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On the superiority of pulsing under a concave advertising market potential function

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Abstract

The authors study the superiority of advertising pulsing policy (turning advertising on and off in a cyclic fashion) over its uniform (constant spending) counterpart that costs the same under the assumption that sales dynamics follow a modified Vidale–Wolfe aggregate advertising model. The authors show that pulsing can be superior if the product of the concave market potential function and the linear or concave advertising response function is convex in advertising. Similar to previous studies in the literature, the average undiscounted profit over the infinite planning horizon is considered as a performance measure according to which alternative advertising pulsation policies are compared.

Employing a well-known data set relating advertising to sales, the above convexity requirement is empirically supported and the superiority of pulsing is established numerically. The performance of the proposed model is found to be superior to two rival models using a one-step-ahead forecasting procedure.

The analytical findings of the study are documented into six theoretical results for which proofs are relegated to a separate appendix. Managerial implications of the study and directions for future research are also discussed.

Introduction

According to the Statistical Abstracts of the United States total advertising expenditure in the US has grown from about 130 billion dollars in 1990 to about 236 billion dollars in 2000. At the individual level of the firm, it is found that in 2002 the largest advertiser (General Motors Corp.) spent more than three billion dollars on advertising ($3,652,000,000 to be exact) while the 100th largest advertiser (Office Depot) spent $312,000,000 (Advertising Age). Investigating better ways of spending such huge amounts of funds would undoubtedly be fruitful. Having established that advertising is an important element in a firm’s marketing efforts, to which significant amounts of resources are usually committed, whether it is best to adopt a cyclic policy of advertising or one of even spending that costs the same has been a fundamental research question in the literature. Sasieni (1971), in a pioneering article, has shown that when there are decreasing returns to scale (concave advertising response function), a cyclic advertising policy can never be superior, in the long run, to a uniform policy of advertising spending that costs the same. Empirical evidence, however, suggests that a cyclic or pulsing advertising policy could be superior to constant spending over time (e.g., Wells and Chnisky, 1965, Ackoff and Emshoff, 1975, Rao and Miller, 1975, Eastlack and Rao, 1986). Due to the contradiction between theoretical and empirical findings, few response models have been published with the purpose of substantiating cyclic pulsation. Notable studies in this regard are briefly highlighted below.

Upon introducing uncertainty in their response models, Tapiero, 1978, Sethi, 1979 found that optimal advertising policies of a Sinusodial form are possible. Employing an S-shaped advertising response function, Mahajan and Muller, 1986, Sasieni, 1989 found that some form of pulsing is superior to the uniform policy provided that average spending over the planning horizon is smaller than the advertising rate at which the tangent drawn from the origin meets the advertising response function. Using the notion of asymmetric response to increases and decreases in advertising spending, Simon, 1982, Mesak, 1985, Mesak, 1992, Luhmer et al., 1988 showed again the superiority of advertising pulsation.

Hahn and Hyun (1991) analyzed the effect of different costs on the optimal advertising policy and found that a pulsing policy is optimal when the ratio of pulsation costs to fixed advertising costs is sufficiently small. Park and Hahn (1991) developed a model of advertising competition that uses discrete-time dynamics. The authors showed that pulsing can be superior even when the change in market share is a concave function in advertising. Näslund, 1979, Naik et al., 1998 articulated response models that incorporate more than one state variable to substantiate advertising pulsation.

Feinberg (1992) found that a pulsation policy (other than chattering in which a firm alternates between high and zero levels of advertising without spending any positive amount of time at any of the two levels) is optimal if there is a gradual build-up in advertising goodwill through the use of an exponential filtering mechanism in the presence of an S-shaped advertising response function. More recently, Feinberg (2001) used optimal control theory to analyze a flexible class of S-shaped response models and showed that non-constant advertising paths may be optimal.

Finally, Villas-Boas, 1993, Desai and Gupta, 1996, Bronnenberg, 1998 showed the optimality of pulsing under the assumption that response is governed by certain discrete Markov processes. The study of Bronnenberg (1998) in particular provides a lucid tutorial on the topics of the shape of advertising response functions and market dynamics in response to changes in the advertising level. Therefore, a review of such issues will not be replicated here.

However, empirical support for most of the above models is lacking in terms of their structure and/or the underlying mechanism that substantiates the superiority of pulsing. In particular, Mantrala (2002, p. 418) indicates that there is limited empirical support for a convex advertising response function or even an S-shaped one. Furthermore, the notion of asymmetric response to increases and decreases in advertising spending in mature markets has not been observed by Sasieni (1989, p. 360) despite his 20 years of experience in studying response data by that time. Because managers do pulse in practice, Little’s (1986) question “What form of response models could support a pulsing strategy?” remains to be an important and relevant research query today.

The present article introduces a modification of the original Vidale–Wolfe model (1957) for which the advertising response function is concave (or linear) and the market potential is concave in advertising. A concave or a linear advertising response function is employed herein as previous studies (e.g., Simon and Arndt, 1980, Hanssens and Parsons, 1993, Vakratsas and Ambler, 1999) cast doubt on the existence of an S-shaped advertising reposonse function over the operating range of advertising.

Earlier studies that advocate market potential as a concave function of advertising include the works of Kotler, 1965, Karnani, 1983. Our study demonstrates that if the advertising response function multiplied by the market potential function is convex in advertising, pulsing could be optimal. This novel result is not only found to be of theoretical appeal but also of empirical relevance. Because our proposed model cannot be cast in the alternative general classes of dynamic advertising models considered in Sasieni, 1971, Feinberg, 2001, its details for a monopolistic market are discussed in the next section.

The rest of the paper is organized as follows. The second section outlines the theoretical model. Then, a comparison of alternative pulsation policies is presented. The forth section subjects the model to some empirical testing. The fifth section summarizes and concludes the paper.

Section snippets

The model

The situation discussed in this section is much suited for an advertiser that sells a single frequently purchased product of low level consumer involvement in a monopolistic market, where advertising is the major element of the firm’s marketing efforts. The monopoly situation may serve as a good approximation in a condition where the market is dominated by one firm that faces a competition from a fringe of many small firms, each of which is too small to influence the market in a noticeable way.

Comparison of alternative pulsation policies

When the three advertising pulsation policies UAP, APMP, and APP are specified to have the same undiscounted total advertising budget in a cycle of duration T, then any given average rate of advertising spending, D, would imply thatt1x1+(T-t1)x2=DT,where x1 and x2 are the high and low advertising rates of the firm whereas t1 and (T  t1) are their related time periods.

Defining the policy parameter λ, 0  λ  1, such that x2 = λD then the different advertising policies that could be employed by the firm

An empirical investigation based on Lydia Pinkham data

The firm analyzed is the frequently studied Lydia E. Pinkham Medicine Company and its product, the Lydia Pinkham vegetable compound, originally examined by Palda (1964). Annual sales and advertising data in thousands of dollars, available from 1907 to 1960, are provided in Palda’s study which made the compound an intensively studied product (Pollay, 1979). Monthly sales and advertising data for that product covering the period January 1954 to July 1960 are available and will be also analyzed in

Discussion and conclusions

The literature reveals that a contradiction exists between empirical research findings and theoretical research results relative to the issue of whether it would be best for the firm to advertise at a constant rate or in a cyclic fashion. As far as the empirical findings are concerned, Ackoff and Emshoff, 1975, Eastlack and Rao, 1986, as notable early examples, conclude after analyzing their field experimental results that an advertising pulsation policy in which a high level of advertising

Acknowledgements

The authors are thankful to Professor Robert Graham Dyson, EJOR Editor, and two anonymous reviewers for their helpful comments and suggestions.

An earlier version of the article is a 2006 Decision Sciences Institute distinguished paper award winner. The award was received on November 21, 2006 at the DSI annual meeting held in San Antonio, TX, USA.

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