While making informed decisions regarding
investments in customer retention and acquisition becomes a
pressing managerial issue, formal models and analysis, which may
provide insight into this topic, are still scarce. In this study
we examine two dynamic models for optimal acquisition and
retention models of a monopoly, the total cost and the cost per
customer models.
These models are analytically analyzed using classical, direct,
methods and asymptotic expansions (for the total cost model).
In order to numerically simulated the models, an innovative
numerical method was developed for solving ODE systems with
initial/final value problems.