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This paper explains the phenomenon of price rigidity (or price smoothing) as the outcome of the optimal inventory policy of a multi-period profit-maximizing firm under demand and output uncertainties. Price smoothing may be manifested in two forms. First, price changes may be moderated with respect to those implied by the demand function; and second, the firm may choose to restrict price fluctuations by establishing upper and/or lower bounds on prices. We show that the extent of the asymmetry in price smoothing depends on the relationship between the inventory holding cost and the backlog penalty cost. Our model accommodates a wide range of price behaviour as observed in empirical studies on the issue.