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Q. I am having trouble deciding if it is “Page and I” or “Page and me” in “Please let Page and me know.”
A. “Me” is correct, because it’s the object of the verb “let.” When you’re having trouble with “I” vs. “me,” try the same sentence without the double object: Please let me know. (You wouldn’t even consider saying “Please let I know.”) The reason “Page and me” sounds odd is that we’ve had it hammered into our brains for so long that “Page and I” is the correct usage when the phrase is the subject of a sentence (“Page and I are going,” not “me and Page are going”). People seem to have developed a fear of the “Page and me” construction. But when it’s the object of a verb or a preposition, it’s correct: Call Page and me when you’re ready. Give the money to Page and me.
I suppose it’s conceivable that centuries from now, as English continues to evolve, “I” and “me” in compound subjects and objects could switch places in usage. “Me and Page are going” and “Call Page and I when you’re ready” are already so common, it wouldn’t surprise me.