  We consider a deterministic continuous time model of monopolistic firm, which
chooses production and pricing strategies of a single good. Firm's goal is to
maximize the discounted profit over infinite time horizon. The no-backlogging
assumption induces the state constraint on the inventory level. The revenue and
production cost functions are assumed to be continuous but, in general, we do
not impose the concavity/convexity property. Using the results form the theory
of viscosity solutions and Young-Fenchel duality, we derive a representation
for the value function, study its regularity properties, and give a complete
description of optimal strategies for this non-convex optimal control problem.
In agreement with the results of Chazal et al. (2003), it is optimal to
liquidate initial inventory in finite time and then use an optimal static
strategy. We give a condition, allowing to distinguish if this static strategy
can be represented by an ordinary or relaxed control. The latter is related to
production cycles. General theory is illustrate by the example of a non-convex
production cost, proposed by Arvan and Moses (1981).
