The voltammetric response of electrodes coated with a redox-active monolayer is computed by finite element simulations based on a generalized model that couples the Butler-Volmer, Nernst-Planck and Poisson equations. The model yields a full description of the electric potential and charge distributions across the monolayer and into the bulk solution, including the potential distribution associated with ohmic resistance in the bulk solution. In this way, it is possible to properly account for electrostatic effects at the molecular film/electrolyte interface, which are present due to the changing charge states of the redox head groups as they undergo electron transfer, under both equilibrium and non-equilibrium conditions. Our numerical simulations also significantly extend previous theoretical predictions by simultaneously including both the effects of finite electron-transfer rates and electrolyte conductivity. Distortion of the voltammetric wave due to ohmic potential drop in the solution is shown to be a function of the supporting electrolyte concentration and scan rate, in agreement with experimental observations. The electric potential and charge distributions across an electrochemically inactive monolayer and into the solution are also simulated as a function of applied potential and are found to agree with the Gouy-Chapman-Stern theory, allowing numerical predictions of the capacitive background currents in voltammetric experiments.