This paper presents a consumer-based methodology for new product pricing and positioning in the face of price competition. The price competition is modelled as a Nash equilibrium for which two complementary approaches are employed: an analytical approach of duopoly provides qualitative insights into the competitive behavior, and a numerical approach of general oligopoly provides quantitative solutions under a wide variety of market scenarios. The optimal product positioning is formulated as a Stackelberg-Nash (leader-followers) equilibrium which can be solved numerically using recent advances in the field of variational inequalities. A small example concerning analgesics is used to illustrate this methodology.