On equilibrium in resource markets with scale economies and stochastic prices

I consider a non-renewable resource market where extraction costs are non-convex and market price is subject to stochastic shocks. While competitive equilibrium cannot exist if costs are non-convex and demand is deterministic, equilibrium can be supported in the context of stochastic demand. The crucial distinction is that the noisy environment can create an incentive for firms to hold inventories. Inventories allow firms to continue producing at a smooth pace at any instant when extraction ceases, e.g. when reserves are exhausted. Accordingly, there are no abrupt changes in the expected price path, in contrast to the deterministic variant of the model