Using the conventional macroscopic description of the bulk photovoltaic effect we analyze the light-induced currents and electric fields arising in the optical configuration with a continuous bottom electrode and a small circular top electrode. This scheme is relevant to recent experiments on the tip-enhanced photovoltaic effect in ferroelectrics. It is shown that a light-induced electric field remains nonzero inside the sample even in the short-circuit regime. Moreover, it is enhanced compared to the photovoltaic field in a large area and strongly enhanced near the top electrode. A field-assisted collection of charge carriers from the illuminated area produces a strong local enhancement of the current density near the top electrode. The tip-enhanced electric field is typically parallel to the photovoltaic current. It is sufficient to repolarize the crystal near the top electrode. The effect of the tip enhancement on the light-current transformation efficiency is considered, and predictions for the tip radius and sample thickness dependencies of the total light-induced current are made.