In this contribution, we develop and investigate a general 2D hopping model for the photovoltaic action in polymer-based thin films. The model takes a microscopic origin and accounts for the molecular photonic and electronic processes by a simple kinetic scheme that eventually leads a linearized master equation for the time evolution of the photovoltaic system. With an emphasis on the topology of blends of donor/acceptor functionalized polymers, we attempt to characterize the dependence of the short-circuit current, internal quantum efficiency, IV characteristics, and fill factors on the morphology of the blend. Several different morphologies for the polymer film are considered, and they show quite different transport and efficiency behavior (e.g., for so-called double cable structures, nearly quantitative conversion efficiencies are computed, and for other structures similar efficiencies may be found, but with short-circuit currents orders of magnitude lower). The model neglects effects such as exciton migration, the built-in potential, and interaction in the third dimension. Nontheless, significant conclusions can be drawn: in particular, we demonstrate that a viable photovoltaic system driven only by concentration gradients of charge carriers (no built-in field) is possible.