  In this paper I investigate a Bayesian inverse problem in the specific
setting of a price setting monopolist facing a randomly growing demand in
multiple possibly interconnected markets. Investigating the Value of
Information of a signal to the monopolist in a fully dynamic discrete model
employing the Kalman-Bucy-Stratonovich filter, we find that it may be
non-monotonic in the variance of the signal. In the classical static settings
of the Value of Information literature this relationship may be convex or
concave, but is always monotonic. The existence of the non-monotonicity depends
critically on the exogenous growth rate of the system.
