Why Isn't Vice-President-Elect Biden Affected by the Emoluments Clause?

Several people have asked: Why isn't Vice-President-Elect Joe Biden presumptively barred from the Vice-Presidency by the Emoluments Clause (which we discussed in connection with Hillary Clinton's nomination to be Secretary of State)? Apparently the Vice-President's salary was raised during the term for which Senator Biden was elected (I haven't independently confirmed that is so, but I will assume it for purposes of this post). Would that mean that he can't hold that job, at least unless a Saxbe Fix temporarily lowers the salary to its earlier level?

No, because the Emoluments Clause says (emphasis added),

No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States, which shall have been created, or the Emoluments whereof shall have been encreased during such time ....
Senator Biden is not being appointed, but has rather been elected -- or, if you prefer, will almost certainly be voted into office as Vice-President on Dec. 15 by the Electors chosen by the voters of each state.

This status of the Vice-Presidency as an elective rather than appointive office is also reflected by the constitutional title — used in the Twentieth Amendment — of "Vice President elect." The Emoluments Clause applies only to appointed officers, just as does the Appointments Clause. ("[The President] shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.")

There's also something of a debate about whether the Presidency and the Vice-Presidency are considered "Office[s]" for the purpose of various constitutional clauses. But I need not engage that debate here, because the limitation to "appointed" offices settles the matter (though the debate might become relevant for a Vice-President who is nominated by the President and confirmed by the Senate pursuant to the Twenty-Fifth Amendment, in the event the elected Vice-President dies, resigns, is impeached, or becomes President).