Controlled New-Product Growth Models

Kurt Helmes*, Rainer Schlosser and Martin Weber

A deterministic control model of new-product adoption is developed that incorporates price and advertising as marketing-mix variables. For a class of models with (constant) isoelastic demand but general adoption functionals and time dependent arrival rates explicit expressions of the optimal controls and rates of sales are derived. A (simple) numerical method is proposed to compute optimal growth paths. The controlled diffusion of innovations with different dynamics will be studied. In particular, v. Bertalanffy type adoption functions, nonuniform influence dynamics and several other well known adoption functions will be analyzed in detail.

Mathematics Subject Classification: 49J15 49L20 34H05 49N40 90C90

Keywords: Optimal control; controlled advertising and pricing models

Minisymposion: Stochastic Models, Control and Applications