Reductions in P

We know that if one wants to prove a problem X to be NP-complete,
suffices to take a known NP-complete problem and reduce it to X, by
means of a polynomial-time reduction.

Question: does it make any sense to reduce a problem P1 in P to another
P2 in P? If yes, what conclusion can I draw from such an reduction? I
don't see the point in reducing in P, because if both P1 and P2 have
poly-time algorithms, what knowledge can I extract from the fact that
there exists a poly-time reduction P1 \le_p P2?

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