VLBI observations of compact radio sources exhibit core-jet structure and apparent superluminal expansion. Both features can be produced by a relativistic jet of radio-emitting plasma beamed toward the observer. This model implies that there should be several fainter unbeamed sources for every beamed source. Partial luminosity functions (the probability distribution functions for the observed flux from a source at a given distance viewed from different directions) are calculated for different relativistic jet models. Kinematical models that approximate relativistic shock fronts are emphasized. These differ from the kinematically simpler models which are usually invoked, in that the velocity of the emitting fluid, which is responsible for the Doppler boosting, is distinct from the velocity of the pattern, which is responsible for the superluminal motion. Numerical calculations of the emission from semidynamical shock models demonstrate that a wide range of partial luminosity functions can be produced. It is concluded that source counts cannot be used as precise probes of relativistic beaming and are of limited use in testing the beaming hypothesis. 27 references.