Am I Unjust in Not Giving Extra Credit?

I don't give extra credit, mostly for practical reasons.  If students know that I regularly give extra credit, then they will have reason to slack off on other "credit" assignments. This creates more work for me and I have plenty of grading to do already.  Furthermore, I have put a lot of thought into the "credit" assignments and think that it is good for students to put forth a modicum of effort on these assignments.  Also, there is no principled end to extra credit giving, as far as I can see.  If students don't do the "credit" assignments nor the first "extra credit" assignment, should I give another?  And another?  Should I give them extra credit indefinitely?  The solution seems to me to cut the infinite regress off right at the stem.

But should I give extra credit?  Or should I not give extra credit?  If the "should" is a matter of whether it's pragmatic, I have already given my reasons why I think I should not.  But if the "should" is a matter of morality or justice, this is a different question.  Am I unjust in not giving extra credit?  Or is giving extra credit unjust?  Here I will only address the former question:
For starters, justice is not a matter of fairness or equal treatment. I could treat my students fairly (equally) but unjustly.  If I gave every student in the class an A I would be treating them fairly and equally, but not necessarily justly.  For instance, if I "dissed" them all as morons but gave them all A's so that I wouldn't have to grade their "lousy" work, I would be treating them equally but unjustly.  Similarly, I could treat my students justly without treating them on grounds of equality.  If some students, due to a lack of effort or native intelligence, earned an F, while some, due to native intelligence or effort, earned an A, it would be just to give them different grades.

Justice is a matter of rendering (or being rendered) what is due.  Justice is a matter of doing one's duty and having one's rights honored.  It seems obvious to me that I have no general duty to give extra credit because there is no general duty to give extra credit.  Extra credit is not a requirement of justice.  It is extra credit.

Students have a right to my requiring them only to do the assignments on the syllabus.  It would be unjust for me to give a 4th test if I only have 3 tests listed on the syllabus (unless of course it says on the syllabus that there might be a 4th test). I have a duty to give students some understanding of the basic requirements of the class.  Now, if I do have on the syllabus that such-and-such extra credit will be given, then I have a duty to make available the extra credit.  But I have no duty to say that extra credit will be given on the syllabus.  It is enough that students know all and only what will be required of them (and for me that includes only "credit" assignments).

Perhaps, though, extra credit should be thought of as an act of mercy and perhaps it's a duty of justice to be merciful.  But it is surely controversial at least and obviously false at best that it is a general duty of justice always to be merciful. For sometimes mercy is either unjust or is all-things-considered morally worse in some other way than rendering harsh or unpleasant treatment that is deserved.  (Punishing one's children sometimes is better for everyone including one's children).  So it can only be the case that sometimes one should be merciful.

Here things get a bit more complicated.  Perhaps it's never a requirement of justice to be merciful, but there is another moral "should" (a requirement to promote a human's welfare?) such that sometimes one should be merciful.  If the "should" is not one of justice, then there's no requirement of justice to be merciful in giving extra credit. Perhaps, though, there is another moral sense of "should" that requires mercy.

 Be that as it may, there is another response available with respect to the issue at hand: there are plenty of other ways to be merciful other than giving extra credit. One could "grade easier," or not give a bad grade to a bad test, or one could change a student's final grade, and so forth.  Of course it is questionable whether such actions are themselves just, but the point here is that giving extra credit is not a requirement of justice.   So just do the work, and don't think you're a victim if you don't get extra credit--there's neither a right to it nor a duty to give it.  And perhaps it's sometimes (always?) unjust to give it.