The flexible accelerator concept has provided the rationale for the regression equations used in several recent econometric studies of inventory behavior. In such a model a desired (or equilibrium) level of inventories is defined, but because of costs involved in changing the level of stocks only a partial adjustment of inventories to their desired level is achieved in any time period. This leads to the familiar decision rule in which current inventory is a linear function of the previous period's stock plus a variable or set of variables representing current demand. The purpose of this note is to question whether there are any significant costs specifically associated with changing the level of inventories other than those directly associated with changes in the level of production which may (or may not) be required to bring about the necessary stock adjustment. If none exist, it is shown that a given time pattern of demand can lead a firm which acts according to the flexible accelerator to behave "irrationally" and incur unnecessary costs. Finally, an amended version of the flexible accelerator is presented, and the resulting equation for inventories is compared with that derived from the original model.

This paper is an attempt to derive empirically testable hypotheses regarding the principal determinants of firms' decisions on production, price, and finished goods inventory. The general approach to the problem is that many of the same factors which affect the optimal value for one variable will also influence decisions on the other two, and that a "proper" model must take into account the interdependence of these variables and the simultaneous nature of the decisions involving them. This is in contrast to literature on the theory of inventories (see Paul Darling and Michael Lovell) in which the firm is assumed to determine the optimal level of inventories with the rate of production taken as given and with price held constant. Similarly there are theories of price formation (see Otto Eckstein and Gary Fromm) in which the rate of production is assumed to have been determined previously, and in which the level of inventories is often ignored entirely. The present paper will attempt to present an "integrated" model of firm behavior in which decisions on all relevant variables are assumed to result from a single optimization process. A principal distinction between this study and previous work in this area (see Gerald Childs and Charles Holt) is the inclusion of price as one of the decision variables. In the past the assumption has been made that price is fixed and therefore that quantity demanded is a datum to the firm. In anything but a purely competitive model, however, the firm does exercise some control over price. The rational firm would use its current pricing policy to select the specific price-quantity combination on the demand curve that best contributes to its overall scheme of profit maximization. Thus the firm whose demand curve is not constant over time but fluctuates from period to period on a random and/or seasonal basis might view price adjustments as one means of achieving production stabilization. If this were so we might expect to find that an increase in demand would be met by continuing to produce at or near the previous rate and raising price to clear the market. More realistically, the entire kit of adjustment tools—inventory, backlog, and price—would be used in some combination to absorb all or part of the increased demand, the specific result depending not only on the particular cost structure assumed, but also on the firm's estimates of what demand will be for several periods hence. The important point is that price must certainly be included as one of these tools. In the remainder of the paper we construct a model which includes many of the variables which are important at the individual firm level, and which treats decisions regarding those variables as being essentially interdependent. The subsequent section discusses the behavioral assumptions which underlie the model and expresses the model in mathematical form. The first-order conditions for maximizing expected profits generate a set of linear decision rules for production, price, and finished goods inventory. On the assumption that firms do attempt to maximize expected profits, these decision rules are suitable for empirical investigation with the appropriate data. In Section II, the model is solved numerically with representative cost parameters. The resulting decision rule coefficients provide predictions regarding the actual regression equations which should be fulfilled if the model accurately reflects the working of the real world. Finally, in Section III, the regressions are performed on two industry groups, and the results compared with the predictions.

Linear decision rules for controlling complex systems are often obtained by matrix inversion, but transform methods offer an alternative approach that yields insights into the structure of the decision problem of maximizing expected payoffs under constraints.