  We consider the effective potential V in the massless Wess-Zumino model. By
using the renormalization group equation, we show that the explicit dependence
of V on the renormalization mass scale mu cancels. If V has an extremum at some
non-vanishing value of the background field, then it follows that V is "flat",
independent of the background field. This is consistent with the general
requirement that V be complex. The consequences for supersymmetric gauge
theories are briefly considered.
