Is there any reason why the same psalm is repeated?
Are these psalms composed by the same author?
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I found this link mentioning their similarity. The writer suggests it may have been an editorial adaptation since they seem to have been written at different times based on the words each uses for God (Psalm 14 = Yahweh, Psalm 53 = Elohim). It could be similar to how some old hymns are currently being updated with modern language to appeal to modern culture. http://truthandpurpose.com/2011/04/the-fool-of-psalm-14/
Wow I never saw this before, great question!
I don't have all the answers but regarding your question "Are these psalms composed by the same author?"
They both state that they are written by David in the header. See here...
One says "A Psalm of David." the other " A Contemplation of David."