A two-dimensional model of the cathode compartment of a polymer electrolyte fuel cell has been developed. The existence of gas channels in the current collector is taken into account. The model is based on continuity equations for concentrations of the gases and Poisson's equations for potentials of membrane and carbon phase, coupled by Tafel relation for reaction kinetics. Stefan-Maxwell and Knudsen diffusion of gases are taken into account. The simulations were performed for high and low values of carbon phase conductivity. The results revealed (i) for a low value of carbon phase conductivity, a "dead zone" in the active layer in front of the gas channel is formed, where the reaction rate is small. One may remove catalyst from this zone without significant loss in cell performance. (ii) For a high carbon phase conductivity value, such a zone is absent, but removal of the catalyst from the same part of the active layer forces the reaction to proceed more rapidly in the remaining parts, with only marginal losses in performance. This conclusion is valid for high diffusivity of oxygen. For low diffusivity; dead zones are formed in front of the current collector, so that catalyst can be removed from these zones. The results, thus, show the possibilities for a considerable reduction of the amount of catalyst.