Hotza’ah is one of the 39 categories of forbidden labor on Shabbat. It prohibits transporting an object from a private domain (reshut ha-yaḥid) to a public domain (reshut ha-rabim) or vice versa, or transporting an object more than four amot in a public domain. In contrast, on Yom Tov, Hotza’ah is included in the melakhot permitted for food preparation. When preparing a Yom Tov meal, it is very useful to be able to carry food, cutlery, and dishes from one home to another (MT, Laws of Yom Tov 1:6).
We have already seen (3:3 above) that once a melakha is permitted (“mitokh”) for purposes of food preparation (le-tzorekh okhel nefesh), it is also permitted for other purposes that bring joy or benefit on Yom Tov. Thus, one may go for a walk in the public domain while pushing a baby carriage, and one may carry a Torah scroll or lulav in the public domain (Beitza 12a, following the opinion of Beit Hillel).
Nevertheless, it is forbidden to carry rocks or other objects that are not needed for the enjoyment of Yom Tov. Therefore, one who enters the public domain must first make certain that there is nothing unnecessary in his pockets. Although some permit carrying on Yom Tov even when no purpose is served (Rashi), the halakha follows most poskim, who maintain that there is a Torah prohibition upon carrying on Yom Tov in such cases (3:3 above and n. 2). It is also forbidden to carry something on Yom Tov for a non-Jew, for an animal, or for weekday purposes, because all of the melakhot that are permitted on Yom Tov are permitted only in order to increase our enjoyment of the day. Accordingly, one may not carry something for someone or something that has no mitzva to enjoy Yom Tov (3:5 above).
If an object may not be carried on Yom Tov, it may also not be carried in a karmelit (a semipublic domain, rabbinically defined as a public domain; Tosafot, Ketubot 7a s.v. “mitokh”; MB 518:8). Nevertheless, an eruv is effective on Yom Tov just as it is on Shabbat, so in a place enclosed by an eruv, objects may be carried even if they are unnecessary on Yom Tov or are meant for the use of a non-Jew or an animal.