We present an approach to the size effect problem in ferroelectric-electrode systems which combines first-principles calculations and phenomenological theory. The parameters of the model can be extracted from calculations on ultrathin films, while experimentally verifiable predictions can be made on thick films. We illustrate the approach for the case of SrRuO3/BaTiO3/SrRuO3 heterostructures with asymmetric interfaces. This enables us to provide a quantitative description of a number of manifestations of such asymmetry in films of technologically meaningful thickness.