A Comparison of Alternative Optimal Models of Advertising Expenditures: Stock Adjustment vs. Control Theoretic Approaches Applied to Japanese Pharmaceutical Companies

Hiroki Tsurumi
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Hiroki Tsurumi: Queen's University

No 69, Working Paper from Economics Department, Queen's University

Abstract: Advertising expenditures may well be regarded as a form of investment. Using this concept, Nerlove and Arrow examined an optimal advertising policy for the firm which maximizes present valued cash flow. In this paper the Nerlove-Arrow model is applied by use of the usual stock adjustment formula to empirical data. In addition, since the stock adjustment model is made in an ad-hoc fashion, a suboptimization model is presented as an attempt to derive a estimable equation directly from optimization behaviour. This model is derived from control theoretic suboptimization procedures incorporating an adjustment cost function.Empirical results from both models are compared. Semi-annual data of eight Japanese pharmaceutical companies from 1963 to 1970 are used for this study. In section II the stock adjustment model is formulated and empirical results are presented. In section III the suboptimization model is derived using an invariant imbedding equation applied to the discrete optimization procedure, and empirical results derived from ths model are presented. Section IV compares the two approaches.

Pages: 27 pages
Date: 1972-01
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