This paper analyzes as a dynamic game the optimal price and storage strategies of, respectively: (a) the seller of a storable good, who must keep pace with inflation but incurs a cost to changing his price; (b) his customers, who speculate on the timing of price adjustments to buy and store just before. A unique (Markov) perfect equilibrium is shown to exist, and is fully characterized. It generally involves a phase of mixed strategies, during which the seller tries to deter speculation by injecting uncertainty into its price dynamics, while speculators store in increasing numbers, with possibly a final "run" on the good. The stochastic price policies of a large number of such firms are shown to aggregate back to a price index growing at the rate of general inflation in response to which they arose. The model thus establishes that: (a) a constant rate of aggregate inflation can at the same time generate and cover up significant uncertainty and social costs at the microeconomic level; (b) speculation can be destabilizing and socially wastful, even in the absence of shocks and imperfect information. Most importantly, they provide a theoretical foundation for the frequently encountered claim that inflation causes price uncertainty.