Inventories and Sticky Prices: Note

Abstract

In a recent contribution to this Review, Alan Blinder provides an interesting analysis of the relationship between optimal inventory decisions and the process of price adjustment. Arguing that inventory permits separation of production and sale decisions, and allows the firm greater flexibility in responding to anticipated demand disturbances, Blinder shows that the responsiveness of relative prices depends critically upon the cost of storage and the temporal structure of the demand shocks. Few economists would fault the intuitive substance of Blinder's basic proposition, and the proposition is justified with characteristic precision. The analysis, however, is considerably less general than Blinder maintains. The formal argument of his paper relies upon a simple model of a monopolist capable of backlogging orders and storing unsold goods. As the model is constructed, order backlogs assume a role of fundamental importance in any stationary equilibrium. This feature of the model vitiates Blinder's extension of his result to situations in which order backlogs are prohibited. The basic monopoly model developed in Sections I and II of Blinder's paper places no restriction upon the sign of inventory. Negative inventory is interpreted as net unfilled orders, while no distinction is drawn between reductions in gross inventory and additions to the order backlog. As a result, the cost of holding inventory is symmetric around an arbitrary minimum point. The only role of inventory is to permit the time paths of production and sales to differ: gross inventory allows production to antedate sales, while order backlogs generate revenue before production costs are borne. Under these circumstances, if future costs and revenues are discounted, it is natural to expect any stationary equilibrium level of net inventory to be negative. This can be shown to be true of Blinder's model. It is useful to distinguish in general between the nonstochastic stationary level of inventory (n-) and the stochastic stationary level (n). The former is realized when the current expected demand disturbance (eo) is zero and production equals sales; the latter, which differs from customary usage, represents the level of inventory expected to prevail when adjustment to the current (nonzero) expected demand disturbance is complete. If the demand disturbance is not a random walk, so that p < 1 in Blinder's (5), the two equilibria coincide. Relatively little attention is devoted to either stationary solution, because Blinder's main interest is in the optimal current solution level (n1). The stochastic stationary level is crucially important, however, since it represents the goal toward which the current choice must provide an optimal first step. To verify that both nand n are negative whenever production is strictly positive, note that Blinder's necessary condition (7) with the coefficient cl set equal to zero, together with the definition of XA as the deviation of the shadow value of inventory (q,) from its nonstochastic stationary value (q), implies

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 50 citations exist upstream.