We show that the equivalence between certain problems of singular stochastic

control (SSC) and related questions of optimal stopping known for convex performance criteria

(see, for example, Karatzas and Shreve (1984)) continues to hold in a non convex problem

provided a related discretionary stopping time is introduced. Our problem is one of storage

and consumption for electricity, a partially storable commodity with both positive and negative

prices in some markets, and has similarities to the finite fuel monotone follower problem. In

particular we consider a non convex infinite time horizon SSC problem whose state consists of an

uncontrolled diffusion representing a real-valued commodity price, and a controlled increasing

bounded process representing an inventory. We analyse the geometry of the action and inaction

regions by characterising the related optimal stopping boundaries.