In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential in a supersymmetric model, and the impacts of this improved calculation in the dynamical symmetry breaking that happens in our model. We consider an N = 1 supersymmetric theory including an Abelian Chern-Simons supereld coupled to N scalar superelds in a (2+1) dimensional space-time. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate perturbative corrections, up to two-loops,to the one- and two-point vertex functions, using dimensional regularization and minimal subtraction scheme. With the knowledge of the renormalization group functions, the RGE can be used to calculate an improved version of the effective superpotential, from which the dynamical symmetry breaking can be studied, and the results compared with those obtained from the unimproved effective superpotential. We show that in the supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case, but it still allows some improvement over the standard calculation.