The effective potential for chiral supersymmetric models is discussed within the framework of the Wess-Zumino model. The effective potential is calculated to two loops using two different renormalization schemes. In a modified minimal-subtraction scheme the effective potential displays pathological behavior such as multivaluedness, complexity, and negativity. It is shown that these features arise from the existence of ghosts in this scheme. A second renormalization procedure, which preserves positivity of kinetic terms in the effective action, is then examined. It is found that quantum corrections in this scheme are small and that supersymmetry is not radiatively broken to the two-loop level. These results are compared with those obtained for O(N)-symmetric chiral models.
