Bereshit Rabbah 90:6 writes that the famine was in three areas besides Egypt, Phoenicia (Lebanon), Arabia and Israel. Similarly, Benno Jacob (1974, p. 280) notes that the phrase "all the earth" in 41:56,57 just refers to the surrounding countries. In fact, since the point of the famine was to "force" Yaakov's family to go to Egypt, there was no need for there to have been a famine everywhere except in Egypt, Syria, Lebanon, Jordan (following the modern names) and the land of Israel.
A related question is, did Yosef sell the grains to anybody who came to Egypt? This would be surprising since one would not expect that the Egyptians would be happy to see the grains that they grew being sold to other people in the midst of famine. It could be that they did not have a say in the matter, but 41:55 records that they were able to cry out to Pharaoh, and 47:15 records that they cried out to Yosef.
Another question about the extent of the famine is that 42:5 records that the famine was in the land of Canaan in the context of the brothers of Yosef travelling down to Egypt. Yet, after 41:54,56,57 record that the famine was in all the lands, and the brothers were going to Egypt due to the famine, why did 42:5 need to record again that the famine was in the land of Canaan? The Radak (on 42:5) explains that this information is to tell us that there were many people coming to Egypt from the land of Canaan at the same time as the brothers. I am not sure how this extra mention of the famine in the land of Canaan enables us to assume that many people were coming to Egypt from the land of Canaan. How many were then coming? Is this unspecified number important? Why did the Torah not simply write that the brothers came to Egypt amongst the people coming from the land of Canaan?
My guess is that the end of 42:5, which specifies that the famine was in the land of Canaan, is coming to tell us that people coming from Canaan due to the famine had a different status than other people who lived outside of Egypt. (A generalization and then a specification, kellal and perat.)
41:57 records that people from all the lands came to Egypt to buy food, but it does not record that they were able to buy food, only that they had to go to Yosef. My guess is that initially Yosef sold some food to anybody who came to Egypt to make it known that people could come to Egypt to buy food since he wanted his family to come to Egypt. However, he was unable to continue with this policy both because of the limit on the amount of food to sell, and that Egyptians would get upset from Yosef selling to foreigners. Once the word got out that food was available in Egypt, Yosef limited sales to people from Canaan (the end of 42:5) since he needed his family to come to Egypt. It could be that this is why 42:6 repeats that Yosef was in charge of Egypt since this authority allowed him to sell large amounts of wheat to foreigners, people from Canaan, even if this would upset the Egyptians. Afterwards, when Yosef first spoke to the brothers he asked where they were from. This was a legitimate question since at that time only people from Canaan had the right to buy food, and the brothers answered that they met this requirement, 42:7. Also, 47:15 records that Yosef had gathered all the money of the people of Egypt and Canaan. We see that people from Canaan were able to buy large quantities of food, but no other foreign country is mentioned. The second half of 47:15 then records that the people of Egypt complained to Yosef, as the people of Canaan, foreigners from the Egyptian perspective, could not complain to Yosef. Yosef then instituted the third stage of his policy, which was only to sell food to Egyptians since once Yosef’s family had come to Egypt, he had no need to keep allowing people from Canaan to buy the Egyptian wheat.
Another question concerning the purchase of the food in Egypt during the famine is that 42:1,2 record that Yaakov told his sons that they should go to Egypt to buy food. While this is a reasonable, why did Yaakov not move to Egypt during the famine, like Avraham did (12:10) and Yitzhak tried to do (26:1,2)? I believe there are six possible answers.
One, it is possible that due to the extensive famine, Egypt was not allowing foreigners to take up residence in Egypt. If this is true, then the fact that Yaakov eventually went to live in Egypt, 46:27, was a special dispensation due to Yosef.
Two, maybe logistically it was not feasible for Avraham or Yitzhak to send somebody to Egypt since their children had not yet been born, were too small, and they did not have enough trustworthy servants to bring back the food from Egypt. However, Yaakov was able to stay in Israel since his sons were old enough to bring back food.
Three, maybe once Yitzhak was told not to go to Egypt, Yaakov thought it was forbidden for him to go to Egypt (see Radak and Bekhor Shor on 46:1). Yaakov had left Israel to go to Haran, but possibly this was permitted while Egypt was not. A problem with this idea is that later, 45:28, Yaakov decided to go to Egypt before G-d told him it was okay. Yet, maybe one could argue that Yaakov was not going to leave without G-d’s approval and that was why he stopped in Be'er-Sheva, 46:1.
Four, maybe Yaakov was worried that if he left the land of Israel then Esav would return to the land of Israel. 36:6 records that Esav left the land of Israel because it was too much for Esav and Yaakov to live together in the land. However, if Yaakov was to leave the land for a substantial amount of time, then it was conceivable that Esav would come back, and Yaakov would have lost the land of Israel to his brother. This approach accords with Luzzatto’s (on 46:1) suggestion that Yaakov stopped in Be'er-Sheva to pray before leaving Egypt not only to inquire as to whether it was permissible for him to go to Egypt but also to ensure that he would not forfeit the land of Israel by going to Egypt.
Five, in the covenant of the pieces, G-d told Avraham that his descendants would suffer in a foreign land, and that the fourth generation would return to Israel, 15:13-16. I understand the fourth generation to be from Avraham which is Yaakov’s children, see our discussion, "Who is the fourth generation?" If this is true, then Yaakov had good reason to fear going down to Egypt since this could be the beginning of the prophecy, as in fact it was (see Ramban on 46:1 and Hizkuni on 46:3). If this approach is correct, then it could be that later Yaakov went to Egypt since his desire to see Yosef prevailed over his fear that the prophecy of the future suffering was about to begin. (This idea could also apply to reason four.)
Bibliography:
Jacob, Benno (1869-1945), 1974, The first book of the bible: Genesis, commentary abridged, edited and translated by Earnest I. Jacob and Walter Jacob, New York: Ktav Publishing House.