The article analyzes a commodity price process with a unique continuous invariant distribution having infinite mean. The models fit the stylized fact that even after the worst production realization there is always a finite market-clearing price, via the adoption of one of two restrictions: demand is specified so that price at consumption equal to minimum harvest is finite, or the probability of minimum harvest is zero. Models incorporating either restriction have implications inconsistent with two additional stylized facts of commodity markets. First, they generate stock-outs with positive probability, contrary to the observation of continually positive stocks for many commodities. Second, price expected for the next period is never below spot price, in contrast to inferences from futures market observations at low stock levels in empirical supply of storage studies in the tradition of working. One way to make the model consistent with all three stylized facts would be to impose a sufficiently large marginal convenience yield at small stock levels.
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