  The inhomogeneous renormalization group equation for the effective potential
is rederived. It is shown that when the effective potential is normalized by
the normalization condition on the generating functional, its renormalization
group equation is homogeneous. This is demonstrated in the case of massive
$\phi^4$-theory. We also show that for the case of spontaneous symmetry
breaking, the normalized effective potential is completely different from the
symmetric case, though the two cases satisfy the same RGE with the same
RG-functions. It is concluded that the vacuum energy density arises only in the
case of SSB.
