Parametric analysis of the Bass model

In this research, the authors explore the influence of the Bass model p, q parameters values on diffusion patterns and map p, q Euclidean space regions accordingly. The boundaries of four different sub-regions are classified and defined, in the region where both p, q are positive, according to the number of inflection point and peak of the non-cumulative sales curve. The researchers extend the p, q range beyond the common positive value restriction to regions where either p or q is negative. The case of negative p, which represents barriers to initial adoption, leads us to redefine the motivation for seeding, where seeding is essential to start the market rather than just for accelerating the diffusion. The case of negative q, caused by a declining motivation to adopt as the number of adopters increases, leads us to cases where the saturation of the market is at partial coverage rather than the usual full coverage at the long run. The authors develop a solution to the special case of p + q = 0, where the Bass solution cannot be used. Some differences are highlighted between the discrete time and continuous time flavors of the Bass model and the implication on the mapping. The distortion is presented, caused by the transition between continuous and discrete time forms, as a function of p, q values in the various regions.