A MODEL OF INVENTORY, OUTPUT, AND PRICE BEHAVIOR

DAVID GLENN BIVIN, Purdue University

Abstract

The thesis develops an optimization model of firm behavior in which the firm is assumed to maximize profits by setting inventories, price, and output at the beginning of each period subject to initial conditions (e.g., initial inventories) and expected demand. The model departs from standard models of inventory investment in three respects. First, the objective of the firm is the maximization of profits rather than the minimization of costs. The use of profit maximization removes the inconsistency associated with cost minimization models in which the firm is operating in a perfectly competitive market and yet somehow possesses a demand constraint. Additionally, it allows for the construction and estimation of a price equation. The second departure is the explicit rejection of the buffer stock motive in the construction of the objective function. Typically, the buffer stock motive is introduced directly into the inventory cost function. The philosophy of this thesis is that if such a motive is appropriate, it should arise naturally out of the firm's attempts to maximize profits. Finally, the model developed in the thesis differs from standard models of inventory investment in that the admissible parameter space is rigorously specified. Typically, parameter space restrictions are dictated by intuition rather than theory. The use of intuition is necessitated either by the lack of an underlying structure or by the complexity of the model. However, given the imperfect relationship between intuition and reality, the use of this methodology has led to the acceptance of counterintuitive results, or the incorrect specification of the admissible parameter space. The formulation yields a reduced-form system in which output and price are expressed as linear functions of the lagged rate of production, lagged inventory holdings, lagged unfilled orders, and expected new orders in the current and following periods. The most interesting aspect of the derived parameter space restrictions is the rejection of the buffer stock motive. Rather, the theory implies that, with a finite horizon and positive unit quadratic costs of production, an increase in the steady state level of new orders will yield a decline in the steady state level of inventories. This is the result of increasing marginal costs which implies that firms will utilize all of the tools at its disposal in response to a perceived shift in its demand curve. The theory is tested through the use of a standard F-test in which the residual sum of squares for the constrained model is compared to the residual sum of squares obtained through unconstrained generalized least squares estimation. Since the null hypothesis is composite, the constrained estimates are obtained through an iterative procedure rather than by standard linear programming techniques. The data are real seasonally adjusted quarterly observations covering the period 1959:II-1977:IV for the 20 two-digit SIC manufacturing industries. Initial results indicated the presence of structural change in virtually all of the industries. As a result, each of the samples were divided into two sub-periods: 1959:II-1968:IV and 1969:I-1977:IV. In total there were 35 samples appropriate for testing. The tests were conducted at the five percent level of significance. Of the 35 samples, 25 could not be rejected at this level. For the first sub-period, ten of the 18 samples could not be rejected, and for the second sub-period, 15 of the 17 samples could not be rejected.

Degree

Ph.D.

Subject Area

Economics

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