Hefker enables the Beis ha'Mikdash to receive their presents even mid'Oraisa.

This topic clearly requires further study, but I hope we may have started the ball rolling.

(See Avnei Milu'im 28:33 in the name of the Bartenura and Tosfos Yom Tov in Shekalim.)

Kol Tuv,

Dovid Bloom

I have now had time, bs'd, to look properly into this question.

1) Tosfos in Gitin (40b, DH v'Kasav) appears to be a source for the Tiferes Yisrael that I cited above. Tosfos writes that the principle that 6-7 year old infants can make transactions applies only to monetary matters, because of Hefker Beis Din Hefker. For matters of what is forbidden and what is permitted, the infants do not possess the power to make transactions (e.g. to free an Eved and thereby allow him to marry a Bas Chorin). One learns from Tosfos that the power that Pe'utos possess to make transactions indeed stems from the rule of Hefker Beis Din Hefker, so it would follow that this works mid'Oraisa.

2) The Ran in Gitin (beginning of 31b of the pages of the Rif)seems to say the same thing as Tosfos. He is commenting on the Gemara on 64b which discusses two types of children: (1) a child who is sufficiently mature to throw away a stone that one gives to him, but he retains a nut; (2) a child who is mature enough to return, when asked to do so, an object given to him. Shmuel states, according to Rav Chisda, that both types of children can acquire for themselves an item given to them by others, but if the child is given an object with the intention of being "Zocheh" for somebody else, the transaction is not effective. The Gemara then challenges Shmuel from a Halachah that a minor may be "Zocheh" the barrel of wine to the other people living in the Mavuy in order to permit carrying in the Mavuy on Shabbos. The Gemara answers that this works only because the prohibition of carrying in a Mavuy is merely d'Rabanan.

3) The Ran (end of 31a of the pages of the Rif) writes that he is amazed; since Shmuel maintains that the minor can acquire an item mid'Rabanan (as one observes from the fact that he can acquire an item for himself), then why can he not be "Zocheh" an item for someone else even if a d'Oraisa transaction is required? Since the Rabanan gave him the power to acquire an item, it should follow that since Hefker Beis Din Hefker he may pass it on to others even if a d'Oraisa Kinyan is required! I am not going to examine the answer of the Ran at the moment, but at any rate according to the question of the Ran it seems that the rule of Hefker Beis Din Hefker is strong enough to make a Kinyan d'Oraisa.

4) I am now going to make a quick suggestion. I admit that this needs to be examined to see if it is consistent with the sources, but there may be an important practical Halachic ramification connected to this question. See Shulchan Aruch, Orach Chaim 658:6, who states that on the first day of Sukos one should not give one's Esrog to a minor before one has fulfilled the Mitzvah oneself, because the minor can acquire the Esrog but cannot return it to others mid'Oraisa, so the Esrog will not belong to the adult. However, the Shulchan Aruch writes that there is an opinion that if the child has reached the Pe'utos age, then one may give him the Esrog because he is capable of returning it.

5) My question is as follows: Is it possible to say that this apparent dispute mentioned by the Shulchan Aruch -- about whether the Pe'utah child can give it back -- depends on the above reasoning? The opinion that he can give it back agrees with Tosfos that Hefker Beis Din Hefker means that the Kinyan works mid'Oraisa. Therefore, the adult who receives it back from the child now owns it mid'Oraisa and can fulfill the Mitzvah of Esrog even on the first day. However, the other opinion maintains that the power of Hefker Beis Din Hefker is limited, and the Rabanan did not give such a strong power to their Takanah to say that it really becomes a d'Oraisa.

This really is a rather large topic but at least we have managed to touch on some of the points.

Kol Tuv,

Dovid Bloom