The design of a high‐luminosity electron‐position collider to study B physics is a challenging task from many points of view. In this paper we consider the influence of collective effects on the machine performance; most of our findings are ‘‘generic,’’ in the sense that they depend rather weakly on the details of the machine design. Both single‐bunch and coupled‐bunch instabilities are described and their effects are estimated based upon an example machine design (APIARY‐IV). In addition, we examine the possibility of emittance growth from intrabeam scattering and calculate the beam lifetime from both Touschek and gas scattering. We find that the single‐bunch instabilities should not lead to difficulty, and that the emittance growth is essentially negligible. At a background gas pressure of 10 nTorr, beam lifetimes of only a few hours are expected. Multibunch growth rates are very severe, even when using an optimized RF system consisting of single‐cell, room‐temperature RF cavities with geometrical shapes typical of superconducting cavities. Thus, a powerful feedback system will be required. In terms of collective effects, it does not appear that there are any fundamental problems standing in the way of successfully designing and building a high‐luminosity B factory.