Ideal ferroelectrics have mostly been modeled as insulators, i.e., infinite band gap materials, having a spontaneous polarization. Based on this assumption, theories for the finite size effect, the domain configuration, and the depolarization field instability have been proposed. However, most of oxide perovskite ferroelectrics have finite band gaps of 3 to 4 eV. We show that the inclusion of the finite band gap effect changes drastically conventional understanding of the finite size effect and others. The conclusions extracted from the present approach are consistent with recent experimental results. In particular, we discuss the stability of ferroelectric memory devices in detail.