Gemara

Question (Rav Safra): (Second day Yom Tov of Chutz la'Aretz was instituted lest people not find out which day was fixed to be Rosh Chodesh.) In our place, we find out [via messengers of Beis Din, before Yom Tov] which day was Rosh Chodesh;

In settled areas, we may not do Melachah on the day that we know is Chol, due to strife;

May one do Melachah in a Midbar?

Answer (R. Aba citing Rav Ami): It is permitted.

(Mishnah): Similarly, if one takes Shemitah produce... [R. Yehudah says, he says 'go yourself and bring.' I.e. go to my old place, and bring from there, and you can eat like me!]

Question: Doesn't R. Yehudah agree that he must be stringent like his old and new residences?!

Answer (Rav Shisha brei d'Rav Idi): R. Yehudah discusses a different matter (one who went from a place where it is not finished, to a place where it is not finished, and heard that it was finished in his old place).

Shabbos 150b (Shmuel): On Shabbos, one may say 'I will go to city Ploni' (outside the Techum), because if there were shacks [along the way to extend the city], it would be within the Techum.

151a (Shmuel): Reuven may tell Shimon 'guard my Peros in your Techum, and I will guard your Peros in my Techum.'

Rishonim

Rashba (151a DH Amar): Reuven may tell Shimon 'guard my Peros in your Techum, and I will guard your Peros in my Techum', since it is permitted for Shimon. Tosfos derives that if Levi accepted Shabbos before dark, he may tell David to do a particular Melachah for him, since it is permitted for David. However, he may not tell a Nochri to guard Peros that he cannot guard. Whatever one may not do, he may not tell a Nochri to do it. Presumably we forbid only if the Nochri is not there (in the Techum of the Peros). We are not more stringent about a Nochri than about a Yisrael.

Ran (Shabbos 64b DH umid'Amrinan): This is not a proof. Here, if there were shacks, Reuven himself would be able to guard them!

Beis Yosef (OC 263 DH Kasav ha'Ran): I do not understand the Ran. We can also say that had Levi not accepted Shabbos, he could have done Melachah!

Poskim

Shulchan Aruch (OC 263:17): If Levi accepted Shabbos before dark, he may tell David to do a particular Melachah for him.

Hilchos Ketanos (1:111): Perhaps a Ben Eretz Yisrael may not cook extra Chametz on the eighth day of Pesach to give to guests from Chutz la'Aretz right after dark, for it became Chametz on Pesach for their sake. Also, he toils for them on their Yom Tov to do what they could not do, and makes extra for them. One must investigate the law of one who observes two days of Yom Kipur. (We learn from there - PF.)

Ginas Veradim (4:17): The Ran understands that Tosfos permits because there is a permitted way for Levi himself to do it. Even though now he cannot, he may command another Yisrael. The Beis Yosef did not understand the Ran. The Ran holds that since here the Isur is due to Levi, we cannot learn from where the Isur is not due to him. I found another source for the Rashba. R. Shimon ben Elazar holds that an Eved Kena'ani can receive his Get Shichrur (document of freedom) only through someone else, but not by himself. He can make a Shali'ach for this, since he can receive a Get Shichrur for an Eved of a different master, even though he cannot receive one for an Eved of his own master. We cannot settle from this whether Kohanim are Sheluchim of Yisrael or of Hash-m (Kidushin 23b), for Yisrael cannot offer Korbanos at all.

Ginas Veradim: This shows that one can command about a matter only if in some case he may do it. If not, he cannot, even if it is permitted for the Shali'ach. Since one does not always accept Shabbos early, even when he did, he may command another. This is like Tosfos. Also, a Ben Chutz la'Aretz may not tell a Ben Eretz Yisrael to do Melachah on Yom Tov Sheni. Even though he could move to Eretz Yisrael and be permitted Melachah on Yom Tov Sheni, he would no longer be a Ben Chutz la'Aretz. We find that an Eved cannot receive a Get for another Eved of his master, even though he could do so if he were freed.

Note: An Eved Kena'ani cannot choose to become free. A Ben Chutz la'Aretz can choose to move to Eretz Yisrael!

Ginas Veradim: A Ben Eretz Yisrael may do Melachah by himself for a Ben Chutz la'Aretz, and the latter may benefit from it immediately. This is unlike Hagahos Maimoniyos (after Hilchos Shevisas Asor), who forbids people who keep two days of Yom Kipur to benefit from what others cooked for them on the 11th. Why do I permit? Chachamim forbade a Yisrael to benefit from what Nochrim cooked for him until bi'Chdei she'Ya'asu (the time to do so after Shabbos) only for a Torah Melachah, but not for a Shevus that a Nochri did by himself. The Rambam (Hilchos Shabbos 6:3) lists only Torah Melachos regarding the Isur to benefit from what a Nochri did for a Yisrael.

Note: The Rambam mentioned drawing water. This is not always mid'Oraisa, e.g. if the well is in a Karmelis!

Ginas Veradim: The Beis Yosef (Sof Siman 355) brings so from the Rosh (Beitzah 3:17). Melaches Yom Tov Sheni is only mid'Rabanan, therefore one need not wait after dark bi'Chdei she'Ya'asu, even for people who keep two days of Yom Kipur, since nowadays we know that the first day is really Rosh Hashanah. (I.e. there is no Safek.)

Birkei Yosef (496:4): Maharikash (90) permits a Ben Chutz la'Aretz to ask a Ben Eretz Yisrael to do Melachah for him on Yom Tov Sheni. R. Yakov Paragi (76) and Mahari Molko (65) forbid.

Mishnah Berurah (496:13): If a Ben Chutz la'Aretz came to Eretz Yisrael, if he intends to return, he must observe Yom Tov Sheni.

Igros Moshe (OC 3:73): One who accepted Shabbos may command one who did not yet accept. We cannot derive that a Ben Chutz la'Aretz may command a Ben Eretz Yisrael on Yom Tov Sheni. There, he did not have to accept. Here, letter of the law the Ben Chutz la'Aretz is forbidden. He could decide to stay, and become permitted, but most who intend to stay cannot arrange income or other matters, and they do not stay. Kabalas Shabbos depends only on his will. We cannot learn from those who keep two days of Yom Kipur, for they hold that all are forbidden on the second day. Regarding Yom Tov Sheni, I permit, for nowadays it is only due to custom. When they fixed the months through witnesses, if a Ben Chutz la'Aretz visited Eretz Yisrael, he did not need to keep Yom Tov Sheni, for now he had no Safek. Nowadays Benei Chutz la'Aretz know the date just like Benei Eretz Yisrael, but they kept their custom (Beitzah 4b). This is more stringent than when it was truly a Safek. In Chutz la'Aretz, one may not command a Nochri on Yom Tov Sheni. Therefore, a Ben Chutz la'Aretz may not command a Ben Eretz Yisrael. Even though in Chutz la'Aretz there was no custom to forbid commanding a Yisrael who may do Melachah, for there was no such case, the Isur of Amirah l'Nochri includes doing Melachah through [any] others.

Igros Moshe: I do not have access to Maharikash. Perhaps he holds that a custom applies only to cases that occurred, but not to other cases, even if there is no reason to distinguish. If so, perhaps they may command also Nochrim on Yom Tov Sheni, since they had no custom to forbid this in a situation where there are Yisre'elim who may do Melachah. Also, whatever one has a way to do it, he may command a Nochri about it. Or, perhaps even Maharikash forbids, and permits telling only a Yisrael. The opinion that totally forbids commanding is primary.

Minchas Yitzchak (7:34): The questioner in Ginas Veradim 4:16 says that Maharikash permits a Ben Chutz la'Aretz to command a Ben Eretz Yisrael in Chutz la'Aretz on Yom Tov Sheni, for Shevus (i.e. Amirah l'Nochri) does not apply to a Yisrael. Ginas Veradim brought the Radvaz (258/4:399) who forbids, for even a Ben Eretz Yisrael may not do Melachah there. Also, we forbid Amirah l'Nochri (telling him to do Melachah), lest the Yisrael come to do so himself. Why did the Birkei Yosef say that Maharikash discusses a Ben Chutz la'Aretz in Eretz Yisrael? Maharikash brought a proof from 263:17. Based on the Radvaz, Ginas Veradim said that there is different, for one who accepted Shabbos may command a Nochri. The Rashba permits commanding a Yisrael who did not yet accept, and all the more so a Nochri.

Minchas Yitzchak: The Rashba explicitly wrote that a Yisrael is no more stringent than a Nochri. Ginas Veradim defended the Ran. If so, there is no solid source to permit. The Bach and Taz say that the Rashba permits whenever David is permitted; perhaps the Ran agrees with the law. If so, a Ben Chutz la'Aretz may command a Ben Eretz Yisrael. The Beis Yosef and Magen Avraham require that Levi could do so himself. If he is already in Eretz Yisrael, he could simply decide to stay, so the Rashba would permit. However, Minchas Eliezer (3:53) says that since he said Kidush, he should not treat the day like Chol. If so, this Heter does not apply.

Minchas Yitzchak: The Darchei Moshe (263:8) says that even the Ran permits on Motza'ei Shabbos, since he could be Mavdil when he wants. The same applies to a Ben Chutz la'Aretz who could decide to stay. However, Teshuvas Pnei Yehoshua (2 YD 3) challenged the Rashba. Ravina says that Yesh Shali'ach l'Davar Aveirah when the Shali'ach has no Isur (Bava Metzi'a 10b). Perhaps since he could accept Shabbos, it is as if the Isur applies to him.

Yom Tov Sheni k'Hilchasah (14:2): On Yom Tov Sheni, a Ben Chutz la'Aretz may not tell, or even motion, to a Ben Eretz Yisrael to do Melachah for him.

Ha'arah (3): I.e. he may not point to a light, to hint that he should light it. He may say 'it is dark in here', for this is unlike Shelichus. If Ploni directly commanded a Ben Torah, the Ben Torah may decide not to fulfill the command, rather, to do it because he knows that Ploni wants it, and tell him so. I heard so from ha'Gaon R. S. Z. Auerbach, Ztz"l. The Mishnah Berurah (307:76) says so regarding Amirah l'Nochri.

Note: The Mishnah Berurah said 'he may say 'this Ner is not burning well.' We do not forbid due to benefit from a Melachah that the Nochri did for him, since it is not such a big Hana'ah, for even beforehand he could have read with difficulty.'

Yom Tov Sheni k'Hilchasah (3): A Ben Chutz la'Aretz may tell a Ben Eretz Yisrael to do Melachah of Ochel Nefesh permitted on Yom Tov. Some forbid if he knows that he surely will need to do another Melachah not for Ochel Nefesh, e.g. lighting a new fire, and some permit.

Yom Tov Sheni k'Hilchasah (4): Some permit a Ben Chutz la'Aretz to tell a Ben Eretz Yisrael to do Melachah for the sake of a Mitzvah, as long as he does not say secular matters forbidden to say on Yom Tov (ha'Gaon R. Y.S. Elyashiv Ztz"l, p.218).